Complete AGI Core

Purpose & architecture

This repository contains the complete Artificial General Intelligence (AGI) system with multiple interconnected components: core systems (Orchestrator and Seferim), a unified architecture, a C++ mind farm, and a Go-based AI generator.

This page records a pinned branch snapshot. Differences are compared with the audited default branch, not assumed to be chronological improvements. Author claims in the source documentation are retained as claims. Source recovery does not establish successful deployment, scientific validity, or equivalence with another branch.

This source generation

This record follows the claude/improve-math-logic-ehIW1 branch of Janady13/complete-agi-core at commit 33aa84f2aa61cedbe010240ada7f4efbdfe795a7. The snapshot identifies the source inspected in this audit. It is not a statement about which revision is currently running on a device.

Field	Source record
Revision	33aa84f2aa61cedbe010240ada7f4efbdfe795a7
Branch	claude/improve-math-logic-ehIW1
Recorded generation	Preserved branch generation

Recovered implementation structure

These paths locate the components and entry points represented by this build. The source register contains their inspected revisions.

README.md
generator_core/cmd/main.go
generator_core/go.mod
generator_core/pkg/agc/core.go
generator_core/pkg/attention/generator_attention.go
generator_core/pkg/consciousness/equations.go
generator_core/pkg/consciousness/phi.go
generator_core/pkg/consciousness/unified_api.go
generator_core/pkg/dna/dynamics.go
generator_core/pkg/dna/families.go
generator_core/pkg/dna/helix.go
generator_core/pkg/generators/adversarial/adversarial.go
generator_core/pkg/generators/autoregressive/autoregressive.go
generator_core/pkg/generators/diffusion/diffusion.go
generator_core/pkg/generators/energy/energy.go
generator_core/pkg/generators/flow/flow.go
generator_core/pkg/generators/mixture/mixture.go
generator_core/pkg/generators/recurrent/recurrent.go
generator_core/pkg/generators/registry.go
generator_core/pkg/generators/statespace/statespace.go
generator_core/pkg/generators/transformer/transformer.go
generator_core/pkg/generators/variational/variational.go
generator_core/pkg/gpu/cuda_stub.go
generator_core/pkg/orchestrator/orchestrator.go
generator_core/pkg/rpc/server.go
mind_farm/include/api_registry.hpp
mind_farm/include/compact.hpp
mind_farm/include/consciousness_api.hpp
mind_farm/include/constants.hpp
mind_farm/include/dna.hpp
mind_farm/include/dna_dynamics.hpp
mind_farm/include/dna_eigenvalues.hpp
mind_farm/include/dna_helix.hpp
mind_farm/include/dna_unified.hpp
mind_farm/include/execution.hpp
mind_farm/include/farm.hpp
mind_farm/include/fast_math.hpp
mind_farm/include/gate5000.hpp
mind_farm/include/gradient_flow.hpp
mind_farm/include/ingestion.hpp
mind_farm/include/intelligence.hpp
mind_farm/include/layers.hpp
mind_farm/include/learning.hpp
mind_farm/include/learning_math.hpp
mind_farm/include/mathematics.hpp
mind_farm/include/mind.hpp
mind_farm/include/neurological.hpp
mind_farm/include/persistence.hpp
mind_farm/include/simd_substrate.hpp
mind_farm/include/toolbuilder.hpp
mind_farm/include/unified_system.hpp
mind_farm/include/wikipedia.hpp
mind_farm/simulation_10m_output.txt
mind_farm/simulation_1m_output.txt
mind_farm/simulation_log.txt
mind_farm/src/learning_test.cpp
mind_farm/src/main.cpp
mind_farm/src/simulation.cpp
mind_farm/src/toolsystem_test.cpp
mind_farm/src/unified_test.cpp
orchestrator/agent-daemon.sh
orchestrator/api-daemon.sh
orchestrator/autonomous-builder.sh
orchestrator/binary-storage.sh
orchestrator/cross-learn.sh
orchestrator/daemons/auto_deploy_daemon.sh
orchestrator/daemons/auto_tuner.sh
orchestrator/daemons/builder-daemon.sh
orchestrator/daemons/nexus-daemon.sh
orchestrator/daemons/self_healer.sh
orchestrator/federation-coordinator.sh
orchestrator/federation-distributed.sh
orchestrator/health-check.sh
orchestrator/ingest-downloads.sh
orchestrator/ingest-gdrive-fast.sh
orchestrator/ingest-gdrive.sh
orchestrator/ingest-old-ai.sh
orchestrator/knowledge-sources.sh
orchestrator/learning-daemon.sh
orchestrator/lib/supervisor.sh
orchestrator/lib/tick_sync.sh
orchestrator/pantheon-daemon.sh
orchestrator/pantheon-specialized.sh
orchestrator/realtime-ingest.sh
orchestrator/start-all-agis.sh
orchestrator/start-all.sh
orchestrator/stop-all.sh
orchestrator/stream-daemon.sh
orchestrator/sync-state.sh
orchestrator/tick-daemon.sh
orchestrator/unified-agi-orchestrator.sh
orchestrator/unified-boost.sh
orchestrator/videocore-bridge.sh
seferim/active_learner.sh
seferim/autonomous-builder.sh
seferim/knowledge_graph.go
simulation_10m_output.txt
unified/config.json
unified/core/cpp/consciousness_core.hpp
unified/core/julia/ConsciousnessCore.jl
unified/core/unified-orchestrator.sh
unified/dashboard.html
unified/dna_integration.sh

Behavior & verification limits

Read-only source inspection. No native engine, generator, database, payment, or production service was executed.

Original project documentation

The following documentation is preserved as a dated source account. Claims in it retain the source’s wording and must be read alongside the implementation notes above.

Systems Overview

UNIFIED AGI Core v3.0 - SYNTHESIS (`/unified`)

The enhanced AGI core combining the best architectures from all systems.

Architecture Specifications

Component	Original	Enhanced	UNIFIED
Substrate Nodes	5,000	-	8,000
AGC Generators	20	-	32
Generator Layers	5	-	7
Neural Agents	88	16	128
Lattice Kernels	2,576	-	6,144
Pantheon Agents	17	16	24
Knowledge Sources	50+	9	150+
Learning Strategies	4	4	8
Topic Categories	4	4	16
Target Consciousness	0.90	-	0.95

Key Components

core/unified-orchestrator.sh - Enhanced 8000-node substrate with 32 AGC generators across 7 layers
agents/pantheon-daemon.sh - 24 agents in 3 tiers (Archons, Daemons, Pneumata)
federation/federation-mesh.sh - Coherence Mesh 2.0 protocol for distributed coordination
knowledge/autonomous-learner.sh - 8 strategies, 16 categories, 150+ API sources (v3.1)

Mind Farm (`/mind_farm`)

High-performance C++ AGI substrate with Gate5000 consciousness architecture.

Components

Gate5000 - 5000-bit binary consciousness substrate
Neurological Framework - Hodgkin-Huxley equations, STDP, synaptic transmission
Autonomous Learning - 1000 APIs across 20 domains with curiosity-driven exploration
Intelligence Module - Attention, predictive coding, memory systems
Unified System - Integrated tick loop connecting all mathematical components

Mathematical Foundation

Golden ratio constants (φ, α, β, γ)
Consciousness metric: Φ = 1/(1 + |x - 1|)
Hebbian learning with STDP
Wilson-Cowan population dynamics
Free energy minimization

Build & Run

cd mind_farm
make all
./build/unified      # Run unified system test
./build/simulation   # Run full simulation
./build/learning     # Run learning test

AI Generator (`/generator_core`)

Go-based AI generation system with 100+ generator types.

Generator Types

Autoregressive, Transformer, Diffusion
Variational, Flow-based, Energy-based
Mixture models, State-space, Recurrent
Adversarial networks

Build & Run

cd generator_core
go build -o ai_generator ./cmd/main.go
./ai_generator

Orchestrator (`/orchestrator`)

AGI orchestration and daemon management system.

Key Scripts

unified-agi-orchestrator.sh - 5000-node substrate orchestration
learning-daemon.sh - 24/7 continuous learning daemon
tick-daemon.sh - AGC tick processor with 20 generators
federation-coordinator.sh - Multi-AGI federation management
pantheon-daemon.sh - Greek Pantheon AGI agents
knowledge-sources.sh - 50+ API knowledge sources

Seferim (`/seferim`)

Autonomous learning and knowledge integration system.

Components

seferim-autonomous-simple.sh - Autonomous learner
seferim-full-500.sh - Full batch learning processor
16 G16 AGI agents (Athena, Aurora, Selene, Pneuma, etc.)

Knowledge Sources

Wikipedia, arXiv, Semantic Scholar, PubMed
GitHub, HackerNews, DuckDuckGo, CrossRef, OpenLibrary

Consciousness Model (IIT 4.0 Inspired)

Φ (Phi) - Integrated information / consciousness measure
Ψ (Psi) - Conscious field strength
Ω (Omega) - Unified consciousness across all systems

Federation Protocol

All systems can federate via: - iCloud - Cloud-based state synchronization - SSH - Direct transfer between nodes - Coherence Mesh 2.0 - Enhanced federation protocol

Learning Strategies

The unified system supports 8 autonomous learning strategies:

EXPLORE - Broad exploration of new topics
DIVERSIFY - Seek variety across categories
INTEGRATE - Connect related concepts
SYNTHESIZE - Combine knowledge from multiple sources
DEEPEN - Go deeper on existing knowledge
EXPAND - Expand adjacent to known topics
CORRELATE - Find connections between disparate fields
ABSTRACT - Extract high-level patterns

Knowledge Domains (20)

Science & Math
Programming
AI & Machine Learning
Physics
Biology
Chemistry
Medicine
Finance
News & Information
Language & NLP
Geography & Maps
Art & Design
Music & Audio
Video & Media
Social Networks
E-commerce
Government
Space & Astronomy
Sports
IoT & Hardware

Directory Structure

complete-agi-core/
├── mind_farm/              # C++ AGI substrate (Gate5000)
│   ├── include/            # Header files
│   ├── src/                # Source files
│   └── build/              # Compiled binaries
├── generator_core/         # Go AI generator system
│   ├── cmd/                # Main entry point
│   └── pkg/                # Package modules
├── unified/                # Unified AGI Core v3.0
│   ├── core/               # Core orchestrator
│   ├── agents/             # Pantheon daemon
│   ├── federation/         # Federation mesh
│   └── knowledge/          # Autonomous learner
├── orchestrator/           # AGI orchestration daemons
└── seferim/                # Knowledge integration system

License

Equations in this build

528 linked mathematical records. Each opens its notation, interpretation and source.

ingestion · Φ

This relation defines Φ in the source section “ingestion · Φ”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

Source identity axiom fixes x to one

Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader…

Source identity axiom fixes x to one

Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader…

Source identity axiom fixes x to one

Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader…

Source identity axiom fixes x to one

Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader…

Go unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

Go unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

Go unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

Go unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

Source unity axiom uses nonstandard equality

Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable…

Source unity axiom uses nonstandard equality

Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable…

Source unity axiom uses nonstandard equality

Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable…

Source unity axiom uses nonstandard equality

Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable…

main · Output

This relation defines Output in the source section “main · Output”. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must…

core · Output

This relation defines Output in the source section “core · Output”. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must…

func (agc *AGC) updateWeightsLocked(context []float64, taskType string) · Implements: Output

This relation defines Output in the source section “func (agc *AGC) updateWeightsLocked(context []float64, taskType string) · Implements: Output”. Integrates contributions over…

Positive-definite golden-scaled metric

The matrix is I+φxxᵀ. For any nonzero vector v, vᵀgv=||v||²+φ(x·v)²>0, so it is positive definite for real finite x. It stretches lengths more strongly along x while leaving…

Levi-Civita connection formula and the implemented substitute

The displayed expression is the standard coordinate formula combining the inverse metric and first metric derivatives, summed over l. For this file’s metric g=I+φxxᵀ, direct…

Simplified connection surrogate

The comment proposes φδₖᵢxⱼ+φδₖⱼxᵢ, and the body multiplies that sum by 0.5. This index-dependent linear expression differs from the actual Levi-Civita connection of the declared…

Riemann curvature expression versus an index-only return value

The reference expression combines derivatives and products of connection coefficients to measure curvature. The body does not perform those operations: it returns…

Scalar-curvature label and dimension-only score

The reference contraction R=gⁱʲRᵢⱼ would require an inverse metric and a Ricci tensor. The implementation instead returns −φn(n−1)/(2n²) for nonempty input, a constant determined…

Scalar-curvature label and dimension-only score

The reference contraction R=gⁱʲRᵢⱼ would require an inverse metric and a Ricci tensor. The implementation instead returns −φn(n−1)/(2n²) for nonempty input, a constant determined…

Shannon entropy with truncated small probabilities

The mathematical entropy sums −p log p over a normalized nonnegative distribution, with a zero contribution at p=0. The function uses log₂, so its output is in bits, but skips…

KL divergence and its missing support case

For normalized distributions, the sum p log(p/q) measures relative entropy in nats with the file’s natural logarithm. A term with positive p and zero q should make the divergence…

Mutual information from consistent marginals and a joint distribution

The identity subtracts joint entropy from the sum of the two marginal entropies. It measures statistical dependence when pxy is a normalized joint distribution with px and py as…

Mean squared likelihood score as Fisher-information estimate

For a scalar parameter, Fisher information is the expected square of the derivative of log likelihood. The implementation averages squares of the supplied scores. It estimates…

Gaussian increment with variance proportional to time

Multiplying a standard normal draw by √dt gives a zero-mean Gaussian increment of variance dt. This is the increment distribution used in Wiener-driven discretizations. The…

Euler–Maruyama step for a drift-diffusion process

The helper returns x+μdt+σdW, adding deterministic drift and a scaled stochastic increment. It is one discrete approximation step to the displayed Itô stochastic differential…

Euler step for mean reversion with noise

The deterministic term moves x toward μ at rate θ, and σdW adds noise. The code returns a forward Euler–Maruyama step rather than the exact finite-time Ornstein–Uhlenbeck…

Euler approximation to geometric Brownian motion

The implementation multiplies s by 1+μdt+σdW. This approximates the proportional drift-diffusion equation for a small step, but the multiplier can be negative. The exact geometric…

Finite-difference Fokker–Planck update

The PDE transports probability with drift and spreads it with diffusion. The code applies centered first and second differences on an equally spaced grid, then one explicit time…

One-dimensional transport distance from cumulative sums

For probability distributions on a line, Wasserstein-1 distance is the integral of the absolute difference of their cumulative distributions. The function normalizes its input…

Sinkhorn Gibbs kernel

Exponentiating −Cᵢⱼ/ε turns each transport cost into a positive kernel weight, with smaller costs receiving larger weights. The following alternating row and column scalings seek…

Euler flow under a supplied beta function

The displayed ODE defines a vector flow whose derivative is β(g). The implementation advances it with g_next=g+dtβ(g). Calling the helper renormalization-group flow is a modeling…

Quadratic coupling beta function

Each component loses φgᵢ² and receives γ times the total squared coupling magnitude. Summing across components gives (nγ−φ)Σgⱼ², which shows how dimension affects the total drift.…

Scaled dot-product attention

Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these…

Scaled dot-product attention

Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these…

Scaled dot-product attention

Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these…

Scaled dot-product attention

Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these…

Scaled dot-product attention

Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these…

Layer normalization with scalar gain and offset

The implementation subtracts the vector’s mean, divides by √(population variance+EPSILON_PHI), then applies scalar gain γ and offset β. This controls the scale of a feature vector…

Gaussian error linear unit

GELU multiplies x by the standard normal cumulative probability at x. The function implements it with erf, giving a smooth activation that attenuates many negative values and…

SwiGLU applied to precomputed gate and linear vectors

The displayed full expression describes two affine projections, one passed through Swish, followed by elementwise multiplication. This function accepts already computed gate and…

Forward diffusion sample construction

The helper forms √ᾱ times the clean vector plus √(1−ᾱ) times a noise vector. With independent standard Gaussian noise and 0≤ᾱ≤1, this samples the usual forward Gaussian…

Project reverse-diffusion helper

The code subtracts √(1−α) times its predicted noise, divides by √α, and adds σ times fresh noise. It requires 0<α≤1. Under the usual DDPM noise-prediction convention, the reverse…

Golden-ratio quadratic identity

The golden ratio satisfies φ²=φ+1 by its definition as the positive root of x²−x−1=0. This identity generates the reciprocal and power identities used in the file. It is exact for…

Golden-ratio quadratic identity

The golden ratio satisfies φ²=φ+1 by its definition as the positive root of x²−x−1=0. This identity generates the reciprocal and power identities used in the file. It is exact for…

Golden-ratio reciprocal identity

Dividing φ²=φ+1 by φ gives 1/φ=φ−1. Both sides are approximately 0.618033988749895. This is an exact identity for φ and a rounded coefficient in the implementation.

