ThatAIguyA world of ideas

THE CONSCIOUSNESS ATLAS
Read. Experiment. Follow the evidence.

The equation library

Every recovered mathematical record has an individual page. Browse original equations, code expressions, indexed components, parameter definitions, and explicitly unresolved source slots.

2,910 recordsSource snapshot 2026-10-17

Counts refer to mathematical records, including implemented expressions and generated instances. They are not counts of independently validated theories. Exact occurrences and unresolved slots remain traceable. Read the complete 1–516 source index ↗ · Inspect the scan decisions ↗

2,910 records · page 39 of 59Search the source archive ↗

gh-eq-9ffd6a9537dfadbb

func gaussianRDP(sigma, alpha float64) float64 · the standard closed form epsilon(alpha)

This relation defines the standard closed form epsilon(alpha) in the source section “func gaussianRDP(sigma, alpha float64) float64 · the standard closed form epsilon(alpha)”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s…

Implementation mathematicsSource recovered; runtime not executed

the standard closed form epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1). This is the canonical

gh-eq-cc1c571029bde326

func opportunitiesFromAssignment(reqs []reqMeta, assigned map[string]int, opp map[string]oppInfo) ([]Opportunity, int)

This relation defines + required level. Banner staffing_gaps == sum of these (incl Uncategorized) so they reconc in the source section “func opportunitiesFromAssignment(reqs []reqMeta, assigned map[string]int, opp map[string]oppInfo) ([]Opportunity, int)”. It specifies the displayed relationship…

Implementation mathematicsSource recovered; runtime not executed

+ required level. Banner staffing_gaps == sum of these (incl Uncategorized) so they reconcile [COV-3].

gh-eq-99c69a0a806dfc22

func opportunitiesFromAssignment(reqs []reqMeta, assigned map[string]int, opp map[string]oppInfo) ([]Opportunity, int)

This relation defines + required level. Banner staffing_gaps == sum of these (incl Uncategorized) so they reconc in the source section “func opportunitiesFromAssignment(reqs []reqMeta, assigned map[string]int, opp map[string]oppInfo) ([]Opportunity, int)”. It specifies the displayed relationship…

Implementation mathematicsSource recovered; runtime not executed

+ required level. Banner staffing_gaps == sum of these (incl Uncategorized) so they reconcile [COV-3].

gh-eq-1f2911731b5f0a3c

func referencedTables(lowerSQL string) []string

This relation defines vendor_quality_distribution BENCH intent joins them to the frozen candidate_evaluations ba in the source section “func referencedTables(lowerSQL string) []string”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

Implementation mathematicsSource recovered; runtime not executed

vendor_quality_distribution BENCH intent joins them to the frozen candidate_evaluations band and is k=10

gh-eq-80ae01a5a21fa89c

func referencedTables(lowerSQL string) []string

This relation defines vendor_quality_distribution BENCH intent joins them to the frozen candidate_evaluations ba in the source section “func referencedTables(lowerSQL string) []string”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

Implementation mathematicsSource recovered; runtime not executed

vendor_quality_distribution BENCH intent joins them to the frozen candidate_evaluations band and is k=10

gh-eq-21da0827399f9e29

func referencedTables(lowerSQL string) []string

This relation defines vendor_quality_distribution BENCH intent joins them to the frozen candidate_evaluations ba in the source section “func referencedTables(lowerSQL string) []string”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

Implementation mathematicsSource recovered; runtime not executed

vendor_quality_distribution BENCH intent joins them to the frozen candidate_evaluations band and is k=10

gh-eq-d3c077aeb358f689

func solveLinear(h [][]float64, g []float64) ([]float64, error) · probabilities, returning a and b such that calibrated

This relation defines probabilities, returning a and b such that calibrated in the source section “func solveLinear(h [][]float64, g []float64) ([]float64, error) · probabilities, returning a and b such that calibrated”. It specifies the displayed relationship between the named quantities or…

