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.
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 ↗
Clipped federation integration step
Takes an explicit Euler step of the federation ODE and clips the stored signal to [0,1]. Clipping bounds the stored value but is not a proof that the unprojected ODE is stable.
Clipped potential update
Retains 95% of the potential, adds an input–velocity interaction, subtracts a quadratic term and clips to [0,1]. This is a source-defined state update, not a direct measurement of conscious experience.
Combined neural drive
Combines input scaled by unused activation capacity, a velocity term and a coupling term. The coefficients fix their relative contribution in this source version.
Combined phase bias
Combines the two phases through the fractional part and recenters the result around zero. Its range is [−0.5,0.5).
DNA memory learning rule
Blends each old memory coefficient with a weighted basis feature of a normalized item hash. Importance is transformed by Φ before scaling the feature. The 16 coefficients form a compressed feature representation, so the source items are not generally recoverable uniquely from this vector alone.
DNA memory query score
Computes an inner product between stored coefficients and basis features of the query hash. This is a retrieval score in the source representation, not a reconstruction of the original training text.
DNA phase increment
Advances the phase by the source’s fixed decimal step and wraps it into [0,1). The source’s separate approximation of this decimal by 1/φ³ is numerically inconsistent.
Federation cross-talk ODE
Combines local decay with coherence-weighted input from other agent signals. Tanh bounds each received signal, while overall stability depends on the weights and coupling strengths.
Fibonacci phase increment
Rotates the phase by the reciprocal golden ratio and wraps it modulo one. The ideal real-valued recurrence and its finite-precision implementation have different repetition properties.
Final normalized state
Multiplies the intermediate triple-prime state by the normalization coefficient. The upstream meaning of the triple-prime state is only partly summarized in this specification.
Gate flip decision
Turns the sign of the combined phase bias into a binary flip flag. A bias equal to zero produces zero under the source’s strict inequality.
Gate5000 binary transition
Applies XOR with the input bit and phase flip, then masks to one bit. Given fixed inputs and flip, XOR is reversible on a single bit; the complete system’s reversibility also depends on preserving those inputs.
Global aggregate state score
Applies tanh to the mean of the 256 strand coordinates. It is a dimensionless aggregate state metric. The source explicitly distinguishes this value from IIT’s partition-based Φ.
Golden-ratio constant
Defines the constant used in phase, feature and normalization formulas. Its value is approximately 1.61803398875.
Golden-ratio state normalization
Produces a factor in (0,1] that decreases as the squared state norm grows. The coefficient is used as a soft attenuation factor in the final state update.
Lattice forward transform
Applies a weighted affine transform followed by tanh. Each output is bounded between −1 and 1 for finite real arguments.
Lattice state blend
Blends the old strand state with the sum of its transformed signal and core feature. It is distinct from the later global aggregation metric.
Local strand integration score
Compresses the strand energy accumulator through tanh. For nonnegative E the result lies in [0,1); it summarizes the accumulator and does not perform a partition search.
Mean pairwise federation coherence
Averages the similarity values of all unordered distinct agent pairs. It requires at least two agents and well-defined pairwise similarities.
Meta-state squared norm
Sums the squares of the 16 components of the meta-state vector. This nonnegative scalar measures vector magnitude.
Neural coupling update
Updates coupling from a potential-driven contribution and a restoring contribution involving k_c. Its stability depends on P, k_c and the rest of the update ordering.
Neural velocity with damping
Adds the recent activation difference to velocity and removes 1% of the previous velocity. The algebra expresses an update, so old/new labels are displayed to make assignment order clear.
Potential-sensitive gate
Transforms a shifted and scaled potential signal through a logistic function and adds a 0.05 floor. The gate therefore lies strictly between 0.05 and 1.05 for finite real inputs.
Unified binding-field score
Sums component magnitudes and maps that nonnegative sum to a saturating score. Larger magnitudes drive the score toward one. In this formula, the score can increase without measuring causal irreducibility.
Unity importance weighting
Gives weight one at x=1 and decreases as the distance from one grows. The expression is positive and bounded by one for finite real x, with a cusp at x=1.
Adaptive strategy-weight update
Updates the strategy distribution by applying softmax to log current weights plus scaled performance pressure.
Bounce rate
Defines the named performance ratio used or referenced in the framework.
Illustrative pressure-input vector
Shows seven example signed input values entering the depicted matrix product.
Performance pressure
Maps the delta vector through a performance matrix to produce pressure for each strategy dimension.
Bitwise majority bundling
Builds a composite signature by voting independently at each bit position. A tie-breaking convention is required when an even number of inputs can split evenly. Bundling is a lossy superposition and does not preserve unlimited recoverable items.
Coalition member trust score
Combines route score with evidence that an organ was invoked, returned parseable output and passed supervision. The response-size bonus is capped at 512 points. The source’s pass flag is an operational test result, not a general proof that the answer is true.
Historical bundling-capacity heuristic
The dossier gives this as a practical rule of thumb for the number of bundled items at dimension D. It predicts about 11.9 at D=512, but capacity depends on the retrieval criterion, noise, encoding and failure probability; the ratio is not a universal information-theoretic law.
ORACLE routing score
Adds binary-signature agreement, literal token overlap, liveness, locality and a priority weight. In the documented 2048-bit setup a single shared token adds 96 points, so the capabilities text can strongly influence routing. The formula ranks eligible organs; later health and invocation rules…
Similarity in permille
Converts Hamming agreement to a value on a nominal 0–1000 scale. Equal signatures score 1000 and complementary signatures score zero. Integer rounding is an implementation detail that must be retained for exact result replication.
mmact action objective
Adds base value, exploration, a theta term and entropy, while subtracting conflict, resource use and repetition. The repetition penalty is intended to discourage repeated actions. Each component’s scale and sign convention affect which action wins.
mmcog coherence diagnostic
Multiplies four diagnostic factors. A zero factor makes the product zero, and rescaling any factor changes Q. The dossier explicitly reports that the organ calls this a coherence diagnostic, not a consciousness proof; constituent definitions and units are needed for comparisons.
mmcog predictive coherence
Converts a nonnegative Hamming prediction discrepancy to a score in (0,1]. Perfect bit agreement gives one; more disagreement lowers the score. The expression measures predictive agreement in the chosen representation.
mmlattice 5,000-cell projection
Declares a projection from the source representation to a 5,000-cell lattice. The surrounding dossier describes majority bundling over neuron regions; the arrow notation alone does not define the projection matrix, regions or encoding.
mmreshit surprise–uncertainty–value objective
The documented kernel favors lower surprise and uncertainty and higher certified value. The shorthand needs an explicit decision variable, domain and definitions of the three scores to determine an optimizer. Its “active inference” label does not alone identify a variational probabilistic model.
mmteach association threshold
Allows an accumulated co-activation association to enter the graph once its integer weight reaches the threshold. This is an implementation threshold for asserting a learned relation; factual validity still depends on the grounding and verification process.
0.618033 · Bond weight
The source describes this relation in the following context: ψ (psi) 0.618033 Bond weight = 1/φ = φ-1 N_agents 88 Neural agents in brain