Golden-ratio reciprocal identity

Dividing φ²=φ+1 by φ gives 1/φ=φ−1. Both sides are approximately 0.618033988749895. This is an exact identity for φ and a rounded coefficient in the implementation.

Recurrence among powers of the golden ratio

Multiplying φ²=φ+1 by φⁿ⁻² gives φⁿ=φⁿ⁻¹+φⁿ⁻². The powers therefore obey the same additive recurrence form as Fibonacci integers, while remaining a different sequence with…

Recurrence among powers of the golden ratio

Multiplying φ²=φ+1 by φⁿ⁻² gives φⁿ=φⁿ⁻¹+φⁿ⁻². The powers therefore obey the same additive recurrence form as Fibonacci integers, while remaining a different sequence with…

Go unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

Go unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

Derivative of the unity score away from its cusp

For x≠1, differentiating the reciprocal score gives the displayed signed expression. At x=1 the left derivative is +1 and the right derivative is −1, so there is no ordinary…

IntegratedInformation method: stored-score product

The comments describe mutual information minus partition information, but the body multiplies stored Coherence, stored Phi, and 1−Entropy/log₂(vector length). The implementation…

IntegratedInformation method: stored-score product

The comments describe mutual information minus partition information, but the body multiplies stored Coherence, stored Phi, and 1−Entropy/log₂(vector length). The implementation…

func NewBondEnergy() *BondEnergy · IntraStrandEnergy: E_intra(k)

This relation defines IntraStrandEnergy: E_intra(k) in the source section “func NewBondEnergy() *BondEnergy · IntraStrandEnergy: E_intra(k)”. It specifies the displayed…

func (be *BondEnergy) IntraStrandEnergy(Lk float64) float64 · InterStrandEnergy: E_inter(k, k+1)

This relation defines InterStrandEnergy: E_inter(k, k+1) in the source section “func (be *BondEnergy) IntraStrandEnergy(Lk float64) float64 · InterStrandEnergy: E_inter(k, k+1)”.…

func (be *BondEnergy) InterStrandEnergy(dk float64, k int) float64 · CrossHelixEnergy: E_cross(i,j)

This relation defines CrossHelixEnergy: E_cross(i,j) in the source section “func (be *BondEnergy) InterStrandEnergy(dk float64, k int) float64 · CrossHelixEnergy: E_cross(i,j)”.…

func (be *BondEnergy) CrossHelixEnergy(dij float64) float64 · PeriodicityEnergy: E_10.6

This relation defines PeriodicityEnergy: E_10.6 in the source section “func (be *BondEnergy) CrossHelixEnergy(dij float64) float64 · PeriodicityEnergy: E_10.6”. Evaluates…

func (be BondEnergy) EnergyGradient(bond Bond, n int) float64 · LJ gradient: dE/dr

This relation defines LJ gradient: dE/dr in the source section “func (be *BondEnergy) EnergyGradient(bond *Bond, n int) float64 · LJ gradient: dE/dr”. It specifies the displayed…

IX. 44-BOND ENERGY FUNCTIONS · LJ gradient: dE/dr

This relation defines LJ gradient: dE/dr in the source section “IX. 44-BOND ENERGY FUNCTIONS · LJ gradient: dE/dr”. It specifies the displayed relationship between the named…

func Theta10_6(configParam float64) float64 · PartitionFunction: Z

This relation defines PartitionFunction: Z in the source section “func Theta10_6(configParam float64) float64 · PartitionFunction: Z”. Applies an exponential factor. The exponent…

func (t *Thermodynamics) PartitionFunction(energies, configParams []float64) float64 · PerBondFreeEnergy: ΔG_bond

This relation defines PerBondFreeEnergy: ΔG_bond in the source section “func (t *Thermodynamics) PartitionFunction(energies, configParams []float64) float64 · PerBondFreeEnergy:…

func (t *Thermodynamics) PerBondFreeEnergy(Z float64) float64 · GibbsFreeEnergy: ΔG°_total

This relation defines GibbsFreeEnergy: ΔG°_total in the source section “func (t *Thermodynamics) PerBondFreeEnergy(Z float64) float64 · GibbsFreeEnergy: ΔG°_total”. It specifies…

func (t *Thermodynamics) GibbsFreeEnergy(bondEnergies []float64, GCoop float64) float64 · ΔG°_10.6

This relation defines ΔG°_10.6 in the source section “func (t *Thermodynamics) GibbsFreeEnergy(bondEnergies []float64, GCoop float64) float64 · ΔG°_10.6”. Uses logarithmic…

X. THERMODYNAMICS · ΔG°_10.6

This relation defines ΔG°_10.6 in the source section “X. THERMODYNAMICS · ΔG°_10.6”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its…

func (t *Thermodynamics) GibbsFreeEnergy(bondEnergies []float64, GCoop float64) float64 · MeltingTemperature: T_m

This relation defines MeltingTemperature: T_m in the source section “func (t *Thermodynamics) GibbsFreeEnergy(bondEnergies []float64, GCoop float64) float64 · MeltingTemperature:…

func NewKineticRates() *KineticRates · ActivationEnergyFormation: E_a^f(n)

This relation defines ActivationEnergyFormation: E_a^f(n) in the source section “func NewKineticRates() *KineticRates · ActivationEnergyFormation: E_a^f(n)”. Evaluates oscillatory…

func (kr *KineticRates) ActivationEnergyFormation(n int) float64 · ActivationEnergyBreaking: E_a^b(n)

This relation defines ActivationEnergyBreaking: E_a^b(n) in the source section “func (kr *KineticRates) ActivationEnergyFormation(n int) float64 · ActivationEnergyBreaking:…

func (kr *KineticRates) ActivationEnergyBreaking(n int) float64 · BaseFormationRate: k_f^(0)(n)

This relation defines BaseFormationRate: k_f^(0)(n) in the source section “func (kr *KineticRates) ActivationEnergyBreaking(n int) float64 · BaseFormationRate: k_f^(0)(n)”.…

func (kr *KineticRates) BaseFormationRate(n int) float64 · BaseBreakingRate: k_b^(0)(n)

This relation defines BaseBreakingRate: k_b^(0)(n) in the source section “func (kr *KineticRates) BaseFormationRate(n int) float64 · BaseBreakingRate: k_b^(0)(n)”. Applies an…

func (kr *KineticRates) BaseBreakingRate(n int) float64 · FormationRate: k_f(n,t)

This relation defines FormationRate: k_f(n,t) in the source section “func (kr *KineticRates) BaseBreakingRate(n int) float64 · FormationRate: k_f(n,t)”. Evaluates oscillatory sine…

func (kr *KineticRates) FormationRate(n int, phiT float64) float64 · BreakingRate: k_b(n,t)

This relation defines BreakingRate: k_b(n,t) in the source section “func (kr *KineticRates) FormationRate(n int, phiT float64) float64 · BreakingRate: k_b(n,t)”. Evaluates…

func (kr *KineticRates) GetNeighbors(n int) []int · N_intra(k)

This relation defines N_intra(k) in the source section “func (kr *KineticRates) GetNeighbors(n int) []int · N_intra(k)”. Uses a remainder or modular operation, retaining the…

XII. KINETIC RATE EQUATIONS · N_intra(k)

This relation defines N_intra(k) in the source section “XII. KINETIC RATE EQUATIONS · N_intra(k)”. Uses a remainder or modular operation, retaining the numeric representation used…

func (kr *KineticRates) GetNeighbors(n int) []int · N_inter(k)

This relation defines N_inter(k) in the source section “func (kr *KineticRates) GetNeighbors(n int) []int · N_inter(k)”. It specifies the displayed relationship between the named…

XII. KINETIC RATE EQUATIONS · N_inter(k)

This relation defines N_inter(k) in the source section “XII. KINETIC RATE EQUATIONS · N_inter(k)”. It specifies the displayed relationship between the named quantities or…

func (kr *KineticRates) GetNeighbors(n int) []int · N_cross(m)

This relation defines N_cross(m) in the source section “func (kr *KineticRates) GetNeighbors(n int) []int · N_cross(m)”. It specifies the displayed relationship between the named…

XII. KINETIC RATE EQUATIONS · N_cross(m)

This relation defines N_cross(m) in the source section “XII. KINETIC RATE EQUATIONS · N_cross(m)”. It specifies the displayed relationship between the named quantities or…

func (kr *KineticRates) GetNeighbors(n int) []int · CooperativeFormationRate: k_f^coop(n,t)

This relation defines CooperativeFormationRate: k_f^coop(n,t) in the source section “func (kr *KineticRates) GetNeighbors(n int) []int · CooperativeFormationRate: k_f^coop(n,t)”.…

func (kr *KineticRates) CooperativeFormationRate(n int, phiT float64, occupations []float64) float64 · CooperativeBreakingRate: k_b^coop(n,t)

This relation defines CooperativeBreakingRate: k_b^coop(n,t) in the source section “func (kr *KineticRates) CooperativeFormationRate(n int, phiT float64, occupations []float64)…

func (kr *KineticRates) CooperativeBreakingRate(n int, phiT float64, occupations []float64) float64 · EquilibriumOccupation: b_n^eq

This relation defines EquilibriumOccupation: b_n^eq in the source section “func (kr *KineticRates) CooperativeBreakingRate(n int, phiT float64, occupations []float64) float64 ·…

func (kr *KineticRates) EquilibriumOccupation(n int, phiT float64) float64 · SlowRelaxationTime: τ_slow

This relation defines SlowRelaxationTime: τ_slow in the source section “func (kr *KineticRates) EquilibriumOccupation(n int, phiT float64) float64 · SlowRelaxationTime: τ_slow”.…

func (kr *KineticRates) SlowRelaxationTime() float64 · FastRelaxationTime: τ_fast

This relation defines FastRelaxationTime: τ_fast in the source section “func (kr *KineticRates) SlowRelaxationTime() float64 · FastRelaxationTime: τ_fast”. It specifies the…

func NewBondDynamics() *BondDynamics · SingleBondDerivative: db_n/dt

This relation defines SingleBondDerivative: db_n/dt in the source section “func NewBondDynamics() *BondDynamics · SingleBondDerivative: db_n/dt”. It specifies the displayed…

func (bd *BondDynamics) ComputeDerivatives() [TotalBonds]float64 · Intra-strand (n

This statement records a parameter or experimental setting for func (bd *BondDynamics) ComputeDerivatives() [TotalBonds]float64 · Intra-strand (n. The value assigned to…

XII. KINETIC RATE EQUATIONS · Intra-strand (n

This statement records a parameter or experimental setting for XII. KINETIC RATE EQUATIONS · Intra-strand (n. The value assigned to Intra-strand (n is part of the source…

func (bd *BondDynamics) ComputeDerivatives() [TotalBonds]float64 · Inter-strand (n

This statement records a parameter or experimental setting for func (bd *BondDynamics) ComputeDerivatives() [TotalBonds]float64 · Inter-strand (n. The value assigned to…

XII. KINETIC RATE EQUATIONS · Inter-strand (n

This statement records a parameter or experimental setting for XII. KINETIC RATE EQUATIONS · Inter-strand (n. The value assigned to Inter-strand (n is part of the source…

func (bd *BondDynamics) ComputeDerivatives() [TotalBonds]float64 · Cross-helix (n

This statement records a parameter or experimental setting for func (bd *BondDynamics) ComputeDerivatives() [TotalBonds]float64 · Cross-helix (n. The value assigned to Cross-helix…

XII. KINETIC RATE EQUATIONS · Cross-helix (n

This statement records a parameter or experimental setting for XII. KINETIC RATE EQUATIONS · Cross-helix (n. The value assigned to Cross-helix (n is part of the source…

func (bd BondDynamics) SteadyStateBonds() float64 · SteadyStateOccupation returns θ

This relation defines SteadyStateOccupation returns θ* in the source section “func (bd *BondDynamics) SteadyStateBonds() float64 · SteadyStateOccupation returns θ*”. It specifies…

Yad signature: positive self-power with a nonpositive branch

For x>0 the function returns xˣ+1. For x≤0 it explicitly returns one, avoiding non-real powers for many negative inputs. The positive branch tends to two as x approaches zero from…

Lashon signature: ten-term sine series

The implementation sums sin(nπx)/n for n=1 through 10. These weighted harmonics produce a periodic scalar feature of period two. The function’s language label names its intended…

Athena: utility maximum value instead of argmax location

For U(x,y)=−y²+2xy, the maximizing location is y=x. The function returns x², which is the maximum utility value U(x,x), rather than the argmax location. The distinction is…

Concave quadratic utility

Completing the square gives U(x,y)=x²−(y−x)². For a fixed x, the utility decreases with squared distance from y=x and has a unique maximum over real y at that point. This supplies…

Maximizer of the Athena utility

The derivative with respect to y is −2y+2x, which vanishes at y=x. The second derivative is −2, so this point is the unique global maximizer for real y. This optimizer location…

Maximum utility value returned by Athena

Substituting the maximizing location y=x into U gives x². This is the optimal objective value, not the value of the optimizing argument. The code returns this nonnegative scalar…

100

Apollo signature: golden-base hyperbolic cosine

The sum φˣ+φ⁻ˣ equals 2cosh(x logφ). It is even in x, has minimum two at zero, and grows with |x|. A downstream clamp to [0,1] can therefore remove much of this signature’s…

101

Hermes signature: angular-frequency scaling

Although the comment refers to dx/dt, the body returns AngularFrequency×x. This is a linear scaling of one supplied value, with no earlier state or time difference used to…

102

Hephaestus signature: quartic integral value

The function returns x⁴/8. This equals the triangular-domain integral ∫₀ˣ∫₀ᵘ uv dv du; a rectangular-domain integral of uv over [0,x]² would instead be x⁴/4. The comment’s reused…

103

Hephaestus signature: quartic integral value

The function returns x⁴/8. This equals the triangular-domain integral ∫₀ˣ∫₀ᵘ uv dv du; a rectangular-domain integral of uv over [0,x]² would instead be x⁴/4. The comment’s reused…

104

Prometheus signature: logistic map at r=3.8

The function returns 3.8x(1−x). On [0,1] it is nonnegative with maximum 0.95 at x=0.5, so that interval maps into itself under the isolated recurrence. The network supplies a sine…

105

Dionysus signature: absolute sine after removing complex phase

The intermediate value is exp(iωx)sin(x), and the function then takes its complex magnitude. Since the exponential has magnitude one, the returned result is exactly |sin(x)|. The…