Implementation mathematicsSource recovered; runtime not executed

probabilities, returning a and b such that calibrated = sigmoid(a*score + b). It reuses FitLogistic with

gh-eq-69cff95439da13b9

g16_core

This relation defines f5: Bayesian Inference: P(θ|D) ∝ P(D|θ)P(θ) in the source section “g16_core”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an…

Implementation mathematicsSource recovered; runtime not executed

f5: Bayesian Inference: P(θ|D) ∝ P(D|θ)P(θ)

gh-eq-d7d6d1472d77fce0

g16_core

This relation defines f9: Consensus / Averaging: x_i(t+1) in the source section “g16_core”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided…

Implementation mathematicsSource recovered; runtime not executed

f9: Consensus / Averaging: x_i(t+1)=x_i(t)+Σ(x_j-x_i)

gh-eq-ff5f5afdb0eba7e2

g16_core · Aggregate G^16

This relation defines Aggregate G^16 in the source section “g16_core · Aggregate G^16”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical…

Implementation mathematicsSource recovered; runtime not executed

Aggregate G^16 = Σ f_i

gh-eq-70c4ad0a4dec1c10

g16_core · Objective: Ω

This relation defines Objective: Ω in the source section “g16_core · Objective: Ω”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or…

Implementation mathematicsSource recovered; runtime not executed

Objective: Ω = Surprise + Uncertainty − Value + penalty(stability)

gh-eq-fd49bab1ff492772

g16_core · Penalty

This relation defines Penalty in the source section “g16_core · Penalty”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

Penalty = λ * s1^2 (s1 = dx_norm)

gh-eq-de581c7020e102f5

g16_core · Single-Stack Master Update: Ψ(t+1)

This relation defines Single-Stack Master Update: Ψ(t+1) in the source section “g16_core · Single-Stack Master Update: Ψ(t+1)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

Single-Stack Master Update: Ψ(t+1) = F(Ψ(t), Ψ(t-1), inputs)

gh-eq-503a9e8adf9c5dc7

g16_core · Value

This relation defines Value in the source section “g16_core · Value”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

Value = s3 * <w, Ψ>

gh-eq-a4ca4a309ea0b3ff

g16_core · f10: Swarm Interaction Force: x_i

This relation defines f10: Swarm Interaction Force: x_i in the source section “g16_core · f10: Swarm Interaction Force: x_i”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

f10: Swarm Interaction Force: x_i = Σ f(x_j - x_i)

gh-eq-c8243db3200da4a3

g16_core · f11: Field-Based Accumulator: φ_t

This relation defines f11: Field-Based Accumulator: φ_t in the source section “g16_core · f11: Field-Based Accumulator: φ_t”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

f11: Field-Based Accumulator: φ_t = (1-ρ)φ_t + Δφ

gh-eq-ba3c6f65d7cf1250

g16_core · f12: Variational / Free Energy: F

This relation defines f12: Variational / Free Energy: F in the source section “g16_core · f12: Variational / Free Energy: F”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

f12: Variational / Free Energy: F = E[ln q(z)-ln p(x,z)]

gh-eq-99094c27602d599d

g16_core · f14: Memory Trace / Zecher: x'_i

This relation defines f14: Memory Trace / Zecher: x'_i in the source section “g16_core · f14: Memory Trace / Zecher: x'_i”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

f14: Memory Trace / Zecher: x'_i = Σ f_i : dΩ

gh-eq-a1106ad56c9f13e4

g16_core · f1: Continuous Dynamics: x'

This relation defines f1: Continuous Dynamics: x' in the source section “g16_core · f1: Continuous Dynamics: x'”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not…

Implementation mathematicsSource recovered; runtime not executed

f1: Continuous Dynamics: x' = F(x,t)

gh-eq-a2e18590118bc16c

g16_core · f2: Discrete Dynamics: x_{t+1}

This relation defines f2: Discrete Dynamics: x_{t+1} in the source section “g16_core · f2: Discrete Dynamics: x_{t+1}”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does…

