Purpose & architecture
The recovered branch adds a distinct C++ system with Gate5000, neurological equations, DNA dynamics, eigenvalue operations, learning mathematics, attention, knowledge ingestion, persistence and a unified tick loop. Its headers expose the component-level formulas and the intended interaction of substrate, neural, learning and consciousness loops. Static review identifies mathematical and implementation limitations alongside the preserved formulas.
This subsystem keeps its own source prefix, equations and generation identity. Shared terminology with other builds is cross-referenced without assuming matching state formats or numerical behavior.
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 | Alternate math branch · C++ Mind Farm |
Recovered implementation structure
These paths locate the components and entry points represented by this build. The source register contains their inspected revisions.
- 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
Behavior & verification limits
Source-defined parameters and outputs require independent numerical and runtime validation.
Equations in this build
355 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…
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…
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…
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.
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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.
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.…
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…
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…
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…
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…
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++…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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”.…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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.…
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…
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.…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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:…
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…
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…
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…
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…
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…
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.…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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.…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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:…
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”.…
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…
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:…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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;…
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…
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…
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…
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…
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…
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…
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…
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…
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:…
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”.…
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…
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”.…
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:…
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:…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…