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 ↗
This current uses the same conductance-times-driving-force structure as the AMPA expression, multiplied by B(V). The additional factor reduces current under magnesium block and changes with membrane voltage. The code separately tracks a rising variable and a slowly decaying synaptic state.
Each agent adds a sum of differences between neighbor states and its own state. Coupling weights, the neighbor graph, and step-size restrictions determine whether agents converge to consensus. With unrestricted unit weights, the written sum can overshoot and does not guarantee averaging behavior.
The logarithmic concentration ratio balances chemical concentration drive against electrical potential for an ion of charge number z. The helper uses a fixed temperature and converts its volt result to millivolts. Concentrations must be positive and z nonzero; this single-ion equilibrium expression…
The field loses activity through a decay term and gains input through a spatially weighted sum of firing responses plus external drive. The implementation samples integer positions, sums all pairwise kernel contributions, and divides by N. This is a particular normalized discrete network model;…
The multiplier b decreases as the squared Euclidean norm of Ψ grows: b=1 at the zero vector and approaches zero as the norm becomes large. If b is computed from the same vector it rescales, the output norm is r/(1+r²/φ), whose maximum is √φ/2 at r=√φ. This is a radial contraction rule with a…
For probability distributions on a line, Wasserstein-1 distance is the integral of the absolute difference of their cumulative distributions. The function normalizes its input masses, computes cumulative sums, and returns their mean absolute difference. This corresponds to a particular equal-grid…
The state moves in the direction of utility−x, with step magnitude 0.2|utility−x|/(1+|utility−x|). For a fixed utility, the error is multiplied by 1−0.2/(1+|error|), which lies between 0.8 and 1; the update reduces that error without crossing the target. This is a target-tracking rule, not the…
Row i specifies which source layers influence target layer i, with column j supplying the source. The constructor normalizes each nonzero row to sum to one. This convention determines the direction of matrix multiplication and should be kept distinct from a transpose convention.
The function f converts a relative displacement into a pairwise contribution, and the sum aggregates contributions from other agents. To interpret the displayed result as motion, the source must specify whether it is a position, velocity, force, or increment. The adjacent scalar target tracker…
The complex mean of unit phase vectors has magnitude r between zero and one and phase ψ. The implementation returns the magnitude, which reaches one when all phases align and is unchanged by a common phase shift. This differs from the older project’s mean cosine score, which depends on the chosen…
For x≠1 the derivative has the displayed signed reciprocal-square form. At x=1 the original function has unequal one-sided derivatives and no ordinary derivative. The C++ compute_phi_grad function below this comment actually returns the derivative of the smoothed formula, so callers need to…
Utility first passes through softsign, making its contribution lie strictly between −0.15 and 0.15; the error term is then subtracted linearly. The combined increment can therefore be unbounded if ed_error is unbounded. The formula defines a state update, while a policy additionally requires an…
The function returns −ω²x, the acceleration term of a harmonic oscillator with displacement x. It does not evaluate the full displayed residual ∂²x/∂t²+ω²x, which would vanish for an exact oscillator solution. No temporal differentiation or spatial wave propagation is performed inside this helper.
The matrix is I+φxxᵀ. For any nonzero vector v, vᵀgv=||v||²+φ(x·v)²>0, so it is positive definite for real finite x. It stretches lengths more strongly along x while leaving directions orthogonal to x unchanged; its eigenvalues are 1+φ||x||² along x and 1 in orthogonal directions.
The exponential β_n decreases as voltage rises and multiplies n in the gate’s closing term. At a fixed voltage, α_n and β_n together yield equilibrium n=α_n/(α_n+β_n) and relaxation time 1/(α_n+β_n). The expression is one component of the coupled membrane model.
The rate α_n contributes α_n(1−n) to potassium-gate opening. The expression has a removable singularity at V=−55 mV, with limit 0.1 per millisecond. The implementation supplies that limit explicitly near the singular point.
The potential retains 95% of its old value, receives the product F_in y, and loses 0.01P². The clamp then bounds the stored result between zero and one. The product can inject or remove potential depending on the signs of input and y, while the square always subtracts.
The derivative with respect to x is p x^(p−1) when the real-valued power is defined and differentiable. The helper treats p as a constant and does not compute an exponent gradient. Negative bases with noninteger p and some zero-base cases require explicit domain handling.
The code subtracts √(1−α) times its predicted noise, divides by √α, and adds σ times fresh noise. It requires 0<α≤1. Under the usual DDPM noise-prediction convention, the reverse mean instead uses (1−αₜ)/√(1−ᾱₜ) as the predicted-noise coefficient; this helper lacks ᾱ and should be described as…
Inputs below zero become zero, inputs above one become one, and values already inside [0,1] remain unchanged. The map is continuous and nonexpansive, but it has derivative changes at the two boundaries and zero derivative outside the interval. It enforces a storage bound, not a calibrated…
The function returns 3.8x(1−x). On [0,1] it is nonnegative with maximum 0.95 at x=0.5, so that interval maps into itself under the isolated recurrence. The network supplies a sine input, which can be negative; the familiar [0,1] logistic-map behavior does not automatically apply to those inputs.
Each component loses φgᵢ² and receives γ times the total squared coupling magnitude. Summing across components gives (nγ−φ)Σgⱼ², which shows how dimension affects the total drift. The subsequent FixedPoint helper only iterates this flow a fixed number of times and does not verify that the…
Squaring dx_norm makes equal positive and negative inputs incur the same cost. For λ≥0, the penalty is nonnegative and grows quadratically, so doubling input magnitude quadruples the cost. λ determines how strongly this contribution competes with the other objective terms.
