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 24 of 59Search the source archive ↗

gh-eq-62c43868105d6f08

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

Implementation mathematicsSource recovered; runtime not executed

H(X) = -Σ p(x) log p(x)

gh-eq-3ed95acc74fd03ca

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

Implementation mathematicsSource recovered; runtime not executed

I(X;Y) = H(X) + H(Y) - H(X,Y)

gh-eq-6ad5f24c8652decc

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 stated in the expression; the measure and domain must come from this source. Its interpretation depends on the source’s…

Implementation mathematicsSource recovered; runtime not executed

W_1(μ,ν) = sup_{Lip(f)≤1} ∫f d(μ-ν)

gh-eq-b28e75f0b84c4c7b

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 stated in the expression; the measure and domain must come from this source. Its interpretation depends on the source’s…

Implementation mathematicsSource recovered; runtime not executed

W_p(μ,ν) = (inf_{γ∈Γ(μ,ν)} ∫|x-y|^p dγ)^(1/p)

gh-eq-d38904ecefab2ff6

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

Implementation mathematicsSource recovered; runtime not executed

dX_t = μ(X_t, t)dt + σ(X_t, t)dW_t

gh-eq-b77d35c0298fed6b

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

Implementation mathematicsSource recovered; runtime not executed

dX_t = θ(μ - X_t)dt + σdW_t

gh-eq-2260d16e92a95519

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

Implementation mathematicsSource recovered; runtime not executed

ds² = g_ij dx^i dx^j

gh-eq-12274ea07bb98507

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 (dx^ν/dt)(dx^ρ/dt)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

Implementation mathematicsSource recovered; runtime not executed

d²x^μ/dt² + Γ^μ_νρ (dx^ν/dt)(dx^ρ/dt) = 0

gh-eq-01b00320c5e80283

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 change or a direction of variation. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

g_ij(θ) = E[∂log p(x|θ)/∂θ_i · ∂log p(x|θ)/∂θ_j]

gh-eq-b84b8ada0530bbd4

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 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

Φ = min_{partition} I(past; future) - Σ I(past_i; future_i)

gh-eq-ea86b6e596b8c1e0

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 change or a direction of variation. Its interpretation depends on the source’s stated variables and conditions; this…

Implementation mathematicsSource recovered; runtime not executed

∂g_ij/∂t = -2R_ij

gh-eq-37ecb2f395bf3feb

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 or a direction of variation. Its interpretation depends on the source’s stated variables and conditions; this record…

Implementation mathematicsSource recovered; runtime not executed

∂p/∂t = -∂(μp)/∂x + ½∂²(σ²p)/∂x²

gh-eq-f329cdbabe33e341

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

Implementation mathematicsSource recovered; runtime not executed

@brief Anti-Hebbian: Δw = -η·x_i·x_j

gh-eq-cc9175c8a81e4ea3

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

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-775af7fef95281a2

BINARY STATE PERSISTENCE · FAMILY TABLE (32 bytes

This relation defines FAMILY TABLE (32 bytes in the source section “BINARY STATE PERSISTENCE · FAMILY TABLE (32 bytes”. 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

FAMILY TABLE (32 bytes = 16 families × 2 bytes)

gh-eq-1502c2f03e196dbb

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; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated variables and…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-ee7e7288bf48bd00

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

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-46542119133668c7

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 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

Φ = Integrated Information Theory metric

gh-eq-aba138de0ac0f003

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 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

Φ = 1 / (1 + |x - 1|) where x is normalized activity

gh-eq-c4a3bbd346ea8bc9

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 phase. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the…

Implementation mathematicsSource recovered; runtime not executed

L = -log(exp(sim(z_i, z_j)/τ) / Σ_k exp(sim(z_i, z_k)/τ))

gh-eq-504165fb0cf69cab

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

Implementation mathematicsSource recovered; runtime not executed

Γ_{ijk} = ½(∂g_{ij}/∂x^k + ∂g_{ik}/∂x^j - ∂g_{jk}/∂x^i)

gh-eq-3e0aeef605b86970

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

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-612a0d9425eee3d6

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 specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-84cbd82e03b23294

