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 ↗
The body computes Σₖ₌₁¹⁶sin(kx)/k. Its indexed terms are harmonics derived from the same scalar x, not readings of sixteen independently stored family activations. It is a finite periodic feature sum that can have positive or negative values.
Although the comment refers to dx/dt, the body returns AngularFrequency×x. This is a linear scaling of one supplied value, with no earlier state or time difference used to estimate a derivative. A derivative interpretation needs a stated model in which that product represents a rate.
The body returns x(1−e⁻⁰·¹), approximately 0.0951626x. It does not read prior inputs or a memory buffer, so it cannot evaluate the displayed exponentially weighted historical integral by itself. A stateful leaky recurrence could approximate such memory, but it would require storing the preceding…
Membrane capacitance times voltage change equals external current minus sodium, potassium, and leak currents. The sodium and potassium conductances are modulated by gating variables m, h, and n. The recovered C++ component advances these coupled equations with Euler steps and explicit millivolt,…
The derivative of tanh(x) is 1−tanh²(x). It is largest at zero and approaches zero in the saturated tails. Reusing the forward output in the backward pass avoids an additional tanh evaluation.
The inhibitory population has its own decay, sigmoid response, refractory factor, and time constant. Excitatory input increases its drive and inhibitory self-coupling subtracts from that drive. The pair of population equations can exhibit multiple dynamical regimes depending on weights and inputs;…
The incoming scalar is perturbed by a Gaussian draw. The accompanying document identifies 0.1 as the standard deviation, so the intended perturbation has mean zero and variance 0.01. Reproducing a trajectory requires the random generator, seed, and draw order as well as this distribution.
The comments describe mutual information minus partition information, but the body multiplies stored Coherence, stored Phi, and 1−Entropy/log₂(vector length). The implementation includes an extra Phi factor absent from the simplified comment. Its entropy field is an average of clipped scalar −p…
The comments describe mutual information minus partition information, but the body multiplies stored Coherence, stored Phi, and 1−Entropy/log₂(vector length). The implementation includes an extra Phi factor absent from the simplified comment. Its entropy field is an average of clipped scalar −p…
The matrix combines a nearest-neighbor ring Laplacian with a diagonal cosine modulation. The ring part is circulant, but the varying diagonal generally breaks that symmetry. Consequently its eigenvalues cannot generally be obtained by simply adding a Fourier-mode ring eigenvalue to a diagonal entry.
For normalized distributions, the sum p log(p/q) measures relative entropy in nats with the file’s natural logarithm. A term with positive p and zero q should make the divergence infinite. The code skips such terms when q is below its cutoff, so it can return a finite value where the mathematical…
Each oscillator advances at its natural frequency and is pulled by the sine of its phase differences with every oscillator. Dividing by N keeps the nominal coupling scale comparable as population size changes. The source initializes phases and frequencies on deterministic index grids despite…
For 0≤λ<1, the geometric weights (1−λ)λⁿ⁻¹ sum to one and mix returns with different lookahead lengths. Small λ emphasizes shorter returns; values near one emphasize longer horizons. A finite stored trajectory requires a terminal or truncation convention, so the infinite series is the reference…
The implementation sums sin(nπx)/n for n=1 through 10. These weighted harmonics produce a periodic scalar feature of period two. The function’s language label names its intended family role; no text representation or language training is performed by this scalar Fourier series.
The body returns exp(z)/(1+exp(z)) with z=wP+b, which is a logistic sigmoid. A softmax over a single scalar would always return one; a two-logit softmax over [z,0] would reproduce this value. Direct exponentiation can overflow for very large positive z, unlike a stable sigmoid implementation.
The body takes sigmoid(w|S|) and multiplies it by 1+0.2sin(arg S). The phase multiplier ranges from 0.8 to 1.2, so the output can exceed one. The source’s phase_alignment placeholder is therefore this specific sinusoidal modulation in the implementation.
The implementation subtracts the vector’s mean, divides by √(population variance+EPSILON_PHI), then applies scalar gain γ and offset β. This controls the scale of a feature vector while preserving relative centered differences. The code uses one gain and one offset for the whole vector rather than…
The source expression adds dx times a sigmoid of the current scalar’s weighted value. The body additionally caps the increment magnitude at 0.2 and clips the final value to the unit interval. These two bounds are part of the implemented transition and affect its response to large inputs.
The body forms increment=Dexp(−F)dt, then returns clamp(0.9Ψ_prev+0.1increment+0.5D). The displayed integral contributes one part of this update, but the decay and extra direct decision term materially change the recurrence. It is a bounded driven accumulator rather than a literal unmodified time…
The magnitude is tanh(αC) and the phase advances as ωt. Under the intended nonnegative C, the magnitude is nonnegative and bounded below one. Keeping the complex value retains phase information for the next stage; taking its magnitude alone would discard that phase.