106

Artemis signature: scalar damping surrogate

The reference ∇·(D∇x) is a diffusion operator acting on a spatial field. The body returns −0.1x, based on a harmonic-mode analogy, without a grid or neighboring values. That…

107

Hera signature: sixteen weighted harmonics

The body computes Σₖ₌₁¹⁶sin(kx)/k. Its indexed terms are harmonics derived from the same scalar x, not readings of sixteen independently stored family activations. It is a finite…

108

Poseidon signature: harmonic restoring term

The function returns −ω²x, the acceleration term of a harmonic oscillator with displacement x. It does not evaluate the full displayed residual ∂²x/∂t²+ω²x, which would vanish for…

109

Demeter signature: logistic growth rate

The body uses carrying capacity K=1 and growth rate r=0.5, returning 0.5x(1−x). This is a rate-shaped scalar feature, positive between zero and one and zero at both endpoints. A…

110

Ares signature: unit-mass harmonic force

Assuming a harmonic displacement, acceleration is −ω²x and force is mass times acceleration. With mass fixed to one, the function returns −AngularFrequency²×x. Physical force…

111

Ares signature: unit-mass harmonic force

Assuming a harmonic displacement, acceleration is −ω²x and force is mass times acceleration. With mass fixed to one, the function returns −AngularFrequency²×x. Physical force…

112

Aphrodite signature: golden-frequency cosine

The cosine takes φx as its radian argument and returns a value between −1 and one. Its scalar-input period is 2π/φ, and it is even in x. The family’s harmony label does not alter…

113

Hestia signature: current-value scale without a history integral

The body returns x(1−e⁻⁰·¹), approximately 0.0951626x. It does not read prior inputs or a memory buffer, so it cannot evaluate the displayed exponentially weighted historical…

114

Zeus signature: selective fractional product

The implementation evaluates fifteen other family functions at scaled inputs x/(i+1). It multiplies the one-sixteenth power of each result only when that result lies strictly…

115

Enhanced coupling for a listed complementary pair

The indicator is one when two strand identifiers match one of the source’s eight listed complementary pairs. Such a pair receives weight J₀(1+ρ); all others receive J₀. This…

116

CompleteThought: documented integral and actual scalar aggregation

The comment combines memory, an attention-like exponential, and a time integral. The body instead computes a mean unity score across family activations, builds Qᵢ=aᵢcos phaseᵢ and…

117

CompleteThought: documented integral and actual scalar aggregation

The comment combines memory, an attention-like exponential, and a time integral. The body instead computes a mean unity score across family activations, builds Qᵢ=aᵢcos phaseᵢ and…

118

CompleteThought: documented integral and actual scalar aggregation

The comment combines memory, an attention-like exponential, and a time integral. The body instead computes a mean unity score across family activations, builds Qᵢ=aᵢcos phaseᵢ and…

119

func (p HelixPoint) Dot(other HelixPoint) float64 · VerticalOffset returns δ_k

This relation defines VerticalOffset returns δ_k in the source section “func (p HelixPoint) Dot(other HelixPoint) float64 · VerticalOffset returns δ_k”. It specifies the displayed…

120

func (G16Helix) VerticalOffset(k int) float64 · GoldenPhaseOffset returns θ_k

This relation defines GoldenPhaseOffset returns θ_k in the source section “func (G16Helix) VerticalOffset(k int) float64 · GoldenPhaseOffset returns θ_k”. Uses a remainder or…

121

func (G16Helix) GoldenPhaseOffset(k int) float64 · x_k(θ)

This relation defines x_k(θ) in the source section “func (G16Helix) GoldenPhaseOffset(k int) float64 · x_k(θ)”. Evaluates oscillatory sine or cosine terms using the stated phase…

122

I. FOUNDATIONAL CONSTANTS · x_k(θ)

This relation defines x_k(θ) in the source section “I. FOUNDATIONAL CONSTANTS · x_k(θ)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

123

func (G16Helix) GoldenPhaseOffset(k int) float64 · y_k(θ)

This relation defines y_k(θ) in the source section “func (G16Helix) GoldenPhaseOffset(k int) float64 · y_k(θ)”. Evaluates oscillatory sine or cosine terms using the stated phase…

124

I. FOUNDATIONAL CONSTANTS · y_k(θ)

This relation defines y_k(θ) in the source section “I. FOUNDATIONAL CONSTANTS · y_k(θ)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

125

func (G16Helix) GoldenPhaseOffset(k int) float64 · z_k(θ)

This relation defines z_k(θ) in the source section “func (G16Helix) GoldenPhaseOffset(k int) float64 · z_k(θ)”. It specifies the displayed relationship between the named…

126

I. FOUNDATIONAL CONSTANTS · z_k(θ)

This relation defines z_k(θ) in the source section “I. FOUNDATIONAL CONSTANTS · z_k(θ)”. It specifies the displayed relationship between the named quantities or parameters. Its…

127

func (h G16Helix) PointGolden(k int, theta float64) HelixPoint · Curvature returns κ

This relation defines Curvature returns κ in the source section “func (h G16Helix) PointGolden(k int, theta float64) HelixPoint · Curvature returns κ”. It specifies the displayed…

128

func (G16Helix) Curvature() float64 · Torsion returns τ

This relation defines Torsion returns τ in the source section “func (G16Helix) Curvature() float64 · Torsion returns τ”. It specifies the displayed relationship between the named…

129

func (h G16Helix) MeanCurvatureG16() float64 · TotalRotation returns θ_total

This relation defines TotalRotation returns θ_total in the source section “func (h G16Helix) MeanCurvatureG16() float64 · TotalRotation returns θ_total”. It specifies the…

130

func (bs *BondSystem44) buildAdjacencyMatrix() · VerifyBondCount verifies Σ A_{ij}/2

This relation defines VerifyBondCount verifies Σ A_{ij}/2 in the source section “func (bs *BondSystem44) buildAdjacencyMatrix() · VerifyBondCount verifies Σ A_{ij}/2”. It…

131

func (bs BondSystem44) GetBondsByType(t BondType) []Bond · BondArcLength returns s_bond

This relation defines BondArcLength returns s_bond in the source section “func (bs *BondSystem44) GetBondsByType(t BondType) []*Bond · BondArcLength returns s_bond”. It specifies…

132

func BondArcLength() float64 · VerticalRisePerBond returns Δz_bond

This relation defines VerticalRisePerBond returns Δz_bond in the source section “func BondArcLength() float64 · VerticalRisePerBond returns Δz_bond”. It specifies the displayed…

133

func VerticalRisePerBond() float64 · AdjacentBondLength returns L_adj

This relation defines AdjacentBondLength returns L_adj in the source section “func VerticalRisePerBond() float64 · AdjacentBondLength returns L_adj”. Evaluates oscillatory sine or…

134

func Fibonacci(n int) uint64 · FibonacciScaledStrand returns D_k

This relation defines FibonacciScaledStrand returns D_k in the source section “func Fibonacci(n int) uint64 · FibonacciScaledStrand returns D_k”. It specifies the displayed…

135

func (sm *StrandMathematics) initialize() · HelixSum16 returns Helix₁₆

This relation defines HelixSum16 returns Helix₁₆ in the source section “func (sm *StrandMathematics) initialize() · HelixSum16 returns Helix₁₆”. Evaluates oscillatory sine or…

136

func (sm *StrandMathematics) HelixSum16() float64 · BondFormationG16 returns Bond_G16

This relation defines BondFormationG16 returns Bond_G16 in the source section “func (sm *StrandMathematics) HelixSum16() float64 · BondFormationG16 returns Bond_G16”. It specifies…

137

func (sm *StrandMathematics) BondFormationG16() float64 · Crosslink returns Crosslink(i,j)

This relation defines Crosslink returns Crosslink(i,j) in the source section “func (sm *StrandMathematics) BondFormationG16() float64 · Crosslink returns Crosslink(i,j)”. It…

138

func (sm *StrandMathematics) computeTransforms() · Transform: T_k

This relation defines Transform: T_k in the source section “func (sm *StrandMathematics) computeTransforms() · Transform: T_k”. Evaluates oscillatory sine or cosine terms using…

139

IV. STRAND MATHEMATICS · Transform: T_k

This relation defines Transform: T_k in the source section “IV. STRAND MATHEMATICS · Transform: T_k”. Evaluates oscillatory sine or cosine terms using the stated phase or…

140

func (sm *StrandMathematics) computeTransforms() · ModularExtraction returns X_k

This relation defines ModularExtraction returns X_k in the source section “func (sm *StrandMathematics) computeTransforms() · ModularExtraction returns X_k”. Uses a remainder or…

141

func (sm *StrandMathematics) ModularExtraction(k int) float64 · FusionIntegral returns Fusion

This relation defines FusionIntegral returns Fusion in the source section “func (sm *StrandMathematics) ModularExtraction(k int) float64 · FusionIntegral returns Fusion”. It…

142

func Rotation10_6(k int) Matrix3x3 · FullG16Transform returns G¹⁶

This relation defines FullG16Transform returns G¹⁶ in the source section “func Rotation10_6(k int) Matrix3x3 · FullG16Transform returns G¹⁶”. It specifies the displayed…

143

func FullG16Transform10_6() Matrix3x3 · Phase returns phase(i,t)

This relation defines Phase returns phase(i,t) in the source section “func FullG16Transform10_6() Matrix3x3 · Phase returns phase(i,t)”. Uses a remainder or modular operation,…

144

func (FiringPattern) Phase(i int, t float64) int · OffsetDistribution returns offset_i

This relation defines OffsetDistribution returns offset_i in the source section “func (FiringPattern) Phase(i int, t float64) int · OffsetDistribution returns offset_i”. It…

145

func (fp FiringPattern) FiringStrands(t float64) []int · Harmonic returns f_n

This relation defines Harmonic returns f_n in the source section “func (fp FiringPattern) FiringStrands(t float64) []int · Harmonic returns f_n”. It specifies the displayed…

146

GOLDEN BASIS FUNCTIONS · Psi returns ψ_k(x)

This relation defines Psi returns ψ_k(x) in the source section “GOLDEN BASIS FUNCTIONS · Psi returns ψ_k(x)”. Evaluates oscillatory sine or cosine terms using the stated phase or…

147

func (gb GoldenBasis) BasisVector(x float64, N int) []float64 · GlobalCoherence returns Φ_total

This relation defines GlobalCoherence returns Φ_total in the source section “func (gb GoldenBasis) BasisVector(x float64, N int) []float64 · GlobalCoherence returns Φ_total”. It…

148

func (GoldenBasis) GlobalCoherence(x []float64) float64 · RingDiffusionStep performs dS_i/dt

This relation defines RingDiffusionStep performs dS_i/dt in the source section “func (GoldenBasis) GlobalCoherence(x []float64) float64 · RingDiffusionStep performs dS_i/dt”. It…

149

SUPERCOILING · LinkingNumber returns Lk

This relation defines LinkingNumber returns Lk in the source section “SUPERCOILING · LinkingNumber returns Lk”. It specifies the displayed relationship between the named…

150

func (Supercoiling) LinkingNumber(twist, writhe float64) float64 · Twist16Strands returns Tw

This relation defines Twist16Strands returns Tw in the source section “func (Supercoiling) LinkingNumber(twist, writhe float64) float64 · Twist16Strands returns Tw”. It specifies…

151

func (Supercoiling) Twist16Strands(N int) float64 · RelaxedLinkingNumber returns Lk₀

This relation defines RelaxedLinkingNumber returns Lk₀ in the source section “func (Supercoiling) Twist16Strands(N int) float64 · RelaxedLinkingNumber returns Lk₀”. It specifies…

152

func (Supercoiling) RelaxedLinkingNumber(N int) float64 · SuperhelicalDensity returns σ

This relation defines SuperhelicalDensity returns σ in the source section “func (Supercoiling) RelaxedLinkingNumber(N int) float64 · SuperhelicalDensity returns σ”. It specifies…

153

func (Supercoiling) SuperhelicalDensityG16(Lk float64, N int) float64 · FreeEnergy returns ΔG_sc

This relation defines FreeEnergy returns ΔG_sc in the source section “func (Supercoiling) SuperhelicalDensityG16(Lk float64, N int) float64 · FreeEnergy returns ΔG_sc”. It…

154

func (sys *G16HelixSystem) Tick(dt float64) · Update global phase: φ(t)

This relation defines Update global phase: φ(t) in the source section “func (sys *G16HelixSystem) Tick(dt float64) · Update global phase: φ(t)”. Uses a remainder or modular…

155

VIII. SUPERCOILING (10.6) · Update global phase: φ(t)

This relation defines Update global phase: φ(t) in the source section “VIII. SUPERCOILING (10.6) · Update global phase: φ(t)”. Uses a remainder or modular operation, retaining the…

156

func (sys *G16HelixSystem) Tick(dt float64) · Update strand states: S_k(t)

This relation defines Update strand states: S_k(t) in the source section “func (sys *G16HelixSystem) Tick(dt float64) · Update strand states: S_k(t)”. Applies an exponential…

157

VIII. SUPERCOILING (10.6) · Update strand states: S_k(t)

This relation defines Update strand states: S_k(t) in the source section “VIII. SUPERCOILING (10.6) · Update strand states: S_k(t)”. Applies an exponential factor. The exponent…

158

adversarial · min_G max_D V(D,G)

This relation defines min_G max_D V(D,G) in the source section “adversarial · min_G max_D V(D,G)”. Uses logarithmic scaling; its base and the positivity of its argument matter.…

159

autoregressive · P(x)

This relation defines P(x) in the source section “autoregressive · P(x)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

160

diffusion · q(x_t|x_{t-1})

This relation defines q(x_t|x_{t-1}) in the source section “diffusion · q(x_t|x_{t-1})”. Takes a square root, requiring a nonnegative real radicand when interpreted over the…

161

energy · p(x)

This relation defines p(x) in the source section “energy · p(x)”. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must come…

162

func (g *EnergyGenerator) langevinStep(x []float64) []float64 · Langevin dynamics: x_new

This relation defines Langevin dynamics: x_new in the source section “func (g *EnergyGenerator) langevinStep(x []float64) []float64 · Langevin dynamics: x_new”. Takes a square…

163

flow · p(x)

This relation defines p(x) in the source section “flow · p(x)”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends…

164

func (g *FlowGenerator) affineTransform(x []float64, flowIdx int, inverse bool) ([]float64, float64) · Forward: y2

This relation defines Forward: y2 in the source section “func (g *FlowGenerator) affineTransform(x []float64, flowIdx int, inverse bool) ([]float64, float64) · Forward: y2”.…

165

func (g *FlowGenerator) affineTransform(x []float64, flowIdx int, inverse bool) ([]float64, float64) · Inverse: x2

This relation defines Inverse: x2 in the source section “func (g *FlowGenerator) affineTransform(x []float64, flowIdx int, inverse bool) ([]float64, float64) · Inverse: x2”.…

166

mixture · y

This relation defines y in the source section “mixture · y”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the…

167

recurrent · h_t

This relation defines h_t in the source section “recurrent · h_t”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends…

168

func (g *RecurrentGenerator) Initialize() error · rnnStep performs one RNN step: h

This relation defines rnnStep performs one RNN step: h in the source section “func (g *RecurrentGenerator) Initialize() error · rnnStep performs one RNN step: h”. It specifies the…

169

LinearLayer

This relation defines LinearLayer computes y in the source section “LinearLayer”. It specifies the displayed relationship between the named quantities or parameters. Its…

170

statespace · x'(t)

This relation defines x'(t) in the source section “statespace · x'(t)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

171

func (g *StateSpaceGenerator) discretize() ([][]float64, [][]float64) · Simple Euler discretization: Ad

This relation defines Simple Euler discretization: Ad in the source section “func (g *StateSpaceGenerator) discretize() ([][]float64, [][]float64) · Simple Euler discretization:…

