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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 41 of 59Search the source archive ↗

gh-eq-bd9bca6d4d813ed6

pairwise · fit, so a fitted coefficient vector w scores a candidate by utility

This relation defines fit, so a fitted coefficient vector w scores a candidate by utility in the source section “pairwise · fit, so a fitted coefficient vector w scores a candidate by utility”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation…

Implementation mathematicsSource recovered; runtime not executed

fit, so a fitted coefficient vector w scores a candidate by utility = w . features and the display order is

gh-eq-0d136e7a72bb1b67

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-8aea970634ade766

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-542aa6f6eb18fb40

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-030475d790184af6

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-02ba2fbfe580b1a0

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-fa3be366d4269af9

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-55fe08b0019606cb

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-38ee8b325a2fcbf6

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-45f00b3d2e7a2bd1

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-5db55a4bdc308c49

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-d03460339480c7c0

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-3c9e628836fc1ae9

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-a960117dff2cff2e

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-8fc235538d4d8e23

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-f6ce09559567ca93

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-6a97e0a114423c0e

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-9bdf7472c7c86aca

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-887424fe1ed00f61

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-aee9f97e284833ad

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-6c1f6b96dbd74d74

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-2eed5e80f36a821d

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-e89ebc8dec8346bf

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-50c75551fd30b957

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-01348dec6f28357e

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-1882673fdd85424d

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-4e507244069d4ac0

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-135d0a69f62ceaab

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-896fb890a3c670d8

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-75d4c95b7bc0f591

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-00e6d74a39d78c18

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-807152a810c0e3fb

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-f96cd10f379796ad

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-7c2a16aad2f1a4aa

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-fdef34712cc33be6

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-821304cc30e2851b

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-2b50e00e6404d976

querier

This relation defines Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion in the source section “querier”. 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

Hybrid retrieval: pgvector cosine kNN fused with full-text rank via Reciprocal Rank Fusion (k=60).

gh-eq-513c50dcc7add6ae

random

This relation defines X ~ G(a,1), Y ~ G(b,1) in the source section “random”. 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

X ~ G(a,1), Y ~ G(b,1) => X / (X + Y) ~ Beta(a, b)

gh-eq-50d3d28f6cd3ced7

random · boost identity G(a)

This relation defines boost identity G(a) in the source section “random · boost identity G(a)”. 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

boost identity G(a) = G(a+1) * U^(1/a).

gh-eq-56c8cff94b93fb6c

rank · MMR

This relation defines MMR in the source section “rank · MMR”. 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 unprovided physical or cognitive meaning to…

Implementation mathematicsSource recovered; runtime not executed

MMR = argmax [ lambda * score(c) - (1 - lambda) * max_sim(c, selected) ]

gh-eq-583b1c3a4613b086

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 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

h_t = f(h_{t-1}, x_t)

gh-eq-6327776c0d5f514e

run · § 9 ConsciousnessEngine (174 + 200

This relation defines § 9 ConsciousnessEngine (174 + 200 in the source section “run · § 9 ConsciousnessEngine (174 + 200”. 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

§ 9 ConsciousnessEngine (174 + 200 = 374)

gh-eq-94c569832b9874ff

seferim-core

This relation defines § 6.1 θ_k ← (1−α)θ_k + α·w·ψ_k(h(item))·Φ(importance) in the source section “seferim-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…

Implementation mathematicsSource recovered; runtime not executed

§ 6.1 θ_k ← (1−α)θ_k + α·w·ψ_k(h(item))·Φ(importance)

gh-eq-9d72f7f9093ef53d

seferim-core · Activation: χ

This relation defines Activation: χ in the source section “seferim-core · Activation: χ”. 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

Activation: χ = σ(α_κ·κ + α_Ψ·Ψ̃ - θ) ← Continuous sigmoid, NOT binary Fibonacci

gh-eq-2898aa07960f8cca

seferim-core · Learning Drive: Γ

This relation defines Learning Drive: Γ in the source section “seferim-core · Learning Drive: Γ”. 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 Drive: Γ = χ × η × κ

gh-eq-efb683ef6bf5ed92

seferim-core · Plasticity: η

This relation defines Plasticity: η in the source section “seferim-core · Plasticity: η”. Applies the stated minimum, maximum, or clamp. These bounds are part of the actual operation. Its interpretation depends on the source’s stated variables and conditions; this record does not assign…

Implementation mathematicsSource recovered; runtime not executed

Plasticity: η = clamp(η_base + η_gain·κ, η_min, η_max)

gh-eq-02bd5c2efa3a3ec0

seferim-core · § 10.1 Registry[k][i][j]

This relation defines § 10.1 Registry[k][i][j] in the source section “seferim-core · § 10.1 Registry[k][i][j]”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Uses a remainder or modular operation, retaining the numeric representation used in the source. Its…

Implementation mathematicsSource recovered; runtime not executed

§ 10.1 Registry[k][i][j] = cos(θ_k) if i==j; sin(θ_k)·0.1 if j==(i+1)%16; else 0; θ_k = 2π·k/φ

gh-eq-147d19ef5df12125

seferim-core · § 10.6 Hebbian on strand 0 (representative); ΔW

This relation defines § 10.6 Hebbian on strand 0 (representative); ΔW in the source section “seferim-core · § 10.6 Hebbian on strand 0 (representative); ΔW”. 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

§ 10.6 Hebbian on strand 0 (representative); ΔW = η·state_i·state_j

gh-eq-35669fa2582e9cb9

seferim-core · § 11.1 / § 11.2 dS_i/dt

This relation defines § 11.1 / § 11.2 dS_i/dt in the source section “seferim-core · § 11.1 / § 11.2 dS_i/dt”. 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

§ 11.1 / § 11.2 dS_i/dt = −λS_i + Σ_{j≠i} w_ij Φ(C_ij) tanh(S_j); Euler + clamp

gh-eq-477780162b454a05

seferim-core · § 2.1 golden basis function ψ_k(x)

This relation defines § 2.1 golden basis function ψ_k(x) in the source section “seferim-core · § 2.1 golden basis function ψ_k(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…

Implementation mathematicsSource recovered; runtime not executed

§ 2.1 golden basis function ψ_k(x) = sin(2π·φ^k·x) + cos(2π·φ^k·x)

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