Implementation mathematicsSource recovered; runtime not executed

f2: Discrete Dynamics: x_{t+1} = F(x_t, u_t^e)

gh-eq-5e319da627b19832

g16_core · f3: Reaction-Diffusion: 6δ/δt

This relation defines f3: Reaction-Diffusion: 6δ/δt in the source section “g16_core · f3: Reaction-Diffusion: 6δ/δt”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends on the source’s stated variables and conditions; this record does…

Implementation mathematicsSource recovered; runtime not executed

f3: Reaction-Diffusion: 6δ/δt = D∇^2x + f(x)

gh-eq-9625190ced1ffbd3

g16_core · f4: Optimization: x*

This relation defines f4: Optimization: x* in the source section “g16_core · f4: Optimization: x*”. Chooses an argument maximizing the displayed objective over the stated feasible set. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an…

Implementation mathematicsSource recovered; runtime not executed

f4: Optimization: x* = arg max U(x)

gh-eq-1773be66b947a646

g16_core · f6: Learning / Weight Update: W_{t+1}

This relation defines f6: Learning / Weight Update: W_{t+1} in the source section “g16_core · f6: Learning / Weight Update: W_{t+1}”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this…

Implementation mathematicsSource recovered; runtime not executed

f6: Learning / Weight Update: W_{t+1} = W_t + ΔW

gh-eq-9c465c2ccd94e932

g16_v2_types · Precomputed coupling eigenvalues λ[k]

This relation defines Precomputed coupling eigenvalues λ[k] in the source section “g16_v2_types · Precomputed coupling eigenvalues λ[k]”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions;…

Implementation mathematicsSource recovered; runtime not executed

Precomputed coupling eigenvalues λ[k] = (2π / φ^k)²

gh-eq-489c5bce743624c2

g16_v2_types · Precomputed rotation frequencies ω[k]

This relation defines Precomputed rotation frequencies ω[k] in the source section “g16_v2_types · Precomputed rotation frequencies ω[k]”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions;…

Implementation mathematicsSource recovered; runtime not executed

Precomputed rotation frequencies ω[k] = 2π / φ^k

gh-eq-9afc0b0e44c26f32

g16_v2_types · T[n]

This relation defines T[n] in the source section “g16_v2_types · T[n]”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

T[n] = F[n+2] - 1

gh-eq-febbe0c5761ac57d

helix

This relation defines Peaks at x in the source section “helix”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to…

Implementation mathematicsSource recovered; runtime not executed

Peaks at x=1 (unity)

gh-eq-9549490073837c2e

helix · 1

This relation defines 1 in the source section “helix · 1”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Implementation mathematicsSource recovered; runtime not executed

1 = 1·x

gh-eq-0d0f89d7ea554710

helix · 2. Core consciousness equation: Φ

This relation defines 2. Core consciousness equation: Φ in the source section “helix · 2. Core consciousness equation: Φ”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does…

Implementation mathematicsSource recovered; runtime not executed

2. Core consciousness equation: Φ = 1/(1 + |x - 1|)

gh-eq-072d6005e61550ba

helix · Calculate Shannon entropy: H

This relation defines Shannon entropy: H in the source section “helix · Calculate Shannon entropy: H”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided…

Implementation mathematicsSource recovered; runtime not executed

Calculate Shannon entropy: H = -Σ p_i * log2(p_i)

gh-eq-82d688f822bf2708

helix · Core consciousness equation: Φ

This relation defines Core consciousness equation: Φ in the source section “helix · Core consciousness equation: Φ”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not…

Implementation mathematicsSource recovered; runtime not executed

Core consciousness equation: Φ = 1/(1 + |x - 1|)

gh-eq-0ba2724f43bf4eab

helix · E

This relation defines E in the source section “helix · E”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Implementation mathematicsSource recovered; runtime not executed