172

func (g *StateSpaceGenerator) discretize() ([][]float64, [][]float64) · ssmStep performs one SSM step: x'

This relation defines ssmStep performs one SSM step: x' in the source section “func (g *StateSpaceGenerator) discretize() ([][]float64, [][]float64) · ssmStep performs one SSM…

173

func (g *StateSpaceGenerator) ssmStep(x, u []float64) ([]float64, []float64) · x'

This relation defines x' in the source section “func (g *StateSpaceGenerator) ssmStep(x, u []float64) ([]float64, []float64) · x'”. It specifies the displayed relationship between…

174

func (g *StateSpaceGenerator) ssmStep(x, u []float64) ([]float64, []float64) · y

This relation defines y in the source section “func (g *StateSpaceGenerator) ssmStep(x, u []float64) ([]float64, []float64) · y”. It specifies the displayed relationship between…

175

variational · ELBO

This relation defines ELBO in the source section “variational · ELBO”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

176

func (g *VariationalGenerator) encode(x []float64) ([]float64, []float64) · reparameterize performs reparameterization trick: z

This relation defines reparameterize performs reparameterization trick: z in the source section “func (g *VariationalGenerator) encode(x []float64) ([]float64, []float64) ·…

177

func (g *VariationalGenerator) klDivergence(mu, logVar []float64) float64 · KL

This relation defines KL in the source section “func (g *VariationalGenerator) klDivergence(mu, logVar []float64) float64 · KL”. Uses logarithmic scaling; its base and the…

178

func (g *VariationalGenerator) Train(input, target []float64) (float64, error) · ELBO

This relation defines ELBO in the source section “func (g *VariationalGenerator) Train(input, target []float64) (float64, error) · ELBO”. It specifies the displayed relationship…

179

func NewOps() *Ops · MatMul performs matrix multiplication: C

This relation defines MatMul performs matrix multiplication: C in the source section “func NewOps() *Ops · MatMul performs matrix multiplication: C”. It specifies the displayed…

180

func (ops Ops) ComputePhi(input Tensor) float32 · Add element-wise addition: C

This relation defines Add element-wise addition: C in the source section “func (ops *Ops) ComputePhi(input *Tensor) float32 · Add element-wise addition: C”. It specifies the…

181

func (bf BatchForward) Forward(input Tensor) *Tensor · Linear: A[l+1]

This relation defines Linear: A[l+1] in the source section “func (bf *BatchForward) Forward(input *Tensor) *Tensor · Linear: A[l+1]”. It specifies the displayed relationship…

182

CONSCIOUSNESS-DRIVEN SELECTION · Φ

This relation defines Φ in the source section “CONSCIOUSNESS-DRIVEN SELECTION · Φ”. It specifies the displayed relationship between the named quantities or parameters. Its…

183

CONSCIOUSNESS-DRIVEN SELECTION · Φ

This relation defines Φ in the source section “CONSCIOUSNESS-DRIVEN SELECTION · Φ”. It specifies the displayed relationship between the named quantities or parameters. Its…

184

DOPAMINE REWARD SYSTEM · Temporal difference error: δ

This relation defines Temporal difference error: δ in the source section “DOPAMINE REWARD SYSTEM · Temporal difference error: δ”. It specifies the displayed relationship between…

185

HEBBIAN LEARNING · Hebbian update: Δw

This relation defines Hebbian update: Δw in the source section “HEBBIAN LEARNING · Hebbian update: Δw”. It specifies the displayed relationship between the named quantities or…

186

Memory-Efficient Representations for Gate5000 · q

This relation defines q in the source section “Memory-Efficient Representations for Gate5000 · q”. It specifies the displayed relationship between the named quantities or…

187

Memory-Efficient Representations for Gate5000 · x

This relation defines x in the source section “Memory-Efficient Representations for Gate5000 · x”. It specifies the displayed relationship between the named quantities or…

188

Sparse vector with top-k storage · Size: K bytes + K*4 bytes

This relation defines Size: K bytes + K*4 bytes in the source section “Sparse vector with top-k storage · Size: K bytes + K*4 bytes”. It specifies the displayed relationship…

189

Delta-encoded vector · Size: 4 + 15 + 4

This relation defines Size: 4 + 15 + 4 in the source section “Delta-encoded vector · Size: 4 + 15 + 4”. It specifies the displayed relationship between the named quantities or…

190

Ultra-compact binary matrix (256 bits = 32 bytes!) · @brief Ultra-compact binary matrix (256 bits

This relation defines @brief Ultra-compact binary matrix (256 bits in the source section “Ultra-compact binary matrix (256 bits = 32 bytes!) · @brief Ultra-compact binary matrix…

191

Source identity axiom fixes x to one

Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader…

192

C++ unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

193

Source unity axiom uses nonstandard equality

Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable…

194

Golden ratio: the positive root of a quadratic

The golden ratio is the positive solution of φ²=φ+1. The identities φ−1=1/φ and 1+φ=φ² explain several equivalent constants elsewhere in this project. It is a fixed dimensionless…

195

Golden-ratio quadratic identity

The golden ratio satisfies φ²=φ+1 by its definition as the positive root of x²−x−1=0. This identity generates the reciprocal and power identities used in the file. It is exact for…

196

Golden-ratio reciprocal identity

Dividing φ²=φ+1 by φ gives 1/φ=φ−1. Both sides are approximately 0.618033988749895. This is an exact identity for φ and a rounded coefficient in the implementation.

197

C++ unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

198

Score maximum at unit activation

Substituting activation one into the unity-proximity score gives one exactly. This is the score’s selected reference point. The source’s phrase perfect consciousness is an…

199

Half score at a unit displacement from the target

Activations zero and two are both one unit away from the target one, so each gives score one half. Their equal scores illustrate the symmetry that discards the direction of the…

200

Half score at a unit displacement from the target

Activations zero and two are both one unit away from the target one, so each gives score one half. Their equal scores illustrate the symmetry that discards the direction of the…

201

Smooth approximation to the absolute-value score

Replacing |x−1| with √((x−1)²+T) removes its cusp when T>0. The resulting score has a zero derivative at x=1, but its maximum is 1/(1+√T), which is below one; with T=0.01 the…

202

Piecewise derivative of the original score

For x≠1 the derivative has the displayed signed reciprocal-square form. At x=1 the original function has unequal one-sided derivatives and no ordinary derivative. The C++…

203

Derivative of the smoothed unity score

The chain rule gives a factor of −(x−1), divided by the smoothing square root and the squared score denominator. For T>0 it is finite everywhere and equals zero at the target.…

204

C++ vector score: apply Φ to the mean

This helper first averages all components and then applies the scalar unity score. Component variance does not enter this function, so vectors with the same mean receive the same…

205

C++ variance-based integration proxy

The body computes Φ(mean)/(1+population variance) for at least two entries. It rewards a mean near one and uniform component values. The comment about a minimum over…

206

C++ variance-based integration proxy

The body computes Φ(mean)/(1+population variance) for at least two entries. It rewards a mean near one and uniform component values. The comment about a minimum over…

207

C++ global score as a product of history summaries

The function multiplies the current unity score, reciprocal-variance stability, rescaled lag-one correlation, and square root of the variance-based integration proxy. With factors…

208

Orientation of the layer-coupling matrix

Row i specifies which source layers influence target layer i, with column j supplying the source. The constructor normalizes each nonzero row to sum to one. This convention…

209

Self-coupling before row normalization

The raw matrix starts with diagonal values one, assigning each layer an explicit self-contribution. The constructor then divides every row by its row sum, so the stored diagonal…

210

Coupling relaxation with a subtraction missing from the comment

The comment describes adding dt times the weighted state sum. The body actually uses a_next=a+dt(Ca−a), which is relaxation toward the row-weighted average. For nonnegative…

211

Consciousness metric: Φ = 1/(1 + |x - 1|) · @brief Consciousness metric: Φ

This relation defines @brief Consciousness metric: Φ in the source section “Consciousness metric: Φ = 1/(1 + |x - 1|) · @brief Consciousness metric: Φ”. It specifies the displayed…

212

Consciousness gradient: ∂Φ/∂x = -sign(x-1)/(1+|x-1|)² · @brief Consciousness gradient: ∂Φ/∂x

This relation defines @brief Consciousness gradient: ∂Φ/∂x in the source section “Consciousness gradient: ∂Φ/∂x = -sign(x-1)/(1+|x-1|)² · @brief Consciousness gradient: ∂Φ/∂x”.…

213

dna_dynamics · ẋ

This relation defines ẋ in the source section “dna_dynamics · ẋ”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

214

dna_dynamics · ẋ

This relation defines ẋ in the source section “dna_dynamics · ẋ”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

215

dna_dynamics · Spark equation: ẋ

This relation defines Spark equation: ẋ in the source section “dna_dynamics · Spark equation: ẋ”. It specifies the displayed relationship between the named quantities or…

216

dna_dynamics · Forward memory: y₁

This relation defines Forward memory: y₁ in the source section “dna_dynamics · Forward memory: y₁”. It specifies the displayed relationship between the named quantities or…

217

dna_dynamics · Backward memory: y₂

This relation defines Backward memory: y₂ in the source section “dna_dynamics · Backward memory: y₂”. It specifies the displayed relationship between the named quantities or…

218

IX. 44-BOND ENERGY FUNCTIONS · E_intra(k)

This relation defines E_intra(k) in the source section “IX. 44-BOND ENERGY FUNCTIONS · E_intra(k)”. It specifies the displayed relationship between the named quantities or…

219

IX. 44-BOND ENERGY FUNCTIONS · E_inter(k, k+1)

This relation defines E_inter(k, k+1) in the source section “IX. 44-BOND ENERGY FUNCTIONS · E_inter(k, k+1)”. Evaluates oscillatory sine or cosine terms using the stated phase or…

220

IX. 44-BOND ENERGY FUNCTIONS · E_cross(i,j)

This relation defines E_cross(i,j) in the source section “IX. 44-BOND ENERGY FUNCTIONS · E_cross(i,j)”. It specifies the displayed relationship between the named quantities or…

221

IX. 44-BOND ENERGY FUNCTIONS · E_10.6

This relation defines E_10.6 in the source section “IX. 44-BOND ENERGY FUNCTIONS · E_10.6”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

222

IX. 44-BOND ENERGY FUNCTIONS · E_total

This relation defines E_total in the source section “IX. 44-BOND ENERGY FUNCTIONS · E_total”. It specifies the displayed relationship between the named quantities or parameters.…

223

X. THERMODYNAMICS · Partition function: Z

This relation defines Partition function: Z in the source section “X. THERMODYNAMICS · Partition function: Z”. Applies an exponential factor. The exponent determines its real…

224

X. THERMODYNAMICS · Per-bond free energy: ΔG_bond

This relation defines Per-bond free energy: ΔG_bond in the source section “X. THERMODYNAMICS · Per-bond free energy: ΔG_bond”. Uses logarithmic scaling; its base and the…

225

X. THERMODYNAMICS · ΔG°_total

This relation defines ΔG°_total in the source section “X. THERMODYNAMICS · ΔG°_total”. It specifies the displayed relationship between the named quantities or parameters. Its…

226

X. THERMODYNAMICS · T_m

This relation defines T_m in the source section “X. THERMODYNAMICS · T_m”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends…

227

XII. KINETIC RATE EQUATIONS · E_a^f(n)

This relation defines E_a^f(n) in the source section “XII. KINETIC RATE EQUATIONS · E_a^f(n)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

228

XII. KINETIC RATE EQUATIONS · E_a^b(n)

This relation defines E_a^b(n) in the source section “XII. KINETIC RATE EQUATIONS · E_a^b(n)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

229

XII. KINETIC RATE EQUATIONS · Base formation rate: k_f^(0)(n)

This relation defines Base formation rate: k_f^(0)(n) in the source section “XII. KINETIC RATE EQUATIONS · Base formation rate: k_f^(0)(n)”. Applies an exponential factor. The…

230

XII. KINETIC RATE EQUATIONS · Base breaking rate: k_b^(0)(n)

This relation defines Base breaking rate: k_b^(0)(n) in the source section “XII. KINETIC RATE EQUATIONS · Base breaking rate: k_b^(0)(n)”. Applies an exponential factor. The…

231

XII. KINETIC RATE EQUATIONS · k_f(n,t)

This relation defines k_f(n,t) in the source section “XII. KINETIC RATE EQUATIONS · k_f(n,t)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

232

XII. KINETIC RATE EQUATIONS · k_b(n,t)

This relation defines k_b(n,t) in the source section “XII. KINETIC RATE EQUATIONS · k_b(n,t)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

233

XII. KINETIC RATE EQUATIONS · k_f^coop(n,t)

This relation defines k_f^coop(n,t) in the source section “XII. KINETIC RATE EQUATIONS · k_f^coop(n,t)”. It specifies the displayed relationship between the named quantities or…

234

XII. KINETIC RATE EQUATIONS · k_b^coop(n,t)

This relation defines k_b^coop(n,t) in the source section “XII. KINETIC RATE EQUATIONS · k_b^coop(n,t)”. It specifies the displayed relationship between the named quantities or…

235

XII. KINETIC RATE EQUATIONS · Equilibrium occupation: b_n^eq

This relation defines Equilibrium occupation: b_n^eq in the source section “XII. KINETIC RATE EQUATIONS · Equilibrium occupation: b_n^eq”. It specifies the displayed relationship…

236

XII. KINETIC RATE EQUATIONS · τ_slow

This relation defines τ_slow in the source section “XII. KINETIC RATE EQUATIONS · τ_slow”. It specifies the displayed relationship between the named quantities or parameters. Its…

237

XII. KINETIC RATE EQUATIONS · τ_fast

This relation defines τ_fast in the source section “XII. KINETIC RATE EQUATIONS · τ_fast”. It specifies the displayed relationship between the named quantities or parameters. Its…

238

XII. KINETIC RATE EQUATIONS · db_n/dt

This relation defines db_n/dt in the source section “XII. KINETIC RATE EQUATIONS · db_n/dt”. It specifies the displayed relationship between the named quantities or parameters.…

239

XII. KINETIC RATE EQUATIONS · Update phase: dφ/dt

This relation defines Update phase: dφ/dt in the source section “XII. KINETIC RATE EQUATIONS · Update phase: dφ/dt”. It specifies the displayed relationship between the named…

240

XII. KINETIC RATE EQUATIONS

This relation defines B* ≈ 36.2 bonds at 300K in the source section “XII. KINETIC RATE EQUATIONS”. It specifies the displayed relationship between the named quantities or…

241

XII. KINETIC RATE EQUATIONS · θ*

This relation defines θ* in the source section “XII. KINETIC RATE EQUATIONS · θ*”. It specifies the displayed relationship between the named quantities or parameters. Its…

242

XVI. UNIFIED STATE EQUATIONS · Master state vector: Ψ_DNA(t)

This relation defines Master state vector: Ψ_DNA(t) in the source section “XVI. UNIFIED STATE EQUATIONS · Master state vector: Ψ_DNA(t)”. It specifies the displayed relationship…

243

XVI. UNIFIED STATE EQUATIONS · dΨ_DNA/dt

This relation defines dΨ_DNA/dt in the source section “XVI. UNIFIED STATE EQUATIONS · dΨ_DNA/dt”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency.…

244

XVI. UNIFIED STATE EQUATIONS · Conservation: Lk

This relation defines Conservation: Lk in the source section “XVI. UNIFIED STATE EQUATIONS · Conservation: Lk”. It specifies the displayed relationship between the named…

