Purpose & architecture
This branch implements a Go framework whose registry allocates one hundred generator IDs across ten families: autoregressive, diffusion, adversarial, variational, flow, energy, transformer, recurrent, state-space and mixture. It adds attention, DNA dynamics, consciousness-named metrics, orchestration and RPC. Registry slots and named implementations are preserved individually; they are not evidence of one hundred trained, evaluated models.
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 · Go Generator Core |
Recovered implementation structure
These paths locate the components and entry points represented by this build. The source register contains their inspected revisions.
- 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
Behavior & verification limits
Source-defined parameters and outputs require independent numerical and runtime validation.
Equations in this build
154 linked mathematical records. Each opens its notation, interpretation and source.
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…
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…
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 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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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”.…
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”.…
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…
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…
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…
LinearLayer
This relation defines LinearLayer computes y in the source section “LinearLayer”. It specifies the displayed relationship between the named quantities or parameters. Its…
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…
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:…
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…
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…
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…
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…
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) ·…
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…
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…
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…
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…
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…
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…