The query is hashed into the same scalar domain, expanded into sixteen basis values, and compared with the stored coefficient vector using a dot product. Contributions with matching signs add to the score, while opposite signs subtract. The result is a numerical retrieval score and is not a…
The net change is 0.05 times utility minus ed_error. Positive utility exceeding error increases the state; equal values leave it unchanged. The formula is a scalar control rule and does not specify a coding rate, a distortion distribution, or the constrained minimization that defines a…
ReLU returns x when positive and zero otherwise. Away from zero its derivative is one on the positive side and zero on the negative side. At the nondifferentiable origin the implementation chooses the conventional subgradient value zero.
The Laplacian ∇²x describes spatial diffusion and f(x) describes a local reaction. A numerical implementation must represent neighboring spatial positions and specify boundary conditions. The project scalar softsign update does not include this Laplacian, so the PDE is contextual rather than an…
The actual scalar update is 0.95x+0.05 softsign(dx_norm). It smooths a bounded transform of the input, approaching that transform when the input is constant. No spatial neighbors, Laplacian, or diffusion coefficient appear in this operation; reaction-diffusion is the family’s motivating label, not…
The angle at index k is a full turn divided by φᵏ. Successive angles shrink by the factor 1/φ. This sequence differs from the angle θₖ=2πk/φ used in this document’s kernel section, so the two formulas are versioned local definitions rather than interchangeable rotations.
The denominator adds one to a sum of squared discrepancies across the selected sites. The score is one when every discrepancy is zero and decreases as their total squared magnitude grows. Its calibration changes with site count and discrepancy scale, so the name C5000 identifies its project role…
The reference expression combines derivatives and products of connection coefficients to measure curvature. The body does not perform those operations: it returns φ⁻¹(l−i)(j−k)/n², which depends on dimension and index labels but not on the coordinate values. That surrogate does not establish the…
The reference contraction R=gⁱʲRᵢⱼ would require an inverse metric and a Ricci tensor. The implementation instead returns −φn(n−1)/(2n²) for nonempty input, a constant determined solely by dimension. It also differs by a factor 1/n² from its nearby simplified comment, so this returned score should…
The reference contraction R=gⁱʲRᵢⱼ would require an inverse metric and a Ricci tensor. The implementation instead returns −φn(n−1)/(2n²) for nonempty input, a constant determined solely by dimension. It also differs by a factor 1/n² from its nearby simplified comment, so this returned score should…
Dividing an unsigned 32-bit hash by its maximum possible value maps it into [0,1]. The result has only 2³² possible exact values before floating-point rounding, including both endpoints. This is a deterministic scalar coordinate for a string hash, not a continuous semantic embedding.
Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these stages with maximum subtraction for numerical stability. Compatible nonempty query/key widths and matching key/value counts…
Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these stages with maximum subtraction for numerical stability. Compatible nonempty query/key widths and matching key/value counts…
Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these stages with maximum subtraction for numerical stability. Compatible nonempty query/key widths and matching key/value counts…
Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these stages with maximum subtraction for numerical stability. Compatible nonempty query/key widths and matching key/value counts…
Query-key dot products are divided by √dₖ, row-wise softmax converts them into weights that sum to one, and those weights average the value vectors. The code implements these stages with maximum subtraction for numerical stability. Compatible nonempty query/key widths and matching key/value counts…
Substituting activation one into the unity-proximity score gives one exactly. This is the score’s selected reference point. The source’s phrase perfect consciousness is an interpretation of that maximum, not an independently measured endpoint.
The raw matrix starts with diagonal values one, assigning each layer an explicit self-contribution. The constructor then divides every row by its row sum, so the stored diagonal is generally smaller than one. The value one describes initialization before normalization.
The mathematical entropy sums −p log p over a normalized nonnegative distribution, with a zero contribution at p=0. The function uses log₂, so its output is in bits, but skips probabilities at or below EPSILON_PHI and near one. It does not validate normalization, making it a truncated entropy…
Each existing entry moves one slot toward the beginning of the buffer and the current x is inserted at the final slot. This keeps the most recent forty-four samples in order after the update. When the oldest entry is used elsewhere in the tick, whether it is read before or after shifting determines…
The comment gives log(x) and derivative 1/x, but the body evaluates log(x+EPSILON) and derivative 1/(x+EPSILON). This positive shift changes both the value and the domain to x+EPSILON>0. It mitigates a zero input but does not make every negative input valid.
The logistic derivative is z(1−z), where z is the forward sigmoid output. Its maximum is one quarter at z=0.5, and it decreases toward zero in either saturated tail. The primitive applies this local sensitivity through the chain rule.
Potential P and coupling parameter k_c set the sigmoid argument, and adding 0.05 creates a positive floor. For finite inputs, the gate lies strictly between 0.05 and 1.05, so it can exceed one. Increasing P increases the gate, while increasing k_c decreases it.
The comment proposes φδₖᵢxⱼ+φδₖⱼxᵢ, and the body multiplies that sum by 0.5. This index-dependent linear expression differs from the actual Levi-Civita connection of the declared metric. The extra factor and the metric mismatch should remain visible rather than treating the function name as…
Exponentiating −Cᵢⱼ/ε turns each transport cost into a positive kernel weight, with smaller costs receiving larger weights. The following alternating row and column scalings seek the supplied marginals. The function finally returns transport cost for the resulting plan; it does not add the entropy…