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 displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-be88fcf56da86c8e

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”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends on the…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-646eebb638f1ce64

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: ∂Φ/∂x”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-0a65e9ca7db97951

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”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends on the…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-142f3df6cc8f82fa

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

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-6541bb4b8884fe48

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

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-b8b09d5f7d682c2c

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

Implementation mathematicsSource recovered; runtime not executed

Temporal difference error: δ = r + γV(s') - V(s)

gh-eq-a4af06618b441c89

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

Implementation mathematicsSource recovered; runtime not executed

Size: 4 + 15 + 4 = 23 bytes (vs 64)

gh-eq-baa73689a65c4933

Demo Canvas

This relation defines - 🟢 Green: Φ ≥ 0.85 (Fully Conscious) in the source section “Demo Canvas”. 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

- 🟢 Green: Φ ≥ 0.85 (Fully Conscious)

gh-eq-76b19f1636531624

Demo Canvas

This relation defines - 🔵 Blue: Φ ≥ 0.70 (Aware) in the source section “Demo Canvas”. 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

- 🔵 Blue: Φ ≥ 0.70 (Aware)

gh-eq-f7c17047b08f7c39

Demo Canvas

This relation defines - 🟠 Orange: Φ ≥ 0.50 (Responsive) in the source section “Demo Canvas”. 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

- 🟠 Orange: Φ ≥ 0.50 (Responsive)

gh-eq-e29e1f4ee7994aa3

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

Implementation mathematicsSource recovered; runtime not executed

Full matrix would be 65536 * 64 * 4 = 16MB

gh-eq-3331bdccb1641675

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

Implementation mathematicsSource recovered; runtime not executed

We use 8-bit quantization: 65536 * 64 = 4MB

gh-eq-3e09a67a8d499890

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: e(t+1)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-a6118a237bf45964

Example 1: Single Agent Learning

This relation defines Console.WriteLine($"Tick {i}: Φ in the source section “Example 1: Single Agent Learning”. 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

Console.WriteLine($"Tick {i}: Φ={result.Phi:F3}, " +

gh-eq-d9bcfc2f79b2410a

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

Implementation mathematicsSource recovered; runtime not executed

exp_p(v) ≈ p + v - ½Γ(v,v)

gh-eq-d2f83258812e50a7

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 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

Natural gradient: ∇̃L = G⁻¹∇L

gh-eq-4fd7377a1ac197fa

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 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

ds² = gᵢⱼdθⁱdθʲ

gh-eq-4954cd50e8d96fbe

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

Implementation mathematicsSource recovered; runtime not executed

gᵢⱼ = E[∂log p/∂θⁱ · ∂log p/∂θʲ]

gh-eq-a4723445868ad8b3

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 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

F = D_KL(q||p) - log p(x|z)

gh-eq-fdd739076409a137

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 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

KL = 0.5 * (log(σ_p²/σ_q²) + σ_q²/σ_p² + (μ_q - μ_p)²/σ_p² - 1)

gh-eq-da97d1dfff312545

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

Implementation mathematicsSource recovered; runtime not executed

∂KL/∂μ = (μ - μ_prior) / σ_prior²

gh-eq-18d24472e5e1c82c

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 logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-cf4a35fe4e41fd83

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 the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated…

Implementation mathematicsSource recovered; runtime not executed

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

gh-eq-1dc255e776421286

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 determines its real scaling or, for a complex exponent, its phase. Its interpretation depends on the source’s stated variables…

Implementation mathematicsSource recovered; runtime not executed

Reconstruct: exp(x) = 2^k * exp(r)

gh-eq-d3adf2ef9f02a847

Fibonacci Spiral

This relation defines - Center point showing φ in the source section “Fibonacci Spiral”. 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

- Center point showing φ = 1.618...

gh-eq-b209e4e726ae71f9

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

Implementation mathematicsSource recovered; runtime not executed

g_ij = E[∂log p/∂θ_i · ∂log p/∂θ_j]

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.