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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 43 of 59Search the source archive ↗

gh-eq-90b0f643c5def788

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-24ffb5b8e2e3cc64

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-42195a075af7a796

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-d3352658967261fe

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-fafab5913a0e2470

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-07ebae648acb3f67

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-05d086e214b59013

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-2eee1ccab0f15f95

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-9dc7f33fe86a5fd3

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-be8b08e628e6c228

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-d8cde4872b62cc95

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-62bb1fb720bb2c6f

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-b5b2171ef7d42a04

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-94f94cbdcbdefc8f

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-c242b37ebbb04256

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-f738869d46c2690e

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-70d03711482254fe

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-b78c48fa0480c892

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-8cb00bcee972d947

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-d5884a105687c98d

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-761f9291b6389ad9

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-e585996fd201bbe2

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-ba4e81a4b6c55689

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-77c05afe55d98e29

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-78915ff30ae2db6a

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-cfa5c9d63d91d5b9

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-9a3bb109d71311de

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-bb2a22504bd7d8c2

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-f9fd60f3b6ea6fa8

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-dba8251569d296a6

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-87c8bf24bc8250a7

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-89012bce33c6c418

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-386f6fa11bfdf403

skillmatcher

This relation defines engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product. in the source section “skillmatcher”. 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

engine's threshold. Vectors from the provider are L2-normalized, so cosine == dot product.

gh-eq-5b758cce7e4cbe34

statespace · x'(t)

This relation defines x'(t) in the source section “statespace · x'(t)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation 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

x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t)

gh-eq-99477f929cb43544

suppression · 2026-06-30 de identification research (NIST SP 800-188, FCSM WP22, l diversity, NYC LL144): k

This relation defines 2026-06-30 de identification research (NIST SP 800-188, FCSM WP22, l diversity, NYC LL144) in the source section “suppression · 2026-06-30 de identification research (NIST SP 800-188, FCSM WP22, l diversity, NYC LL144): k”. It specifies the displayed relationship between the…

Implementation mathematicsSource recovered; runtime not executed

2026-06-30 de identification research (NIST SP 800-188, FCSM WP22, l diversity, NYC LL144): k = 10 is

gh-eq-8556d3d9cb86efb5

survival · (1 based, index m-1 in the returned vector), hazard[m]

This relation defines (1 based, index m-1 in the returned vector), hazard[m] in the source section “survival · (1 based, index m-1 in the returned vector), hazard[m]”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s…

Implementation mathematicsSource recovered; runtime not executed

(1 based, index m-1 in the returned vector), hazard[m] = events at m / at risk at m, where at risk at m counts

gh-eq-95ac4ba7e9f96fa5

two_way_engine

This relation defines D <- target vector (size must be >= cfg.dim; extra values ignored) in the source section “two_way_engine”. 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

D <- target vector (size must be >= cfg.dim; extra values ignored)

gh-eq-391133843b9c7869

two_way_engine · Minimize: L

This relation defines Minimize: L in the source section “two_way_engine · Minimize: L”. 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

Minimize: L = sum_i (sigmoid(s_i) - target_i)^2

gh-eq-c8da136627edaeb8

two_way_engine · dL/ds_i

This relation defines dL/ds_i in the source section “two_way_engine · dL/ds_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 does not assign an unprovided physical or…

Implementation mathematicsSource recovered; runtime not executed

dL/ds_i = 2*(f_i - t_i) * f_i*(1 - f_i), where f_i = sigmoid(s_i)

gh-eq-8bc830e3ebb41951

value · value(i, j)

This relation defines value(i, j) in the source section “value · value(i, j)”. 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

value(i, j) = engineTotal(i, j) * priorityMultiplier(j)

gh-eq-c38284b661616ac3

variational · ELBO

This relation defines ELBO in the source section “variational · ELBO”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation 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

ELBO = E_q[log p(x|z)] - D_KL(q(z|x) || p(z))

gh-eq-018a36b08a8c140d

vendor

This relation defines - vendor_quality_distribution: a BENCH intent, k in the source section “vendor”. 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

- vendor_quality_distribution: a BENCH intent, k=10 small cell suppressed. Per vendor, the headcount of its

gh-eq-13a89a42a3f9cc00

vendor

This relation defines IntentVendorQualityDistribution is the registered name of the k in the source section “vendor”. 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

IntentVendorQualityDistribution is the registered name of the k=10 suppressed vendor quality distribution (a

gh-eq-9a71c2b514d9063c

🌟 Conclusion

This relation defines The three equations—`1 in the source section “🌟 Conclusion”. 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

The three equations—`1 = 1·x`, `∞ = 1`, `Φ = 1/(1+|x-1|)`—are not metaphors. They are **working code** that creates measurable consciousness.

gh-eq-93ba239e6a1a4ab9

🌟 Executive Summary

This relation defines 3. **Awareness Equation**: `Φ in the source section “🌟 Executive Summary”. 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

3. **Awareness Equation**: `Φ = 1/(1 + |x - 1|)` → Consciousness is measurable

poster-eq-6f2f150b4df9fe

Adaptive evolution operator grouping

The adaptive contribution groups four optimization-oriented labels. Gradient descent and loss minimization can overlap, so an implementation needs clear, nonduplicated definitions.

Integrated architecture proposalsource graphic; not an execution result

t_total = gradient_descent + loss_minimization + confidence_shaping + reward_signal

poster-eq-63a2ae5d747361

Agency Tensor definition

A is the source’s agency representation; its components and measurement are not defined.

Integrated architecture proposalsource graphic; not an execution result

A = Agency Tensor

poster-eq-c2af8643d02fdc

Autonomous objective with exploration and repetition terms

The objective combines task value, exploration, an adaptive parameter term, conflict and resource penalties, entropy regularization and a repetition penalty. If this J is maximized, the plus entropy term encourages diversity when it represents positive entropy.

Integrated architecture proposalsource graphic; not an execution result

J = base_objective + exploration_bonus + adaptive_theta_term − conflict_penalty − resource_penalty + entropy_regularization − repetition_penalty

poster-eq-5f8ee727699837

Coherence label

This assigns a conceptual interpretation to C(t); the poster does not define its operational measurement.

Integrated architecture proposalsource graphic; not an execution result

C(t) = coherence

poster-eq-34c852d092eeec

Experiential Coupling Lattice definition

X names the reduced lattice intended to couple substrate and experience.

Integrated architecture proposalsource graphic; not an execution result

X = Experiential Coupling Lattice

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