THE CONSCIOUSNESS ATLAS
Read. Experiment. Follow the evidence.
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 ↗
Multiplying sixteen families by five thousand sites per family gives eighty thousand sites. This version’s allocation differs from an architecture with five thousand gates total split across families. The count is a design or array-size statement and must remain associated with this particular…
The indicator is one when two strand identifiers match one of the source’s eight listed complementary pairs. Such a pair receives weight J₀(1+ρ); all others receive J₀. This function is a clear discrete weighting rule, independent of the separate distance-denominator defect in FamilyNetwork…
Squaring each component, summing, and taking a square root gives the Euclidean norm. It is nonnegative, equals zero only for the zero vector, and scales linearly with the absolute magnitude of a common multiplier. The variable name energy describes the software’s state magnitude; physical energy…
The implementation multiplies s by 1+μdt+σdW. This approximates the proportional drift-diffusion equation for a small step, but the multiplier can be negative. The exact geometric Brownian transition uses an exponential and preserves a positive starting value, so these two updates should not be…
The displayed ODE defines a vector flow whose derivative is β(g). The implementation advances it with g_next=g+dtβ(g). Calling the helper renormalization-group flow is a modeling interpretation; the function performs a general Euler step and requires a defined beta function and a justified scale…
The matrix first transforms the state. The stored state then moves by dt times the difference between that transformed, externally driven value and its current value. This is a forward Euler discretization of a linear relaxation with forcing; its stability depends on the matrix spectrum and dt.
The first line advances an agent state by dt times its current derivative estimate. The second clips that proposal into [0,1]. This makes every stored scalar bounded for finite arithmetic, while the resulting projected recurrence can differ substantially from the unconstrained continuous-time…
The deterministic term moves x toward μ at rate θ, and σdW adds noise. The code returns a forward Euler–Maruyama step rather than the exact finite-time Ornstein–Uhlenbeck transition. With positive θ, an excessively large dt can make the discretized deterministic part unstable even though the…
The helper returns x+μdt+σdW, adding deterministic drift and a scaled stochastic increment. It is one discrete approximation step to the displayed Itô stochastic differential equation. For state-dependent coefficients, callers must evaluate the drift and diffusion consistently at the step’s…
Excitatory activity decays toward zero while a sigmoid of its net recurrent and external input replenishes it. The factor 1−r_E E reduces the responsive fraction as activity rises, and τ_E sets the time scale. The code applies an Euler step and clips the stored activity to [0,1].
The real exponential is its own derivative. The backward pass therefore multiplies the incoming gradient by the already computed output. Large positive inputs can overflow floating-point range, while very negative inputs can underflow toward zero.
Between spikes, the trace decays with time constant τ_AMPA. Each ideal impulse increases it by one. The code implements those two operations separately: receive_spike adds one and step multiplies by exp(−dt/τ), giving the exact between-spike decay.
The algorithm starts from a fixed offset, XORs each input byte into the state, and multiplies by a fixed prime with reduction modulo 2³². Processing bytes in order yields a deterministic 32-bit integer. It is a noncryptographic hash with finitely many outputs, so different strings can collide and…
The mixing coefficient ρ=1/(1+φ)=1/φ²≈0.381966. Each update retains about 61.8% of the old state and takes about 38.2% of dx_norm. This is an exponential moving average: with a constant target, the remaining error is multiplied by 1−ρ=1/φ each time.
The helper first forms r=ΦΨC/(1+F), then returns a clipped cubic r²(3−2r). The cubic is smoothstep and is monotone from zero to one only on r∈[0,1]. The ratio requires F≠−1, and interpreting the result needs the ranges of its component scores.
The PDE transports probability with drift and spreads it with diffusion. The code applies centered first and second differences on an equally spaced grid, then one explicit time step. Stability, nonnegative densities, and total-mass preservation require suitable step sizes and boundary treatment;…
The difference of consecutive V values divided by dt estimates its average rate over one discrete interval. It is not an exact continuous derivative unless an appropriate limiting or interpolation model is supplied. A negative observed difference is local evidence of decrease over that interval,…
The helper forms √ᾱ times the clean vector plus √(1−ᾱ) times a noise vector. With independent standard Gaussian noise and 0≤ᾱ≤1, this samples the usual forward Gaussian corruption distribution. The left-hand q denotes a distribution in theory, while the right-hand expression is a sample…
The state receives the increment 0.05(utility−|dx_norm|). The absolute-value term penalizes input magnitude regardless of its sign, while utility contributes with its sign intact. This operation does not compute variational free energy, because it contains neither the variational distribution q nor…
GELU multiplies x by the standard normal cumulative probability at x. The function implements it with erf, giving a smooth activation that attenuates many negative values and approaches x for large positive values. The Φ in this formula is a Gaussian CDF, not the project’s unity score or an IIT…
Multiplying a standard normal draw by √dt gives a zero-mean Gaussian increment of variance dt. This is the increment distribution used in Wiener-driven discretizations. The function’s callback must supply an independent standard normal draw and dt must be nonnegative; the callback type itself does…
The kernel is one for identical inputs and decreases with their squared distance. The positive bandwidth σ sets the scale: a distance σ gives exp(−1/2). It is a similarity function, not by itself a normalized probability density.