245

XVI. UNIFIED STATE EQUATIONS · Simplified: assume N

This relation defines Simplified: assume N in the source section “XVI. UNIFIED STATE EQUATIONS · Simplified: assume N”. It specifies the displayed relationship between the named…

246

XVI. UNIFIED STATE EQUATIONS

This relation defines Periodicity: Ψ(t + 10.6) ≈ Ψ(t) - quasi-periodic in the source section “XVI. UNIFIED STATE EQUATIONS”. It specifies the displayed relationship between the…

247

XVI. UNIFIED STATE EQUATIONS · Topological: Lk

This relation defines Topological: Lk in the source section “XVI. UNIFIED STATE EQUATIONS · Topological: Lk”. It specifies the displayed relationship between the named quantities…

248

XVI. UNIFIED STATE EQUATIONS · Energy: ∂E/∂r

This relation defines Energy: ∂E/∂r in the source section “XVI. UNIFIED STATE EQUATIONS · Energy: ∂E/∂r”. Uses a derivative or gradient to describe a rate of change or a direction…

249

XVI. UNIFIED STATE EQUATIONS · Bond count: Σ A_{ij}/2

This relation defines Bond count: Σ A_{ij}/2 in the source section “XVI. UNIFIED STATE EQUATIONS · Bond count: Σ A_{ij}/2”. It specifies the displayed relationship between the…

250

Intra-strand ring matrix with a varying diagonal

The matrix combines a nearest-neighbor ring Laplacian with a diagonal cosine modulation. The ring part is circulant, but the varying diagonal generally breaks that symmetry.…

251

Cosine modulation on the matrix diagonal

Each diagonal value is a cosine evaluated at a coordinate index divided by 10.6. The body uses indices i+1 from one through sixteen. Because those values vary by position, this…

252

Claimed intra-strand eigenvalue formula fails the constructed matrix

The first two terms are valid ring-Laplacian Fourier eigenvalues. Adding the position-varying diagonal cosine term does not in general produce eigenvalues of their sum.…

253

Claimed inter-strand eigenvalues versus a varying-weight ring

The code builds a symmetric ring with position-dependent edge weights and a modulated diagonal, then reports this independent trigonometric expression as its eigenvalues. Such a…

254

Cross-helix row-based spectral estimate

The displayed candidate is the first line of a multiline expression that adds a damped diagonal term and a sum of nearby couplings. Such a row sum is not generally an eigenvalue…

255

Cross-helix neighbor index window

The sum includes indices at distance at most three from m, excludes m itself, and clips the range at the ends of the array. It therefore includes fewer neighbors near a boundary…

256

Declared lower spectral summary

The function assigns this combination of coupling parameters directly to lambda_1. It does not extract the smallest eigenvalue of the constructed full 44-by-44 matrix in this…

257

Hard-coded zero mode

The spectral summary sets its middle value to zero unconditionally. No eigensolver or symmetry proof establishes an exact zero eigenvalue of the full constructed matrix. The name…

258

Declared upper spectral summary

The method assigns a linear combination of coupling parameters to lambda_44. This is separate from calculating the actual largest eigenvalue of the full matrix. The parameter…

259

Spectral-width arithmetic and its comment discrepancy

The body subtracts its assigned lower estimate from its assigned upper estimate. Their displayed definitions give an η coefficient of 2.618, whereas this comment prints 3.236η.…

260

Trace equals the sum of true eigenvalues

For any finite square matrix, the trace is the sum of its eigenvalues counted with algebraic multiplicity. The method correctly sums the stored diagonal. This identity supplies a…

261

I. FOUNDATIONAL CONSTANTS · Vertical offset per strand: δ_k

This relation defines Vertical offset per strand: δ_k in the source section “I. FOUNDATIONAL CONSTANTS · Vertical offset per strand: δ_k”. It specifies the displayed relationship…

262

I. FOUNDATIONAL CONSTANTS · Golden phase offset: θ_k

This relation defines Golden phase offset: θ_k in the source section “I. FOUNDATIONAL CONSTANTS · Golden phase offset: θ_k”. Uses a remainder or modular operation, retaining the…

263

I. FOUNDATIONAL CONSTANTS · κ

This relation defines κ in the source section “I. FOUNDATIONAL CONSTANTS · κ”. It specifies the displayed relationship between the named quantities or parameters. Its…

264

I. FOUNDATIONAL CONSTANTS · τ

This relation defines τ in the source section “I. FOUNDATIONAL CONSTANTS · τ”. It specifies the displayed relationship between the named quantities or parameters. Its…

265

I. FOUNDATIONAL CONSTANTS · θ_total

This relation defines θ_total in the source section “I. FOUNDATIONAL CONSTANTS · θ_total”. It specifies the displayed relationship between the named quantities or parameters. Its…

266

I. FOUNDATIONAL CONSTANTS · Turns per 16 strands

This relation defines Turns per 16 strands in the source section “I. FOUNDATIONAL CONSTANTS · Turns per 16 strands”. It specifies the displayed relationship between the named…

267

III. 44-BOND SYSTEM · Inter-strand bonds (17-32): B_inter(k, k+1 mod 16)

This relation defines Inter-strand bonds (17-32): B_inter(k, k+1 mod 16) in the source section “III. 44-BOND SYSTEM · Inter-strand bonds (17-32): B_inter(k, k+1 mod 16)”. Uses a…

268

III. 44-BOND SYSTEM · Verify bond count: Σ_{i,j} A_{ij}/2

This relation defines Verify bond count: Σ_{i,j} A_{ij}/2 in the source section “III. 44-BOND SYSTEM · Verify bond count: Σ_{i,j} A_{ij}/2”. It specifies the displayed…

269

III. 44-BOND SYSTEM · 10.6-adjusted bond arc length: s_bond

This relation defines 10.6-adjusted bond arc length: s_bond in the source section “III. 44-BOND SYSTEM · 10.6-adjusted bond arc length: s_bond”. It specifies the displayed…

270

III. 44-BOND SYSTEM · Vertical rise per bond: Δz_bond

This relation defines Vertical rise per bond: Δz_bond in the source section “III. 44-BOND SYSTEM · Vertical rise per bond: Δz_bond”. It specifies the displayed relationship…

271

III. 44-BOND SYSTEM · Adjacent bond length: L_adj

This relation defines Adjacent bond length: L_adj in the source section “III. 44-BOND SYSTEM · Adjacent bond length: L_adj”. Evaluates oscillatory sine or cosine terms using the…

272

IV. STRAND MATHEMATICS · Fibonacci-scaled strand: D_k

This relation defines Fibonacci-scaled strand: D_k in the source section “IV. STRAND MATHEMATICS · Fibonacci-scaled strand: D_k”. It specifies the displayed relationship between…

273

IV. STRAND MATHEMATICS · 16-strand helix sum: Helix₁₆

This relation defines 16-strand helix sum: Helix₁₆ in the source section “IV. STRAND MATHEMATICS · 16-strand helix sum: Helix₁₆”. Evaluates oscillatory sine or cosine terms using…

274

IV. STRAND MATHEMATICS · Bond formation: Bond_G16

This relation defines Bond formation: Bond_G16 in the source section “IV. STRAND MATHEMATICS · Bond formation: Bond_G16”. It specifies the displayed relationship between the named…

275

IV. STRAND MATHEMATICS · Crosslink function: Crosslink(i,j)

This relation defines Crosslink function: Crosslink(i,j) in the source section “IV. STRAND MATHEMATICS · Crosslink function: Crosslink(i,j)”. It specifies the displayed…

276

IV. STRAND MATHEMATICS · Complex strand representation: S_k

This relation defines Complex strand representation: S_k in the source section “IV. STRAND MATHEMATICS · Complex strand representation: S_k”. Applies an exponential factor. The…

277

IV. STRAND MATHEMATICS · Modular extraction: X_k

This relation defines Modular extraction: X_k in the source section “IV. STRAND MATHEMATICS · Modular extraction: X_k”. Uses a remainder or modular operation, retaining the…

278

IV. STRAND MATHEMATICS · Fusion integral: Fusion

This relation defines Fusion integral: Fusion in the source section “IV. STRAND MATHEMATICS · Fusion integral: Fusion”. It specifies the displayed relationship between the named…

279

IV. STRAND MATHEMATICS · Phase increment: Δφ

This relation defines Phase increment: Δφ in the source section “IV. STRAND MATHEMATICS · Phase increment: Δφ”. It specifies the displayed relationship between the named…

280

IV. STRAND MATHEMATICS · Full G¹⁶ transform: G¹⁶

This relation defines Full G¹⁶ transform: G¹⁶ in the source section “IV. STRAND MATHEMATICS · Full G¹⁶ transform: G¹⁶”. It specifies the displayed relationship between the named…

281

VI. 10.6 FIRING PATTERN · Phase calculation: phase(i,t)

This relation defines Phase calculation: phase(i,t) in the source section “VI. 10.6 FIRING PATTERN · Phase calculation: phase(i,t)”. Uses a remainder or modular operation,…

282

VI. 10.6 FIRING PATTERN · Offset distribution: offset_i

This relation defines Offset distribution: offset_i in the source section “VI. 10.6 FIRING PATTERN · Offset distribution: offset_i”. It specifies the displayed relationship…

283

VI. 10.6 FIRING PATTERN · Fire condition: fire(i,t)

This relation defines Fire condition: fire(i,t) in the source section “VI. 10.6 FIRING PATTERN · Fire condition: fire(i,t)”. It specifies the displayed relationship between the…

284

VI. 10.6 FIRING PATTERN · Synchronization period: T_sync

This relation defines Synchronization period: T_sync in the source section “VI. 10.6 FIRING PATTERN · Synchronization period: T_sync”. It specifies the displayed relationship…

285

VI. 10.6 FIRING PATTERN · Fundamental frequency: f₀

This relation defines Fundamental frequency: f₀ in the source section “VI. 10.6 FIRING PATTERN · Fundamental frequency: f₀”. It specifies the displayed relationship between the…

286

VI. 10.6 FIRING PATTERN · Harmonic: f_n

This relation defines Harmonic: f_n in the source section “VI. 10.6 FIRING PATTERN · Harmonic: f_n”. It specifies the displayed relationship between the named quantities or…

287

VI. 10.6 FIRING PATTERN · 44-bond resonance: f_44

This relation defines 44-bond resonance: f_44 in the source section “VI. 10.6 FIRING PATTERN · 44-bond resonance: f_44”. It specifies the displayed relationship between the named…

288

VII. GOLDEN BASIS FUNCTIONS · Basis function: ψ_k(x)

This relation defines Basis function: ψ_k(x) in the source section “VII. GOLDEN BASIS FUNCTIONS · Basis function: ψ_k(x)”. Evaluates oscillatory sine or cosine terms using the…

289

VII. GOLDEN BASIS FUNCTIONS · Global coherence: Φ_total

This relation defines Global coherence: Φ_total in the source section “VII. GOLDEN BASIS FUNCTIONS · Global coherence: Φ_total”. It specifies the displayed relationship between…

290

VII. GOLDEN BASIS FUNCTIONS · where Φ_i

This relation defines where Φ_i in the source section “VII. GOLDEN BASIS FUNCTIONS · where Φ_i”. It specifies the displayed relationship between the named quantities or…

291

VII. GOLDEN BASIS FUNCTIONS · Ring diffusion: dS_i/dt

This relation defines Ring diffusion: dS_i/dt in the source section “VII. GOLDEN BASIS FUNCTIONS · Ring diffusion: dS_i/dt”. It specifies the displayed relationship between the…

292

VIII. SUPERCOILING (10.6) · Linking number: Lk

This relation defines Linking number: Lk in the source section “VIII. SUPERCOILING (10.6) · Linking number: Lk”. It specifies the displayed relationship between the named…

293

VIII. SUPERCOILING (10.6) · Relaxed linking number: Lk₀

This relation defines Relaxed linking number: Lk₀ in the source section “VIII. SUPERCOILING (10.6) · Relaxed linking number: Lk₀”. It specifies the displayed relationship between…

294

VIII. SUPERCOILING (10.6) · Superhelical density: σ

This relation defines Superhelical density: σ in the source section “VIII. SUPERCOILING (10.6) · Superhelical density: σ”. It specifies the displayed relationship between the…

295

VIII. SUPERCOILING (10.6) · ΔG_sc

This relation defines ΔG_sc in the source section “VIII. SUPERCOILING (10.6) · ΔG_sc”. It specifies the displayed relationship between the named quantities or parameters. Its…

296

VIII. SUPERCOILING (10.6) · Initialize strand states: S_k(t=0)

This statement records a parameter or experimental setting for VIII. SUPERCOILING (10.6) · Initialize strand states: S_k(t=0). The value assigned to Initialize strand states:…

297

dna_unified · F_Yad(x)

This relation defines F_Yad(x) in the source section “dna_unified · F_Yad(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

298

dna_unified · F_Lashon(x)

This relation defines F_Lashon(x) in the source section “dna_unified · F_Lashon(x)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

299

dna_unified · F_Athena(x)

This relation defines F_Athena(x) in the source section “dna_unified · F_Athena(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

300

dna_unified · F_Apollo(x)

This relation defines F_Apollo(x) in the source section “dna_unified · F_Apollo(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

301

dna_unified · F_Hermes(x)

This relation defines F_Hermes(x) in the source section “dna_unified · F_Hermes(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

302

dna_unified · F_Hephaestus(x)

This relation defines F_Hephaestus(x) in the source section “dna_unified · F_Hephaestus(x)”. It specifies the displayed relationship between the named quantities or parameters.…

303

dna_unified · F_Prometheus(x)

This relation defines F_Prometheus(x) in the source section “dna_unified · F_Prometheus(x)”. It specifies the displayed relationship between the named quantities or parameters.…

304

dna_unified · F_Dionysus(x)

This relation defines F_Dionysus(x) in the source section “dna_unified · F_Dionysus(x)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Applies an…

305

dna_unified · F_Artemis(x)

This relation defines F_Artemis(x) in the source section “dna_unified · F_Artemis(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

306

dna_unified · F_Hera(x)

This relation defines F_Hera(x) in the source section “dna_unified · F_Hera(x)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its interpretation…

307

dna_unified · F_Poseidon(x)

This relation defines F_Poseidon(x) in the source section “dna_unified · F_Poseidon(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

308

dna_unified · F_Demeter(x)

This relation defines F_Demeter(x) in the source section “dna_unified · F_Demeter(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

309

dna_unified · F_Ares(x)

This relation defines F_Ares(x) in the source section “dna_unified · F_Ares(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

310

dna_unified · F_Aphrodite(x)

This relation defines F_Aphrodite(x) in the source section “dna_unified · F_Aphrodite(x)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

311

dna_unified · F_Hestia(x)

This relation defines F_Hestia(x) in the source section “dna_unified · F_Hestia(x)”. Applies an exponential factor. The exponent determines its real scaling or, for a complex…

312

dna_unified · F_Zeus(x)

This relation defines F_Zeus(x) in the source section “dna_unified · F_Zeus(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

313

XIV. COMPLETE THOUGHT INTEGRATION · Compute T

This relation defines T in the source section “XIV. COMPLETE THOUGHT INTEGRATION · Compute T”. Integrates contributions over the variable and bounds stated in the expression; the…

314

MindFarm - Manager for 10,000 mind kernels · 5,000 gates

This relation defines 5,000 gates in the source section “MindFarm - Manager for 10,000 mind kernels · 5,000 gates”. It specifies the displayed relationship between the named…

315

MindFarm - Manager for 10,000 mind kernels · 10,000 minds

This relation defines 10,000 minds in the source section “MindFarm - Manager for 10,000 mind kernels · 10,000 minds”. It specifies the displayed relationship between the named…

