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THE CONSCIOUSNESS ATLAS
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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 29 of 59Search the source archive ↗

gh-eq-843a24f9f27ad9a6

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

Implementation mathematicsSource recovered; runtime not executed

k_b^coop(n,t) = k_b(n,t) · Π[1 - σ_b·b_m(t)]

gh-eq-ec00c25af0c593c2

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

Implementation mathematicsSource recovered; runtime not executed

k_f(n,t) = k_f^(0)(n) · [1 + μ_f·cos(2πn/10.6 + φ(t))]

gh-eq-abaee8d83ea2afd8

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

Implementation mathematicsSource recovered; runtime not executed

k_f^coop(n,t) = k_f(n,t) · Π[1 + σ_f·b_m(t)]

gh-eq-10528324fd1dbe5d

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 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* = B*/44 ≈ 0.82

gh-eq-29b77d6de60b4a99

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

Implementation mathematicsSource recovered; runtime not executed

τ_fast = 1/(k_f^max + k_b^max)

gh-eq-5ab88fd5ab8c511d

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

Implementation mathematicsSource recovered; runtime not executed

τ_slow = 1/(k_f^min + k_b^min) · [1 + 43·σ_eff]

gh-eq-89f87197f24757e9

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 measure and domain must come from this source. Applies an exponential factor. The exponent determines its real scaling…

Implementation mathematicsSource recovered; runtime not executed

Compute T = Φ · ∫[M(t')·exp((QK^T/√d_k)V)] dt'

gh-eq-ab21c66baac81cb4

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 named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

Periodicity: Ψ(t + 10.6) ≈ Ψ(t) - quasi-periodic

gh-eq-9d8445809bd2679d

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 named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

Bond count: Σ A_{ij}/2 = 44

gh-eq-a77d180e0bb7c8b3

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

Implementation mathematicsSource recovered; runtime not executed

Conservation: Lk = Tw + Wr = N/10.6 = constant

gh-eq-f24dc2312e2fe0d5

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

Implementation mathematicsSource recovered; runtime not executed

Energy: ∂E/∂r = 0 at equilibrium

gh-eq-aef9052222b4c0ff

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 between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions;…

Implementation mathematicsSource recovered; runtime not executed

Master state vector: Ψ_DNA(t) = [S⃗(t), B⃗(t), θ⃗(t), φ_10.6(t)]ᵀ

gh-eq-89a7a709418e358a

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 quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does…

Implementation mathematicsSource recovered; runtime not executed

Simplified: assume N = total progression

gh-eq-8a9f1f1f027750cc

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

Implementation mathematicsSource recovered; runtime not executed

Topological: Lk = constant

gh-eq-87aa288ebb9c6e8a

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

Implementation mathematicsSource recovered; runtime not executed

dΨ_DNA/dt = M_DNA · Ψ_DNA + F(t) + Ω·sin(2πt/10.6)·Ψ_DNA + η(t)

gh-eq-c83961603bee51e7

accountant · Gaussian mechanism depends only on the noise multiplier sigma

This relation defines Gaussian mechanism depends only on the noise multiplier sigma in the source section “accountant · Gaussian mechanism depends only on the noise multiplier sigma”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

Implementation mathematicsSource recovered; runtime not executed

Gaussian mechanism depends only on the noise multiplier sigma = NoiseSigma / C, the noise measured in

gh-eq-d12b8ea29b85f07f

accountant · noiseMultiplier returns sigma

This relation defines noiseMultiplier returns sigma in the source section “accountant · noiseMultiplier returns sigma”. 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

noiseMultiplier returns sigma = NoiseSigma / ClipNorm, the noise measured in units of the sensitivity, the

gh-eq-2eedb15f9e05e8ab

accountant · units, C

This relation defines units, C in the source section “accountant · units, C”. 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

units, C = 1) the multiplier is just NoiseSigma. The per release Renyi differential privacy at order alpha

gh-eq-0390971682a62822

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

Implementation mathematicsSource recovered; runtime not executed

min_G max_D V(D,G) = E[log D(x)] + E[log(1-D(G(z)))]

gh-eq-19302a670d3a13ac

analytics_math · S(t)

This relation defines S(t) in the source section “analytics_math · S(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 does not assign an unprovided physical or cognitive…

Implementation mathematicsSource recovered; runtime not executed

S(t) = product over event times ti <= t of (1 - di / ni), where ni is the number still at risk

gh-eq-d332fba6072b85f5

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 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

P(x) = Π_t P(x_t | x_1, ..., x_{t-1})

gh-eq-136ed8484ca5cb60

coefficients but writes nothing. minEvents <= 0 auto

This relation defines coefficients but writes nothing. minEvents <= 0 auto computes the floor as twenty decided in the source section “coefficients but writes nothing. minEvents <= 0 auto”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

Implementation mathematicsSource recovered; runtime not executed

coefficients but writes nothing. minEvents <= 0 auto computes the floor as twenty decided events per fitted

gh-eq-efa75bf421b64829

confidence · confidence

This relation defines confidence in the source section “confidence · confidence”. 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

confidence = wFit * (total / 100) + wProvenance * provenanceScore + wCompleteness * completeness

gh-eq-08606ee171fff473

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 come from this source. Its interpretation depends on the source’s stated variables and conditions; this record does not…