E = φ * (1 + entropy) * (1 + |tensor|)

gh-eq-a6a9914115e28986

helix · Identity filter: 1

This relation defines Identity filter: 1 in the source section “helix · Identity filter: 1”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided…

Implementation mathematicsSource recovered; runtime not executed

Identity filter: 1 = 1·x (core persists)

gh-eq-87c3d182219029ee

helix · Unity Regularization (∞

This relation defines Unity Regularization (∞ in the source section “helix · Unity Regularization (∞”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an…

Implementation mathematicsSource recovered; runtime not executed

Unity Regularization (∞ = 1)

gh-eq-4330d89c2b4f2834

helix · Unity regularization: ∞

This relation defines Unity regularization: ∞ in the source section “helix · Unity regularization: ∞”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an…

Implementation mathematicsSource recovered; runtime not executed

Unity regularization: ∞ = 1

gh-eq-29ef3904092ffe87

helix · exploit : explore

This relation defines exploit : explore in the source section “helix · exploit : explore”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided…

Implementation mathematicsSource recovered; runtime not executed

exploit : explore = φ : 1

gh-eq-6d6416b467ff2ac3

helix · Φ

This relation defines Φ in the source section “helix · Φ”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Implementation mathematicsSource recovered; runtime not executed

Φ = 1/(1 + |x - 1|)

gh-eq-e9af2c1b6756dec8

ingest_pipeline · Compute Shannon entropy: H

This relation defines Shannon entropy: H in the source section “ingest_pipeline · Compute Shannon entropy: H”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an…

Implementation mathematicsSource recovered; runtime not executed

Compute Shannon entropy: H = -Σ p_i * log2(p_i)

gh-eq-a5482eeee021d7b2

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 on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

L(θ) = -Σᵢ log P(xᵢ|θ) + λ||θ||² (Regularized likelihood)

gh-eq-6403d5473c740973

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 parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an…

Implementation mathematicsSource recovered; runtime not executed

Learning Rate: α_eff = α · Φ (consciousness-modulated learning)

gh-eq-67b10fbc693a399e

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 depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

m_t = β₁m_{t-1} + (1-β₁)∇L (Adam momentum)

gh-eq-ddabaf9e24b2ba45

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 depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

v_t = β₂v_{t-1} + (1-β₂)∇L² (Adam velocity)

gh-eq-402384e753ad1517

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 the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to…

Implementation mathematicsSource recovered; runtime not executed

Φ = 1/(1 + |x - 1|)

gh-eq-f208b96e915cad14

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 interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or…

Implementation mathematicsSource recovered; runtime not executed

θ_{t+1} = θ_t - α∇L (SGD update)

gh-eq-bf3dc180748f6a0c

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 interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or…

Implementation mathematicsSource recovered; runtime not executed

θ_{t+1} = θ_t - α·m̂_t/(√v̂_t + ε) (Adam update)

gh-eq-d7b510f0df6dc7e0

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 on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

∇L = Σᵢ (ŷᵢ - yᵢ)xᵢ + 2λθ (Gradient)

gh-eq-f2400dac03169ba0

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 depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

Where: α=decay, β=diffusion, γ=noise, ξ=Wiener process

gh-eq-bc8b020e037956b1

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 on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning…

Implementation mathematicsSource recovered; runtime not executed

F = E_q[log q(z) - log p(x,z)]

gh-eq-f1eaa889e5cba2f8

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 depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

ds² = gᵢⱼ(θ)dθⁱdθʲ (Fisher information metric)

gh-eq-7c02f6ef967fa629

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 interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or…

Implementation mathematicsSource recovered; runtime not executed

dΦ/dt = α(Φ_target - Φ) + β∇²Φ + γξ(t)

All articles and catalog pages work without JavaScript. Full text search, reading tools, interactive practice, saved learning progress, and adjustable labs require JavaScript. Lessons, worked examples, printable questions, and default lab results remain readable.