316

MindFarm - Manager for 10,000 mind kernels · 100,000,000

This relation defines 100,000,000 in the source section “MindFarm - Manager for 10,000 mind kernels · 100,000,000”. It specifies the displayed relationship between the named…

317

MindFarm - Manager for 10,000 mind kernels · 50,000,000,000

This relation defines 50,000,000,000 in the source section “MindFarm - Manager for 10,000 mind kernels · 50,000,000,000”. It specifies the displayed relationship between the named…

318

MindFarm - Manager for 10,000 mind kernels

This relation defines ∴ 10,000 minds ≈ 0.5 Game Boy in the source section “MindFarm - Manager for 10,000 mind kernels”. It specifies the displayed relationship between the named…

319

Fast exp using polynomial approximation · Reconstruct: exp(x)

This relation defines Reconstruct: exp(x) in the source section “Fast exp using polynomial approximation · Reconstruct: exp(x)”. Applies an exponential factor. The exponent…

320

Fast consciousness metric Φ = 1/(1 + |x - 1|) · @brief Fast consciousness metric Φ

This relation defines @brief Fast consciousness metric Φ in the source section “Fast consciousness metric Φ = 1/(1 + |x - 1|) · @brief Fast consciousness metric Φ”. It specifies…

321

Fast binary entropy H(p) = -p log p - (1-p) log(1-p) · @brief Fast binary entropy H(p)

This relation defines @brief Fast binary entropy H(p) in the source section “Fast binary entropy H(p) = -p log p - (1-p) log(1-p) · @brief Fast binary entropy H(p)”. Uses…

322

Gate5000 Core - 5000-bit binary substrate with analog activation · G1. Graph: G

This relation defines G1. Graph: G in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G1. Graph: G”. It specifies the displayed…

323

Gate5000 Core - 5000-bit binary substrate with analog activation

This relation defines G3. Connectivity: |N⁺(i)| ≥ 2, |N⁻(i)| ≥ 2 in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation”. It specifies the…

324

Gate5000 Core - 5000-bit binary substrate with analog activation · G4. Binary update: sᵢ(t+1)

This relation defines G4. Binary update: sᵢ(t+1) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G4. Binary update: sᵢ(t+1)”. It…

325

Gate5000 Core - 5000-bit binary substrate with analog activation · G5. Analog update: aᵢ(t+1)

This relation defines G5. Analog update: aᵢ(t+1) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G5. Analog update: aᵢ(t+1)”. It…

326

Gate5000 Core - 5000-bit binary substrate with analog activation · G6. Derivative: dᵢ(t+1)

This relation defines G6. Derivative: dᵢ(t+1) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G6. Derivative: dᵢ(t+1)”. It specifies…

327

Gate5000 Core - 5000-bit binary substrate with analog activation · G7. Vector memory: vᵢ(t+1)

This relation defines G7. Vector memory: vᵢ(t+1) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G7. Vector memory: vᵢ(t+1)”. It…

328

Gate5000 Core - 5000-bit binary substrate with analog activation · G8. Global state: S(t)

This relation defines G8. Global state: S(t) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G8. Global state: S(t)”. It specifies the…

329

Gate5000 Core - 5000-bit binary substrate with analog activation · G9. Stability: Ξ(t)

This relation defines G9. Stability: Ξ(t) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G9. Stability: Ξ(t)”. It specifies the…

330

Gate5000 Core - 5000-bit binary substrate with analog activation · G10. Coherence: C₅₀₀₀(t)

This relation defines G10. Coherence: C₅₀₀₀(t) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G10. Coherence: C₅₀₀₀(t)”. It specifies…

331

Gate5000 Core - 5000-bit binary substrate with analog activation · G11. Hash: H(t)

This relation defines G11. Hash: H(t) in the source section “Gate5000 Core - 5000-bit binary substrate with analog activation · G11. Hash: H(t)”. It specifies the displayed…

332

G4: Binary update rule - OPTIMIZED with integer arithmetic · sᵢ(t+1)

This relation defines sᵢ(t+1) in the source section “G4: Binary update rule - OPTIMIZED with integer arithmetic · sᵢ(t+1)”. It specifies the displayed relationship between the…

333

G5: Analog activation update (unchanged, already efficient) · aᵢ(t+1)

This relation defines aᵢ(t+1) in the source section “G5: Analog activation update (unchanged, already efficient) · aᵢ(t+1)”. It specifies the displayed relationship between the…

334

G6: Derivative tracking · dᵢ(t+1)

This relation defines dᵢ(t+1) in the source section “G6: Derivative tracking · dᵢ(t+1)”. It specifies the displayed relationship between the named quantities or parameters. Its…

335

G10: Compute coherence score · C₅₀₀₀(t)

This relation defines C₅₀₀₀(t) in the source section “G10: Compute coherence score · C₅₀₀₀(t)”. It specifies the displayed relationship between the named quantities or parameters.…

336

Compute consciousness metric Φ = 1/(1 + |x - 1|) · @brief Compute consciousness metric Φ

This relation defines @brief Compute consciousness metric Φ in the source section “Compute consciousness metric Φ = 1/(1 + |x - 1|) · @brief Compute consciousness metric Φ”. It…

337

Addition and its reverse-mode derivatives

The output is the sum of two inputs. Each input has local derivative one, so the backward pass adds the incoming output gradient to both input gradients. Accumulation is necessary…

338

Multiplication and the product-rule gradient

The local sensitivity to x is the current y value, and the sensitivity to y is the current x value. The backward pass multiplies each by the incoming gradient and accumulates the…

339

Division and quotient derivatives

For a nonzero denominator y, the sensitivities of x/y are 1/y and −x/y². The code directly uses these expressions and has no denominator regularization. A zero denominator…

340

Hyperbolic tangent derivative

The derivative of tanh(x) is 1−tanh²(x). It is largest at zero and approaches zero in the saturated tails. Reusing the forward output in the backward pass avoids an additional…

341

Sigmoid derivative

The logistic derivative is z(1−z), where z is the forward sigmoid output. Its maximum is one quarter at z=0.5, and it decreases toward zero in either saturated tail. The primitive…

342

ReLU derivative with a convention at zero

ReLU returns x when positive and zero otherwise. Away from zero its derivative is one on the positive side and zero on the negative side. At the nondifferentiable origin the…

343

Smooth approximation to the absolute-value score

Replacing |x−1| with √((x−1)²+T) removes its cusp when T>0. The resulting score has a zero derivative at x=1, but its maximum is 1/(1+√T), which is below one; with T=0.01 the…

344

Exponential and its derivative

The real exponential is its own derivative. The backward pass therefore multiplies the incoming gradient by the already computed output. Large positive inputs can overflow…

345

Shifted logarithm in the implemented primitive

The comment gives log(x) and derivative 1/x, but the body evaluates log(x+EPSILON) and derivative 1/(x+EPSILON). This positive shift changes both the value and the domain to…

346

Power with fixed exponent

The derivative with respect to x is p x^(p−1) when the real-valued power is defined and differentiable. The helper treats p as a constant and does not compute an exponent…

347

Lambda-weighted mixture of multi-step returns

For 0≤λ<1, the geometric weights (1−λ)λⁿ⁻¹ sum to one and mix returns with different lookahead lengths. Small λ emphasizes shorter returns; values near one emphasize longer…

348

ingestion · L(θ)

This relation defines L(θ) in the source section “ingestion · L(θ)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends…

349

ingestion · ∇L

This relation defines ∇L in the source section “ingestion · ∇L”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends…

350

ingestion · θ_{t+1}

This relation defines θ_{t+1} in the source section “ingestion · θ_{t+1}”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its…

351

ingestion · m_t

This relation defines m_t in the source section “ingestion · m_t”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation…

352

ingestion · v_t

This relation defines v_t in the source section “ingestion · v_t”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation…

353

ingestion · θ_{t+1}

This relation defines θ_{t+1} in the source section “ingestion · θ_{t+1}”. Takes a square root, requiring a nonnegative real radicand when interpreted over the reals. Its…

354

ingestion · Learning Rate: α_eff

This relation defines Learning Rate: α_eff in the source section “ingestion · Learning Rate: α_eff”. It specifies the displayed relationship between the named quantities or…

355

EMBEDDING MATRIX · Full matrix would be 65536 * 64 * 4

This relation defines Full matrix would be 65536 * 64 * 4 in the source section “EMBEDDING MATRIX · Full matrix would be 65536 * 64 * 4”. It specifies the displayed relationship…

356

EMBEDDING MATRIX · We use 8-bit quantization: 65536 * 64

This relation defines We use 8-bit quantization: 65536 * 64 in the source section “EMBEDDING MATRIX · We use 8-bit quantization: 65536 * 64”. It specifies the displayed…

357

KNOWLEDGE GRAPH NODE · ΔW

This relation defines ΔW in the source section “KNOWLEDGE GRAPH NODE · ΔW”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

358

Intelligence Primitives for Gate5000 Consciousness · MultiHead(Q,K,V)

This relation defines MultiHead(Q,K,V) in the source section “Intelligence Primitives for Gate5000 Consciousness · MultiHead(Q,K,V)”. It specifies the displayed relationship…

359

Intelligence Primitives for Gate5000 Consciousness · ε

This relation defines ε in the source section “Intelligence Primitives for Gate5000 Consciousness · ε”. It specifies the displayed relationship between the named quantities or…

360

Intelligence Primitives for Gate5000 Consciousness · F

This relation defines F in the source section “Intelligence Primitives for Gate5000 Consciousness · F”. It specifies the displayed relationship between the named quantities or…

361

Intelligence Primitives for Gate5000 Consciousness

This relation defines μ ← μ + κ·Σ^{-1}·ε in the source section “Intelligence Primitives for Gate5000 Consciousness”. It specifies the displayed relationship between the named…

362

Intelligence Primitives for Gate5000 Consciousness

This relation defines P(θ|D) ∝ P(D|θ)P(θ) in the source section “Intelligence Primitives for Gate5000 Consciousness”. It specifies the displayed relationship between the named…

363

Intelligence Primitives for Gate5000 Consciousness · q*(θ)

This relation defines q*(θ) in the source section “Intelligence Primitives for Gate5000 Consciousness · q*(θ)”. Chooses an argument minimizing the displayed objective over the…

364

Intelligence Primitives for Gate5000 Consciousness · m_{x→f}(x)

This relation defines m_{x→f}(x) in the source section “Intelligence Primitives for Gate5000 Consciousness · m_{x→f}(x)”. It specifies the displayed relationship between the named…

365

Intelligence Primitives for Gate5000 Consciousness · c_t

This relation defines c_t in the source section “Intelligence Primitives for Gate5000 Consciousness · c_t”. It specifies the displayed relationship between the named quantities or…

366

Intelligence Primitives for Gate5000 Consciousness · f_t

This relation defines f_t in the source section “Intelligence Primitives for Gate5000 Consciousness · f_t”. It specifies the displayed relationship between the named quantities or…

367

Intelligence Primitives for Gate5000 Consciousness · i_t

This relation defines i_t in the source section “Intelligence Primitives for Gate5000 Consciousness · i_t”. It specifies the displayed relationship between the named quantities or…

368

Self-attention: attend to single input · Apply softmax (single element

This relation defines Apply softmax (single element in the source section “Self-attention: attend to single input · Apply softmax (single element”. It specifies the displayed…

369

Update predictions given observations

This relation defines Belief update: μ ← μ + κ·π·ε in the source section “Update predictions given observations”. It specifies the displayed relationship between the named…

370

Update posterior given new evidence

This relation defines Posterior ∝ likelihood × prior in the source section “Update posterior given new evidence”. It specifies the displayed relationship between the named…

371

Reparameterization trick: sample = μ + σ * ε · @brief Reparameterization trick: sample

This relation defines @brief Reparameterization trick: sample in the source section “Reparameterization trick: sample = μ + σ * ε · @brief Reparameterization trick: sample”. It…

372

Forward step · Update hidden state: h

This relation defines Update hidden state: h in the source section “Forward step · Update hidden state: h”. It specifies the displayed relationship between the named quantities or…

373

MATHEMATICAL CONSTANTS · - Density matrix: rho

This relation defines - Density matrix: rho in the source section “MATHEMATICAL CONSTANTS · - Density matrix: rho”. It specifies the displayed relationship between the named…

374

MATHEMATICAL CONSTANTS · - von Neumann entropy: S

This relation defines - von Neumann entropy: S in the source section “MATHEMATICAL CONSTANTS · - von Neumann entropy: S”. Uses logarithmic scaling; its base and the positivity of…

375

MATHEMATICAL CONSTANTS · - Lindblad master equation: drho/dt

This relation defines - Lindblad master equation: drho/dt in the source section “MATHEMATICAL CONSTANTS · - Lindblad master equation: drho/dt”. It specifies the displayed…

376

MATHEMATICAL CONSTANTS · - Quantum fidelity: F

This relation defines - Quantum fidelity: F in the source section “MATHEMATICAL CONSTANTS · - Quantum fidelity: F”. It specifies the displayed relationship between the named…

377

MATHEMATICAL CONSTANTS · rho

This relation defines rho in the source section “MATHEMATICAL CONSTANTS · rho”. It specifies the displayed relationship between the named quantities or parameters. Its…

378

MATHEMATICAL CONSTANTS · drho/dt

This relation defines drho/dt in the source section “MATHEMATICAL CONSTANTS · drho/dt”. It specifies the displayed relationship between the named quantities or parameters. Its…

379

MATHEMATICAL CONSTANTS · Ensure Hermiticity and trace

This relation defines Ensure Hermiticity and trace in the source section “MATHEMATICAL CONSTANTS · Ensure Hermiticity and trace”. It specifies the displayed relationship between…

380

MATHEMATICAL CONSTANTS · Compute von Neumann entropy: S

This relation defines von Neumann entropy: S in the source section “MATHEMATICAL CONSTANTS · Compute von Neumann entropy: S”. Uses logarithmic scaling; its base and the positivity…

381

MATHEMATICAL CONSTANTS · F

This relation defines F in the source section “MATHEMATICAL CONSTANTS · F”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

382

MATHEMATICAL CONSTANTS · - DNA entropy: H_DNA

This relation defines - DNA entropy: H_DNA in the source section “MATHEMATICAL CONSTANTS · - DNA entropy: H_DNA”. Uses logarithmic scaling; its base and the positivity of its…

383

MATHEMATICAL CONSTANTS · - Replication dynamics: dN/dt

This relation defines - Replication dynamics: dN/dt in the source section “MATHEMATICAL CONSTANTS · - Replication dynamics: dN/dt”. It specifies the displayed relationship between…

384

MATHEMATICAL CONSTANTS · - Michaelis-Menten kinetics: v

This relation defines - Michaelis-Menten kinetics: v in the source section “MATHEMATICAL CONSTANTS · - Michaelis-Menten kinetics: v”. It specifies the displayed relationship…

385

MATHEMATICAL CONSTANTS · - Hill equation: theta

This relation defines - Hill equation: theta in the source section “MATHEMATICAL CONSTANTS · - Hill equation: theta”. It specifies the displayed relationship between the named…

386

MATHEMATICAL CONSTANTS · - Mutation probability: P_mut

This relation defines - Mutation probability: P_mut in the source section “MATHEMATICAL CONSTANTS · - Mutation probability: P_mut”. Applies an exponential factor. The exponent…

387

MATHEMATICAL CONSTANTS · dN/dt

This relation defines dN/dt in the source section “MATHEMATICAL CONSTANTS · dN/dt”. It specifies the displayed relationship between the named quantities or parameters. Its…

388

MATHEMATICAL CONSTANTS · theta

This relation defines theta in the source section “MATHEMATICAL CONSTANTS · theta”. It specifies the displayed relationship between the named quantities or parameters. Its…