Implementation mathematicsSource recovered; runtime not executed

Output = ∫ Σᵢ₌₁¹⁰⁰ wᵢ(t, context) · Gᵢ(input, state) dt

gh-eq-c43a30985373b715

cross_tool_consistency_integration_test · relocate to while still being available (50). 25 + 25 + 15 + 0 + 5 + 5

This relation defines relocate to while still being available (50). 25 + 25 + 15 + 0 + 5 + 5 in the source section “cross_tool_consistency_integration_test · relocate to while still being available (50). 25 + 25 + 15 + 0 + 5 + 5”. It specifies the displayed relationship between the named quantities…

Implementation mathematicsSource recovered; runtime not executed

relocate to while still being available (50). 25 + 25 + 15 + 0 + 5 + 5 = 75.00.

gh-eq-490a7c50bb91b887

def face_xml(name) · image includes a 4 px pad: pivot in image px

This relation defines image includes a 4 px pad: pivot in image px in the source section “def face_xml(name) · image includes a 4 px pad: pivot in image px”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated…

Implementation mathematicsSource recovered; runtime not executed

image includes a 4 px pad: pivot in image px = piv + 4. The mirrored variant is the same plate under a scaleX=-1 node,

gh-eq-3792871c3408bade

def nid() · re-base: sheet px -> part-local 1x px (origin

This relation defines re-base: sheet px -> part-local 1x px (origin in the source section “def nid() · re-base: sheet px -> part-local 1x px (origin”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and…

Implementation mathematicsSource recovered; runtime not executed

re-base: sheet px -> part-local 1x px (origin = the kit rect's top-left), i.e. x' = (x - l.x)/4

gh-eq-854d7e73bbf0c013

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

Implementation mathematicsSource recovered; runtime not executed

q(x_t|x_{t-1}) = N(√(1-β_t)x_{t-1}, β_t I)

gh-eq-315c4c17769d263a

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

Implementation mathematicsSource recovered; runtime not executed

Backward memory: y₂ = Σ_{k=0}^{43} x(t + k)

gh-eq-4b7b80a9d0057b11

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

Implementation mathematicsSource recovered; runtime not executed

Forward memory: y₁ = Σ_{k=0}^{43} x(t - k)

gh-eq-833ef38f1435727b

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 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

Spark equation: ẋ = αF(t)Q(x,t)(1 - x) + βΣx(t - k)

gh-eq-5946bb007b7bb5c4

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

Implementation mathematicsSource recovered; runtime not executed

ẋ = 2αF(t)(1^{x(t)} + 1)(1 - x) + βy₁ - γy₂

gh-eq-1acb003073573f5d

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

Implementation mathematicsSource recovered; runtime not executed

ẋ = αF(t)(x^x + 1)(1 - x) + βy₂

gh-eq-77d0388d7d8aea18

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

Implementation mathematicsSource recovered; runtime not executed

F_Aphrodite(x) = cos(φ·x) (harmony)

gh-eq-f37174ed52c737eb

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 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

F_Apollo(x) = φ^x + φ^{-x}

gh-eq-46f52036544666d8

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 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

F_Ares(x) = m·(-ω²·x) (force)

gh-eq-47a77579771370f3

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

Implementation mathematicsSource recovered; runtime not executed

F_Artemis(x) = -D·x (diffusion)

gh-eq-3d9651591fbbf024

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 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

F_Athena(x) = x² (utility maximization)

gh-eq-05c6f5f2915ecf21

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

Implementation mathematicsSource recovered; runtime not executed

F_Demeter(x) = r·x·(1-x/K) (logistic growth)

gh-eq-98b8adbab684fbd1

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 exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase. Its interpretation…

Implementation mathematicsSource recovered; runtime not executed

F_Dionysus(x) = |e^{iωx}·sin(x)| (creative oscillation)

gh-eq-b04d2683114f715d

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

Implementation mathematicsSource recovered; runtime not executed

F_Hephaestus(x) = x⁴/8 (engineering integral)

gh-eq-c79da3d0dc7eb3e4

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

Implementation mathematicsSource recovered; runtime not executed

F_Hera(x) = Σ w_k·sin(k·x) (integration)

gh-eq-af47bfaad6137692

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 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

F_Hermes(x) = ω·x (communication rate)

gh-eq-c5fe4537454c7c56

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 exponent, its phase. Its interpretation depends on the source’s stated variables and conditions; this record does not assign…

Implementation mathematicsSource recovered; runtime not executed

F_Hestia(x) = x·(1-e^{-1/τ}) (memory)

gh-eq-895616d63749a299

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 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

F_Lashon(x) = Σ a_n·sin(nπx)

gh-eq-b1a3c3da267a3369

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

Implementation mathematicsSource recovered; runtime not executed

F_Poseidon(x) = -ω²·x (wave equation)

gh-eq-387fcac3401c2b80

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

Implementation mathematicsSource recovered; runtime not executed

F_Prometheus(x) = r·x·(1-x) (logistic map)

gh-eq-e77410f30466c95b

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 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

F_Yad(x) = x^x + 1

gh-eq-339d25b64981daad

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 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

F_Zeus(x) = coordinated product

gh-eq-b59f3b43bbb49586

drivers

This relation defines drivers computes the four "inventory coverage" drivers (a requirement is COVERED iff >=1 q in the source section “drivers”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and…

Implementation mathematicsSource recovered; runtime not executed

drivers computes the four "inventory coverage" drivers (a requirement is COVERED iff >=1 qualified

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