A stored weight matrix is changed by an increment ΔW. This equation is bookkeeping common to many learning rules; the content of learning comes from how that increment is computed from data, errors, or objectives. The project family supplies an additive scalar increment rather than a complete…
F maps a current state and input to the next state. This is the general form of a driven discrete dynamical system. Reproduction requires the actual mapping, initial state, and input sequence; the nearby weighted-average family supplies one particular example.
Starting from the declared seed core_eq[−1]=0.5, each indexed value is 0.5 plus a sine-modulated half of the preceding value. By induction, every value stays in [0,1], since the sine lies in [−1,1]. With no input or time variable in this displayed recurrence, the formula specifies one deterministic…
Each supplemental value reuses a core value selected by i modulo 174 and multiplies it by a cosine envelope. The cosine can be negative, so the supplements can lie below zero even when the core values are nonnegative. These are generated variations of the core sequence, with reuse beginning when…
ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target. The code’s consciousness interpretation is a project hypothesis, distinct from an IIT cause-effect or partition…
ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target. The code’s consciousness interpretation is a project hypothesis, distinct from an IIT cause-effect or partition…
ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target. The code’s consciousness interpretation is a project hypothesis, distinct from an IIT cause-effect or partition…
ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target. The code’s consciousness interpretation is a project hypothesis, distinct from an IIT cause-effect or partition…
ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target. The code’s consciousness interpretation is a project hypothesis, distinct from an IIT cause-effect or partition…
ComputePhi returns 1/(1+|x−1|), assigning one to x=1 and smaller positive values as x departs from that reference. The function measures scalar proximity to the selected target. The code’s consciousness interpretation is a project hypothesis, distinct from an IIT cause-effect or partition…
The golden ratio is the positive solution of φ²=φ+1. The identities φ−1=1/φ and 1+φ=φ² explain several equivalent constants elsewhere in this project. It is a fixed dimensionless number; using it as a coefficient does not, by itself, give a recurrence a convergence or optimization property.
The golden ratio is the positive solution of φ²=φ+1. The identities φ−1=1/φ and 1+φ=φ² explain several equivalent constants elsewhere in this project. It is a fixed dimensionless number; using it as a coefficient does not, by itself, give a recurrence a convergence or optimization property.
For each index k, this function maps the scalar x to sin(a)+cos(a), where a=2πφᵏx. The two terms combine into √2 sin(a+π/4), so each component has amplitude √2 and range [−√2,√2]. Different k values provide different frequencies; when x comes from a string hash, these are numerical features of that…
The golden ratio satisfies φ²=φ+1 by its definition as the positive root of x²−x−1=0. This identity generates the reciprocal and power identities used in the file. It is exact for the mathematical constant, subject to rounding when stored in float64.
The golden ratio satisfies φ²=φ+1 by its definition as the positive root of x²−x−1=0. This identity generates the reciprocal and power identities used in the file. It is exact for the mathematical constant, subject to rounding when stored in float64.
The golden ratio satisfies φ²=φ+1 by its definition as the positive root of x²−x−1=0. This identity generates the reciprocal and power identities used in the file. It is exact for the mathematical constant, subject to rounding when stored in float64.
This expression combines sodium, potassium, and chloride concentrations weighted by their relative permeabilities. Chloride’s inside and outside positions are reversed because it is an anion. The implementation uses fixed concentrations and permeability settings to produce a membrane-potential…
For fixed coherence and free energy, the Ω derivative of the displayed objective is 2(Ω−Ω*). The body multiplies its negative by a rate and Ω(1−Ω), then adds further coherence and free-energy terms. These modifications mean it is not simply the Euclidean negative gradient of the displayed V, so…
Activations zero and two are both one unit away from the target one, so each gives score one half. Their equal scores illustrate the symmetry that discards the direction of the displacement. They are direct evaluations of the project formula.
Activations zero and two are both one unit away from the target one, so each gives score one half. Their equal scores illustrate the symmetry that discards the direction of the displacement. They are direct evaluations of the project formula.
The spectral summary sets its middle value to zero unconditionally. No eigensolver or symmetry proof establishes an exact zero eigenvalue of the full constructed matrix. The name Goldstone mode is therefore a source interpretation that is not justified by this assignment alone.
The product of two state components changes their connection: equal signs increase it and opposite signs decrease it when η is positive. Clipping after addition keeps each stored weight in [−1,1]. This is a Hebbian-style update, but a memory-retrieval or capacity claim additionally requires the…
The function returns x⁴/8. This equals the triangular-domain integral ∫₀ˣ∫₀ᵘ uv dv du; a rectangular-domain integral of uv over [0,x]² would instead be x⁴/4. The comment’s reused x and unspecified nested bounds are ambiguous, so the exact polynomial returned by the code is the reproducible…
The function returns x⁴/8. This equals the triangular-domain integral ∫₀ˣ∫₀ᵘ uv dv du; a rectangular-domain integral of uv over [0,x]² would instead be x⁴/4. The comment’s reused x and unspecified nested bounds are ambiguous, so the exact polynomial returned by the code is the reproducible…
The function returns x⁴/8. This equals the triangular-domain integral ∫₀ˣ∫₀ᵘ uv dv du; a rectangular-domain integral of uv over [0,x]² would instead be x⁴/4. The comment’s reused x and unspecified nested bounds are ambiguous, so the exact polynomial returned by the code is the reproducible…