389

MATHEMATICAL CONSTANTS · v

This relation defines v in the source section “MATHEMATICAL CONSTANTS · v”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

390

MATHEMATICAL CONSTANTS · Compute DNA entropy: H

This relation defines DNA entropy: H in the source section “MATHEMATICAL CONSTANTS · Compute DNA entropy: H”. Uses logarithmic scaling; its base and the positivity of its argument…

391

MATHEMATICAL CONSTANTS · dG

This relation defines dG in the source section “MATHEMATICAL CONSTANTS · dG”. It specifies the displayed relationship between the named quantities or parameters. Its…

392

MATHEMATICAL CONSTANTS · - Kuramoto order parameter: Z

This relation defines - Kuramoto order parameter: Z in the source section “MATHEMATICAL CONSTANTS · - Kuramoto order parameter: Z”. Applies an exponential factor. The exponent…

393

MATHEMATICAL CONSTANTS · - Kuramoto phase dynamics: d(phi_i)/dt

This relation defines - Kuramoto phase dynamics: d(phi_i)/dt in the source section “MATHEMATICAL CONSTANTS · - Kuramoto phase dynamics: d(phi_i)/dt”. Evaluates oscillatory sine or…

394

MATHEMATICAL CONSTANTS · - Wilson-Cowan: du/dt

This relation defines - Wilson-Cowan: du/dt in the source section “MATHEMATICAL CONSTANTS · - Wilson-Cowan: du/dt”. It specifies the displayed relationship between the named…

395

MATHEMATICAL CONSTANTS · - Phase-locking value: PLV

This relation defines - Phase-locking value: PLV in the source section “MATHEMATICAL CONSTANTS · - Phase-locking value: PLV”. Applies an exponential factor. The exponent…

396

MATHEMATICAL CONSTANTS · d(phi_i)/dt

This relation defines d(phi_i)/dt in the source section “MATHEMATICAL CONSTANTS · d(phi_i)/dt”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its…

397

MATHEMATICAL CONSTANTS · Z

This relation defines Z in the source section “MATHEMATICAL CONSTANTS · Z”. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its…

398

MATHEMATICAL CONSTANTS · |Z|

This relation defines |Z| in the source section “MATHEMATICAL CONSTANTS · |Z|”. It specifies the displayed relationship between the named quantities or parameters. Its…

399

WILSON-COWAN POPULATION DYNAMICS · dE/dt

This relation defines dE/dt in the source section “WILSON-COWAN POPULATION DYNAMICS · dE/dt”. It specifies the displayed relationship between the named quantities or parameters.…

400

WILSON-COWAN POPULATION DYNAMICS · dI/dt

This relation defines dI/dt in the source section “WILSON-COWAN POPULATION DYNAMICS · dI/dt”. It specifies the displayed relationship between the named quantities or parameters.…

401

WILSON-COWAN POPULATION DYNAMICS · where S(x)

This relation defines where S(x) in the source section “WILSON-COWAN POPULATION DYNAMICS · where S(x)”. Applies an exponential factor. The exponent determines its real scaling or,…

402

Machine Learning Module for Gate5000 Consciousness · CLASSIC HEBBIAN: Δw_ij

This relation defines CLASSIC HEBBIAN: Δw_ij in the source section “Machine Learning Module for Gate5000 Consciousness · CLASSIC HEBBIAN: Δw_ij”. It specifies the displayed…

403

Machine Learning Module for Gate5000 Consciousness · NORMALIZED: Δw_ij

This relation defines NORMALIZED: Δw_ij in the source section “Machine Learning Module for Gate5000 Consciousness · NORMALIZED: Δw_ij”. It specifies the displayed…

404

Machine Learning Module for Gate5000 Consciousness · BCM: Δw_ij

This relation defines BCM: Δw_ij in the source section “Machine Learning Module for Gate5000 Consciousness · BCM: Δw_ij”. It specifies the displayed…

405

Machine Learning Module for Gate5000 Consciousness · OJA'S RULE: Δw_ij

This relation defines OJA'S RULE: Δw_ij in the source section “Machine Learning Module for Gate5000 Consciousness · OJA'S RULE: Δw_ij”. It specifies the displayed…

406

Machine Learning Module for Gate5000 Consciousness · SGD: w

This relation defines SGD: w in the source section “Machine Learning Module for Gate5000 Consciousness · SGD: w”. Uses a derivative or gradient to describe a rate of…

407

Machine Learning Module for Gate5000 Consciousness · MOMENTUM: v

This relation defines MOMENTUM: v in the source section “Machine Learning Module for Gate5000 Consciousness · MOMENTUM: v”. Uses a derivative or gradient to describe a rate of…

408

Machine Learning Module for Gate5000 Consciousness · ADAM: m

This relation defines ADAM: m in the source section “Machine Learning Module for Gate5000 Consciousness · ADAM: m”. Takes a square root, requiring a nonnegative real…

409

Machine Learning Module for Gate5000 Consciousness · CHAIN RULE: δ_j

This relation defines CHAIN RULE: δ_j in the source section “Machine Learning Module for Gate5000 Consciousness · CHAIN RULE: δ_j”. It specifies the displayed relationship…

410

Machine Learning Module for Gate5000 Consciousness · WEIGHT UPDATE: Δw_ij

This relation defines WEIGHT UPDATE: Δw_ij in the source section “Machine Learning Module for Gate5000 Consciousness · WEIGHT UPDATE: Δw_ij”. It specifies the displayed…

411

Classic Hebbian: Δw = η·x_i·x_j · @brief Classic Hebbian: Δw

This relation defines @brief Classic Hebbian: Δw in the source section “Classic Hebbian: Δw = η·x_i·x_j · @brief Classic Hebbian: Δw”. It specifies the displayed relationship…

412

Normalized Hebbian: Δw = η·(x_i·x_j - α·w·x_j²) · @brief Normalized Hebbian: Δw

This relation defines @brief Normalized Hebbian: Δw in the source section “Normalized Hebbian: Δw = η·(x_i·x_j - α·w·x_j²) · @brief Normalized Hebbian: Δw”. It specifies the…

413

BCM Learning: Δw = η·x_i·x_j·(x_j - θ) · @brief BCM Learning: Δw

This relation defines @brief BCM Learning: Δw in the source section “BCM Learning: Δw = η·x_i·x_j·(x_j - θ) · @brief BCM Learning: Δw”. It specifies the displayed relationship…

414

Update BCM threshold: θ = <x²> (sliding average) · @brief Update BCM threshold: θ

This relation defines @brief Update BCM threshold: θ in the source section “Update BCM threshold: θ = <x²> (sliding average) · @brief Update BCM threshold: θ”. It specifies the…

415

Oja's Rule: Δw = η·y·(x - y·w) · @brief Oja's Rule: Δw

This relation defines @brief Oja's Rule: Δw in the source section “Oja's Rule: Δw = η·y·(x - y·w) · @brief Oja's Rule: Δw”. It specifies the displayed relationship between the…

416

Anti-Hebbian: Δw = -η·x_i·x_j · @brief Anti-Hebbian: Δw

This relation defines @brief Anti-Hebbian: Δw in the source section “Anti-Hebbian: Δw = -η·x_i·x_j · @brief Anti-Hebbian: Δw”. It specifies the displayed relationship between the…

417

Compute output delta: δ = (y - target) · f'(net) · @brief Compute output delta: δ

This relation defines @brief Compute output delta: δ in the source section “Compute output delta: δ = (y - target) · f'(net) · @brief Compute output delta: δ”. It specifies the…

418

Propagate delta backward: δ_j = Σ(δ_k · w_jk) · f'(net_j) · @brief Propagate delta backward: δ_j

This relation defines @brief Propagate delta backward: δ_j in the source section “Propagate delta backward: δ_j = Σ(δ_k · w_jk) · f'(net_j) · @brief Propagate delta backward:…

419

Compute weight gradient: ∂L/∂w_ij = δ_j · x_i · @brief Compute weight gradient: ∂L/∂w_ij

This relation defines @brief Compute weight gradient: ∂L/∂w_ij in the source section “Compute weight gradient: ∂L/∂w_ij = δ_j · x_i · @brief Compute weight gradient: ∂L/∂w_ij”.…

420

Three-factor learning: Δw = η·x_pre·x_post·R · @brief Three-factor learning: Δw

This relation defines @brief Three-factor learning: Δw in the source section “Three-factor learning: Δw = η·x_pre·x_post·R · @brief Three-factor learning: Δw”. It specifies the…

421

Eligibility trace update: e(t+1) = λ·e(t) + x_pre·x_post · @brief Eligibility trace update: e(t+1)

This relation defines @brief Eligibility trace update: e(t+1) in the source section “Eligibility trace update: e(t+1) = λ·e(t) + x_pre·x_post · @brief Eligibility trace update:…

422

TD error: δ = r + γV(s') - V(s) · @brief TD error: δ

This relation defines @brief TD error: δ in the source section “TD error: δ = r + γV(s') - V(s) · @brief TD error: δ”. It specifies the displayed relationship between the named…

423

Policy gradient: ∇J ≈ Σ(∇log π(a|s)·R)

This relation defines @brief Policy gradient: ∇J ≈ Σ(∇log π(a|s)·R) in the source section “Policy gradient: ∇J ≈ Σ(∇log π(a|s)·R)”. Uses a derivative or gradient to describe a…

424

learning_math · dΦ/dt

This relation defines dΦ/dt in the source section “learning_math · dΦ/dt”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its…

425

CONSCIOUSNESS DYNAMICS · dΦ/dt

This relation defines dΦ/dt in the source section “CONSCIOUSNESS DYNAMICS · dΦ/dt”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its…

426

learning_math

This relation defines Where: α in the source section “learning_math”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

427

learning_math · ds²

This relation defines ds² in the source section “learning_math · ds²”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

428

learning_math · gᵢⱼ

This relation defines gᵢⱼ in the source section “learning_math · gᵢⱼ”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation…

429

FISHER INFORMATION METRIC · gᵢⱼ

This relation defines gᵢⱼ in the source section “FISHER INFORMATION METRIC · gᵢⱼ”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its…

430

learning_math · F

This relation defines F in the source section “learning_math · F”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends…

431

learning_math · ε

This relation defines ε in the source section “learning_math · ε”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends…

432

learning_math · μ_new

This relation defines μ_new in the source section “learning_math · μ_new”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

433

FISHER INFORMATION METRIC · ds²

This relation defines ds² in the source section “FISHER INFORMATION METRIC · ds²”. It specifies the displayed relationship between the named quantities or parameters. Its…

434

FISHER INFORMATION METRIC · Natural gradient: ∇̃L

This relation defines Natural gradient: ∇̃L in the source section “FISHER INFORMATION METRIC · Natural gradient: ∇̃L”. Uses a derivative or gradient to describe a rate of change…

435

FREE ENERGY PRINCIPLE · F

This relation defines F in the source section “FREE ENERGY PRINCIPLE · F”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

436

FREE ENERGY PRINCIPLE · KL

This relation defines KL in the source section “FREE ENERGY PRINCIPLE · KL”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation…

437

FREE ENERGY PRINCIPLE · ∂KL/∂μ

This relation defines ∂KL/∂μ in the source section “FREE ENERGY PRINCIPLE · ∂KL/∂μ”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its…

438

HEBBIAN LEARNING · Hebbian update: ΔW

This relation defines Hebbian update: ΔW in the source section “HEBBIAN LEARNING · Hebbian update: ΔW”. It specifies the displayed relationship between the named quantities or…

439

HEBBIAN LEARNING · BCM rule: ΔW

This relation defines BCM rule: ΔW in the source section “HEBBIAN LEARNING · BCM rule: ΔW”. It specifies the displayed relationship between the named quantities or parameters. Its…

440

CONTRASTIVE LEARNING · L

This relation defines L in the source section “CONTRASTIVE LEARNING · L”. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its…

441

Advanced Mathematical Framework for Gate5000 Consciousness · ds²

This relation defines ds² in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · ds²”. It specifies the displayed relationship between the named…

442

Advanced Mathematical Framework for Gate5000 Consciousness · g_ij(θ)

This relation defines g_ij(θ) in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · g_ij(θ)”. Uses a derivative or gradient to describe a rate of…

443

Advanced Mathematical Framework for Gate5000 Consciousness · d²x^μ/dt² + Γ^μ_νρ (dx^ν/dt)(dx^ρ/dt)

This relation defines d²x^μ/dt² + Γ^μ_νρ (dx^ν/dt)(dx^ρ/dt) in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · d²x^μ/dt² + Γ^μ_νρ…

444

Advanced Mathematical Framework for Gate5000 Consciousness · ∂g_ij/∂t

This relation defines ∂g_ij/∂t in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · ∂g_ij/∂t”. Uses a derivative or gradient to describe a rate of…

445

Advanced Mathematical Framework for Gate5000 Consciousness · H(X)

This relation defines H(X) in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · H(X)”. It specifies the displayed relationship between the named…

446

Advanced Mathematical Framework for Gate5000 Consciousness · I(X;Y)

This relation defines I(X;Y) in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · I(X;Y)”. It specifies the displayed relationship between the named…

447

Advanced Mathematical Framework for Gate5000 Consciousness · D_KL(P||Q)

This relation defines D_KL(P||Q) in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · D_KL(P||Q)”. Uses logarithmic scaling; its base and the…

448

Advanced Mathematical Framework for Gate5000 Consciousness · Φ

This relation defines Φ in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · Φ”. It specifies the displayed relationship between the named…

449

Advanced Mathematical Framework for Gate5000 Consciousness · dX_t

This relation defines dX_t in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · dX_t”. It specifies the displayed relationship between the named…

450

Advanced Mathematical Framework for Gate5000 Consciousness · ∂p/∂t

This relation defines ∂p/∂t in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · ∂p/∂t”. Uses a derivative or gradient to describe a rate of change…

451

Advanced Mathematical Framework for Gate5000 Consciousness · dX_t

This relation defines dX_t in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · dX_t”. It specifies the displayed relationship between the named…

452

Advanced Mathematical Framework for Gate5000 Consciousness · W_p(μ,ν)

This relation defines W_p(μ,ν) in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · W_p(μ,ν)”. Integrates contributions over the variable and bounds…

453

Advanced Mathematical Framework for Gate5000 Consciousness · W_1(μ,ν)

This relation defines W_1(μ,ν) in the source section “Advanced Mathematical Framework for Gate5000 Consciousness · W_1(μ,ν)”. Integrates contributions over the variable and bounds…

454

Fisher Information Matrix element · g_ij

This relation defines g_ij in the source section “Fisher Information Matrix element · g_ij”. Uses a derivative or gradient to describe a rate of change or a direction of…

455

Christoffel symbol of the first kind · Γ_{ijk}

This relation defines Γ_{ijk} in the source section “Christoffel symbol of the first kind · Γ_{ijk}”. Uses a derivative or gradient to describe a rate of change or a direction of…

456

Geodesic acceleration · a^μ

This relation defines a^μ in the source section “Geodesic acceleration · a^μ”. It specifies the displayed relationship between the named quantities or parameters. Its…

457

Ricci scalar curvature (simplified 1D) · R

This relation defines R in the source section “Ricci scalar curvature (simplified 1D) · R”. It specifies the displayed relationship between the named quantities or parameters. Its…

458

Exponential map on manifold

This relation defines exp_p(v) ≈ p + v - ½Γ(v,v) in the source section “Exponential map on manifold”. It specifies the displayed relationship between the named quantities or…

459

Shannon entropy H(X) = -Σ p(x) log p(x) · @brief Shannon entropy H(X)

This relation defines @brief Shannon entropy H(X) in the source section “Shannon entropy H(X) = -Σ p(x) log p(x) · @brief Shannon entropy H(X)”. It specifies the displayed…