The distance d=|x′−x_c| enters both a unity score Φ(d) and a Gaussian centered at d=0. The Gaussian favors exact agreement, but Φ(d) favors distance one; at exact agreement Φ(0)=0.5. Their product is therefore not simply two identical measures of closeness and requires its own interpretation.
The update is y_new=0.99y_old+x−x_old. It retains most of the previous y and adds a displacement measured against the history value called x_old. When that value is the oldest element of the forty-four-sample buffer, this is a delayed-displacement accumulator rather than an instantaneous…
The old stored quantity is multiplied by 1−ρ and a new increment is added. When 0<ρ≤1, earlier contributions decay geometrically. This reference uses an arbitrary increment Δφ, whereas the neighboring implemented family specifically uses ρ times its input.
Each application adds one tenth of dx_norm to the current scalar. With a fixed input d, the isolated recurrence has the exact solution xₙ=x₀+0.1nd. This can serve as an update increment, but it has no decay or saturation by itself and should only be described as weight learning when x is actually a…
The displayed expression is the standard coordinate formula combining the inverse metric and first metric derivatives, summed over l. For this file’s metric g=I+φxxᵀ, direct differentiation gives Γᵏᵢⱼ=φxₖδᵢⱼ/(1+φ||x||²). The function instead returns one half of φ(δₖᵢxⱼ+δₖⱼxᵢ), so it does not…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
The model adds an intercept to the sum of each coefficient times its corresponding feature. Applying a logistic transform converts that log-odds score into a value between zero and one. The source uses decimal arithmetic for the linear combination and an isolated floating-point conversion for the…
This reciprocal transform assigns score one to zero state magnitude and approaches zero as magnitude grows. A magnitude equal to φ produces a score of one half. The equation therefore favors lower activity magnitude; the label coherence does not change that operational interpretation.
Here τ is defined to be 1/(2π), approximately 0.159154943. Multiplying an angle in radians by this constant converts it into a fraction of a full turn. This local notation must be kept distinct from the widespread convention τ=2π.
The raw score is the sigmoid of an intercept-plus-feature-weight sum. The implementation then maps that value through stored calibration bins, or leaves it unchanged when no bins exist. A monotone remap preserves ordering, but empirical probability accuracy still requires evaluation on data…
The sigmoid maps every finite real input to (0,1), gives 0.5 at zero, and increases monotonically. Its derivative is σ(x)(1−σ(x)), with maximum slope one quarter at zero. Numerical implementations can avoid overflow for large negative inputs by using a sign-dependent equivalent expression.
For nonnegative magnesium concentration, the denominator is at least one and the factor lies between zero and one. Increasing voltage reduces the exponential term and increases the unblocked fraction. The coefficients assume the voltage and concentration units stated in the source.
The first quarter-weighted component is zero and all remaining component scores are 100. The weighted sum is therefore 75, which the source test assigns to Yellow. This illustrates how one component can reduce the final score even when every other component is maximal.
The derivative with respect to y is −2y+2x, which vanishes at y=x. The second derivative is −2, so this point is the unique global maximizer for real y. This optimizer location differs from the x² returned by the function.
This score averages cos(k_m,i), producing a value in [−1,1]. It measures phase alignment with the chosen zero-angle axis: perfectly aligned phases at zero give 1, while perfectly aligned phases at π/2 give 0. It therefore differs from the phase-origin-invariant modulus commonly used to measure…
The global value is the arithmetic mean of the sixteen local scores. If each local value is in (0,1], the mean is also in that range. Averaging summarizes the marginal scores, but no pairwise interaction or integration term is introduced by the average itself.
There are n(n−1)/2 unordered pairs among n agents, so multiplying their sum by 2/[n(n−1)] yields the mean pairwise cosine similarity. For valid cosine inputs the result lies in [−1,1]. It summarizes representational alignment, including anticorrelation, rather than directly measuring collective…
For a scalar parameter, Fisher information is the expected square of the derivative of log likelihood. The implementation averages squares of the supplied scores. It estimates that information only when the inputs actually are likelihood-score samples drawn from the intended model; arbitrary scalar…
The update stores an increment equal to 0.02 times the sum of normalized input and utility. Repeated updates accumulate their history in a single scalar, so different histories with the same accumulated sum are indistinguishable. No forgetting factor appears in this individual rule.
The local sensitivity to x is the current y value, and the sensitivity to y is the current x value. The backward pass multiplies each by the incoming gradient and accumulates the result. This is the product rule applied to one node of a computational graph.
The identity subtracts joint entropy from the sum of the two marginal entropies. It measures statistical dependence when pxy is a normalized joint distribution with px and py as its marginals. The function trusts its three supplied arrays and inherits the entropy cutoff, so inconsistent inputs need…
The output averages the current state and the logistic transform of dx_norm. A constant input drives the state toward σ(dx_norm), and deviations halve on each update. This expression does not estimate mutual information: that quantity requires a joint probability distribution or an explicitly…