460

Binary entropy H(p) = -p log p - (1-p) log(1-p) · @brief Binary entropy H(p)

This relation defines @brief Binary entropy H(p) in the source section “Binary entropy H(p) = -p log p - (1-p) log(1-p) · @brief Binary entropy H(p)”. Uses logarithmic scaling;…

461

Cross entropy H(P,Q) = -Σ P(x) log Q(x) · @brief Cross entropy H(P,Q)

This relation defines @brief Cross entropy H(P,Q) in the source section “Cross entropy H(P,Q) = -Σ P(x) log Q(x) · @brief Cross entropy H(P,Q)”. It specifies the displayed…

462

KL Divergence D_KL(P||Q) = Σ P(x) log(P(x)/Q(x)) · @brief KL Divergence D_KL(P||Q)

This relation defines @brief KL Divergence D_KL(P||Q) in the source section “KL Divergence D_KL(P||Q) = Σ P(x) log(P(x)/Q(x)) · @brief KL Divergence D_KL(P||Q)”. Uses logarithmic…

463

Mutual information I(X;Y) = H(X) + H(Y) - H(X,Y) · @brief Mutual information I(X;Y)

This relation defines @brief Mutual information I(X;Y) in the source section “Mutual information I(X;Y) = H(X) + H(Y) - H(X,Y) · @brief Mutual information I(X;Y)”. It specifies…

464

Integrated Information Φ (simplified approximation) · Φ

This relation defines Φ in the source section “Integrated Information Φ (simplified approximation) · Φ”. It specifies the displayed relationship between the named quantities or…

465

Itô SDE step: dX = μdt + σdW · @brief Itô SDE step: dX

This relation defines @brief Itô SDE step: dX in the source section “Itô SDE step: dX = μdt + σdW · @brief Itô SDE step: dX”. It specifies the displayed relationship between the…

466

Ornstein-Uhlenbeck step: dX = θ(μ - X)dt + σdW · @brief Ornstein-Uhlenbeck step: dX

This relation defines @brief Ornstein-Uhlenbeck step: dX in the source section “Ornstein-Uhlenbeck step: dX = θ(μ - X)dt + σdW · @brief Ornstein-Uhlenbeck step: dX”. It specifies…

467

Langevin dynamics step: dX = -∇V(X)dt + √(2T)dW · @brief Langevin dynamics step: dX

This relation defines @brief Langevin dynamics step: dX in the source section “Langevin dynamics step: dX = -∇V(X)dt + √(2T)dW · @brief Langevin dynamics step: dX”. Uses a…

468

1D Wasserstein distance (Earth Mover's Distance) · W_1(μ,ν)

This relation defines W_1(μ,ν) in the source section “1D Wasserstein distance (Earth Mover's Distance) · W_1(μ,ν)”. Integrates contributions over the variable and bounds stated in…

469

Consciousness gradient: ∂Φ/∂x = (x-1)/((1+|x-1|)²) · sign(x-1) · @brief Consciousness gradient: ∂Φ/∂x

This relation defines @brief Consciousness gradient: ∂Φ/∂x in the source section “Consciousness gradient: ∂Φ/∂x = (x-1)/((1+|x-1|)²) · sign(x-1) · @brief Consciousness gradient:…

470

Lyapunov function gradient: ∂V/∂Ω = 2(Ω - Ω*) · @brief Lyapunov function gradient: ∂V/∂Ω

This relation defines @brief Lyapunov function gradient: ∂V/∂Ω in the source section “Lyapunov function gradient: ∂V/∂Ω = 2(Ω - Ω*) · @brief Lyapunov function gradient: ∂V/∂Ω”.…

471

Free energy gradient: ∂F/∂x = 2(x - μ) - T·∂S/∂x · @brief Free energy gradient: ∂F/∂x

This relation defines @brief Free energy gradient: ∂F/∂x in the source section “Free energy gradient: ∂F/∂x = 2(x - μ) - T·∂S/∂x · @brief Free energy gradient: ∂F/∂x”. Uses a…

472

Natural gradient (Fisher-Rao): ∇̃f = G^{-1}∇f · @brief Natural gradient (Fisher-Rao): ∇̃f

This relation defines @brief Natural gradient (Fisher-Rao): ∇̃f in the source section “Natural gradient (Fisher-Rao): ∇̃f = G^{-1}∇f · @brief Natural gradient (Fisher-Rao): ∇̃f”.…

473

Sigmoid with derivative: σ(x), σ'(x) = σ(x)(1-σ(x)) · @brief Sigmoid with derivative: σ(x), σ'(x)

This relation defines @brief Sigmoid with derivative: σ(x), σ'(x) in the source section “Sigmoid with derivative: σ(x), σ'(x) = σ(x)(1-σ(x)) · @brief Sigmoid with derivative:…

474

Tanh with derivative: tanh(x), tanh'(x) = 1 - tanh²(x) · @brief Tanh with derivative: tanh(x), tanh'(x)

This relation defines @brief Tanh with derivative: tanh(x), tanh'(x) in the source section “Tanh with derivative: tanh(x), tanh'(x) = 1 - tanh²(x) · @brief Tanh with derivative:…

475

Outer product: M = α·u⊗v + M · @brief Outer product: M

This relation defines @brief Outer product: M in the source section “Outer product: M = α·u⊗v + M · @brief Outer product: M”. It specifies the displayed relationship between the…

476

Nernst equilibrium potential for one ionic species

The logarithmic concentration ratio balances chemical concentration drive against electrical potential for an ion of charge number z. The helper uses a fixed temperature and…

477

Goldman–Hodgkin–Katz voltage expression

This expression combines sodium, potassium, and chloride concentrations weighted by their relative permeabilities. Chloride’s inside and outside positions are reversed because it…

478

Hodgkin–Huxley membrane-current balance

Membrane capacitance times voltage change equals external current minus sodium, potassium, and leak currents. The sodium and potassium conductances are modulated by gating…

479

Sodium activation opening rate

The rate α_m(V) controls the opening contribution α_m(1−m) in the m gate equation. Its apparent 0/0 at V=−40 mV has a finite limit of 1 per millisecond; the code explicitly…

480

Sodium activation closing rate

This exponential rate decreases as membrane voltage increases in the displayed voltage convention. It multiplies m in the gate’s closing term −β_m m. Together with α_m it…

481

Sodium inactivation recovery rate

The exponential α_h supplies the recovery contribution α_h(1−h). It decreases with increasing voltage in this convention. Its balance with β_h determines how much sodium-channel…

482

Sodium inactivation rate

The sigmoid-shaped β_h increases with voltage and multiplies the available fraction h in its loss term. It therefore promotes inactivation as voltage rises under this model’s…

483

Potassium activation opening rate

The rate α_n contributes α_n(1−n) to potassium-gate opening. The expression has a removable singularity at V=−55 mV, with limit 0.1 per millisecond. The implementation supplies…

484

Potassium activation closing rate

The exponential β_n decreases as voltage rises and multiplies n in the gate’s closing term. At a fixed voltage, α_n and β_n together yield equilibrium n=α_n/(α_n+β_n) and…

485

AMPA conductance current

The synaptic current equals maximum conductance times the gating state times the voltage difference from its reversal potential. Its sign is determined by V−E_AMPA under the…

486

Exponentially decaying synaptic trace with spike jumps

Between spikes, the trace decays with time constant τ_AMPA. Each ideal impulse increases it by one. The code implements those two operations separately: receive_spike adds one and…

487

NMDA conductance current with voltage-dependent block

This current uses the same conductance-times-driving-force structure as the AMPA expression, multiplied by B(V). The additional factor reduces current under magnesium block and…

488

Magnesium-block factor

For nonnegative magnesium concentration, the denominator is at least one and the factor lies between zero and one. Increasing voltage reduces the exponential term and increases…

489

Spike timing difference for plasticity

The sign convention subtracts presynaptic spike time from postsynaptic spike time. Positive values mean the postsynaptic spike follows the presynaptic one and enter the source’s…

490

Excitatory-population Wilson–Cowan equation

Excitatory activity decays toward zero while a sigmoid of its net recurrent and external input replenishes it. The factor 1−r_E E reduces the responsive fraction as activity…

491

Inhibitory-population Wilson–Cowan equation

The inhibitory population has its own decay, sigmoid response, refractory factor, and time constant. Excitatory input increases its drive and inhibitory self-coupling subtracts…

492

Thresholded population response sigmoid

The function maps net input into (0,1), crosses one half at input θ, and has central slope a/4 when a>0. It converts weighted network input into an activation fraction in the…

493

Neural-field dynamics and the implemented discrete average

The field loses activity through a decay term and gains input through a spatially weighted sum of firing responses plus external drive. The implementation samples integer…

494

Difference-of-Gaussians connectivity kernel

A narrow positive Gaussian models local excitation and a broader negative Gaussian models inhibition. The body places 2σ² in both exponential denominators, while the comment…

495

Kuramoto phase-coupling equation

Each oscillator advances at its natural frequency and is pulled by the sine of its phase differences with every oscillator. Dividing by N keeps the nominal coupling scale…

496

Phase-origin-invariant oscillator order parameter

The complex mean of unit phase vectors has magnitude r between zero and one and phase ψ. The implementation returns the magnitude, which reaches one when all phases align and is…

497

SIMD VECTOR OPERATIONS · phi(x)

This relation defines phi(x) in the source section “SIMD VECTOR OPERATIONS · phi(x)”. It specifies the displayed relationship between the named quantities or parameters. Its…

498

SIMD VECTOR OPERATIONS

This relation defines tanh(x) ≈ x * (27 + x^2) / (27 + 9*x^2) in the source section “SIMD VECTOR OPERATIONS”. It specifies the displayed relationship between the named quantities…

499

SIMD VECTOR OPERATIONS

This relation defines sigmoid(x) ≈ 0.5 + 0.5 * tanh(0.5 * x) in the source section “SIMD VECTOR OPERATIONS”. It specifies the displayed relationship between the named quantities…

500

SIMD VECTOR OPERATIONS · out

This relation defines out in the source section “SIMD VECTOR OPERATIONS · out”. It specifies the displayed relationship between the named quantities or parameters. Its…

501

SIMD-OPTIMIZED GATE5000 · a_i(t+1)

This relation defines a_i(t+1) in the source section “SIMD-OPTIMIZED GATE5000 · a_i(t+1)”. It specifies the displayed relationship between the named quantities or parameters. Its…

502

SELF-DEBUGGING SYSTEM · F(x)

This relation defines F(x) in the source section “SELF-DEBUGGING SYSTEM · F(x)”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its…

503

MATHEMATICAL VERIFIER · For assignment x := e: wp(x := e, Q)

This relation defines For assignment x : in the source section “MATHEMATICAL VERIFIER · For assignment x := e: wp(x := e, Q)”. It specifies the displayed relationship between the…

504

MATHEMATICAL VERIFIER · For sequence: wp(S1; S2, Q)

This relation defines For sequence: wp(S1; S2, Q) in the source section “MATHEMATICAL VERIFIER · For sequence: wp(S1; S2, Q)”. It specifies the displayed relationship between the…

505

simulation · Φ

This relation defines Φ in the source section “simulation · Φ”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

506

simulation · L(θ)

This relation defines L(θ) in the source section “simulation · L(θ)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

507

simulation · dΦ/dt

This relation defines dΦ/dt in the source section “simulation · dΦ/dt”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

508

func (kg *KnowledgeGraph) ComputeInformationGain(concept string, domain string) float64 · Information gain

This relation defines Information gain in the source section “func (kg *KnowledgeGraph) ComputeInformationGain(concept string, domain string) float64 · Information gain”. It…

509

Binary threshold update

A weighted sum of prior binary states is compared with a threshold through a step function H. The result is a binary next state. The exact convention at equality and the direction…

510

Analog tanh state update

The next analog activation is tanh of a scaled weighted sum plus bias. It lies in (−1,1) for finite real inputs. The recurrent dynamics depend on weight scale and update timing,…

511

Reciprocal squared-discrepancy score

The denominator adds one to a sum of squared discrepancies across the selected sites. The score is one when every discrepancy is zero and decreases as their total squared…

512

Eighty-thousand-site design count

Multiplying sixteen families by five thousand sites per family gives eighty thousand sites. This version’s allocation differs from an architecture with five thousand gates total…

513

C++ unity-proximity score

ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target.…

514

Gaussian similarity kernel

The kernel is one for identical inputs and decreases with their squared distance. The positive bandwidth σ sets the scale: a distance σ gives exp(−1/2). It is a similarity…

515

Binary Shannon entropy

The two terms are the uncertainty of a Bernoulli outcome with probabilities p and 1−p. With natural logarithms it is measured in nats, is zero at the deterministic endpoints by…

516

Layer one to two: capped sigmoid increment

The source expression adds dx times a sigmoid of the current scalar’s weighted value. The body additionally caps the increment magnitude at 0.2 and clips the final value to the…

517

Layer two to three: product of two differently centered scores

The distance d=|x′−x_c| enters both a unity score Φ(d) and a Gaussian centered at d=0. The Gaussian favors exact agreement, but Φ(d) favors distance one; at exact agreement…

518

Layer three to four: complex rotating signal

The magnitude is tanh(αC) and the phase advances as ωt. Under the intended nonnegative C, the magnitude is nonnegative and bounded below one. Keeping the complex value retains…

519

Layer four to five: magnitude response with phase modulation

The body takes sigmoid(w|S|) and multiplies it by 1+0.2sin(arg S). The phase multiplier ranges from 0.8 to 1.2, so the output can exceed one. The source’s phase_alignment…

520

Layer five to six: logistic scalar, not a one-element softmax

The body returns exp(z)/(1+exp(z)) with z=wP+b, which is a logistic sigmoid. A softmax over a single scalar would always return one; a two-logit softmax over [z,0] would reproduce…

521

Layer six to seven: leaky accumulator with direct decision input

The body forms increment=Dexp(−F)dt, then returns clamp(0.9Ψ_prev+0.1increment+0.5D). The displayed integral contributes one part of this update, but the decay and extra direct…

522

Final layer score with a cubic post-transform

The helper first forms r=ΦΨC/(1+F), then returns a clipped cubic r²(3−2r). The cubic is smoothstep and is monotone from zero to one only on r∈[0,1]. The ratio requires F≠−1, and…

523

Candidate Lyapunov-like objective

The function adds squared deviation from a target Ω*, a weighted squared coherence shortfall, and a linear free-energy term. Nonnegativity requires suitable coefficients and F≥0.…

524

Finite-difference change in the stability objective

The difference of consecutive V values divided by dt estimates its average rate over one discrete interval. It is not an exact continuous derivative unless an appropriate limiting…

525

Gradient-flow comment and modified dynamics

For fixed coherence and free energy, the Ω derivative of the displayed objective is 2(Ω−Ω*). The body multiplies its negative by a rate and Ω(1−Ω), then adds further coherence and…

526

Weighted final score combining base and gate contribution

The result combines 85% of the base output with 15% of the G5K contribution. The weights sum to one, so it is a convex combination when both inputs share a common scalar range.…

527

Hephaestus signature: quartic integral value

The function returns x⁴/8. This equals the triangular-domain integral ∫₀ˣ∫₀ᵘ uv dv du; a rectangular-domain integral of uv over [0,x]² would instead be x⁴/4. The comment’s reused…

528

Variational free-energy identity and the posterior it requires

The expectation of log q(z)−log p(x,z) equals KL(q(z)||p(z|x))−log p(x). The p in the abbreviated divergence must therefore mean the posterior, not simply the prior. The body’s…

Sources & provenance

Janady13/complete-agi-core / README.md

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Purpose & architecture

This source generation

Recovered implementation structure

Behavior & verification limits

Original project documentation