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 ↗
Assuming a harmonic displacement, acceleration is −ω²x and force is mass times acceleration. With mass fixed to one, the function returns −AngularFrequency²×x. Physical force units and measured acceleration are not supplied; the operational result is a linear restoring term.
The bias is the ordinary mean of two numbers in [0,1), so it also lies in that interval. Because phases wrap at one turn, this average is sensitive to the chosen cut: phases 0.99 and 0.01 average to 0.50 even though they are close on the circle. That matters when the value controls a gate threshold.
The reference ∇·(D∇x) is a diffusion operator acting on a spatial field. The body returns −0.1x, based on a harmonic-mode analogy, without a grid or neighboring values. That result is linear damping of a scalar; its equivalence to diffusion holds only for a specifically identified spatial eigenmode…
For U(x,y)=−y²+2xy, the maximizing location is y=x. The function returns x², which is the maximum utility value U(x,x), rather than the argmax location. The distinction is substantive: at x=2 the location is two and the returned value is four.
The aggregate adds the eighty-eight potential values and divides by their count. Because each P is clipped to [0,1], their arithmetic mean also lies in [0,1]. The source calls this output consciousness; its operational meaning in the displayed equations is mean potential across the units.
This expression returns the arithmetic mean of the binding_field array. Its interpretation and range depend on how the 174 core and 200 supplemental values enter that array and whether additional transformations occur. Because the supplemental formula can produce negative values, a [0,1] bound does…
For each order α>1, the expression converts a valid accumulated Rényi-divergence privacy bound into an (ε,δ) bound, then selects the smallest candidate. It is the basic conversion bound associated with Mironov’s analysis. The comment’s further attribution to the current Google accountant is…
The numerator adds utility to the current state, the denominator attenuates that sum by 1+|utility|, and the final clamp restricts the output to [0,1]. For nonnegative utility, the un-clipped expression is a weighted average of x and 1. The expression contains no likelihood, prior distribution, or…
The posterior is proportional to the likelihood times the prior, with the evidence providing normalization. This formula updates a distribution over hypotheses using observed data. The neighboring scalar clamp expression does not supply the probability distributions needed to implement it.
The two terms are the uncertainty of a Bernoulli outcome with probabilities p and 1−p. With natural logarithms it is measured in nats, is zero at the deterministic endpoints by continuity, and has maximum log2 at p=0.5. The input must lie in [0,1].
A weighted sum of prior binary states is compared with a threshold through a step function H. The result is a binary next state. The exact convention at equality and the direction of each stored weight index must be supplied by the implementation.
Half the result comes from the weighted family update. The other half is an interpolant between the previous and current states, with weights 2−φ and φ−1; these weights are positive and sum to one. The displayed term is therefore interpolation within the two prior values, although the source calls…
The function multiplies the current unity score, reciprocal-variance stability, rescaled lag-one correlation, and square root of the variance-based integration proxy. With factors in [0,1], a low factor suppresses the total rather than being compensated by a high one. These are related summaries of…
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 body computes Φ(mean)/(1+population variance) for at least two entries. It rewards a mean near one and uniform component values. The comment about a minimum over mutual-information partitions is not implemented here: there is no joint distribution, cut enumeration, or causal transition model.
The body computes Φ(mean)/(1+population variance) for at least two entries. It rewards a mean near one and uniform component values. The comment about a minimum over mutual-information partitions is not implemented here: there is no joint distribution, cut enumeration, or causal transition model.
This helper first averages all components and then applies the scalar unity score. Component variance does not enter this function, so vectors with the same mean receive the same score. Empty input returns 0.5 by convention; the Go function with a similar name also penalizes variance and returns…
The function adds squared deviation from a target Ω*, a weighted squared coherence shortfall, and a linear free-energy term. Nonnegativity requires suitable coefficients and F≥0. Calling it a Lyapunov function additionally requires showing that it decreases along the actual coupled dynamics and is…
The code builds a symmetric ring with position-dependent edge weights and a modulated diagonal, then reports this independent trigonometric expression as its eigenvalues. Such a varying-weight matrix is not a uniform circulant ring. The independently reconstructed default matrix disagrees by about…
The first two terms are valid ring-Laplacian Fourier eigenvalues. Adding the position-varying diagonal cosine term does not in general produce eigenvalues of their sum. Independently reconstructing the default matrix and applying NumPy eigvalsh gives maximum sorted disagreement about 0.06062893;…
The mixing coefficient is 0.01(φ−1)≈0.00618034. The state takes a little over six tenths of one percent of the gap to the supplied stability value on each update. A fixed stability target is approached geometrically; the formula does not independently establish that the target is a valid measure of…
The drive combines three terms: input is attenuated by 1−x, the velocity-like state contributes with weight 1.2, and coupling state c contributes with weight 0.6. If x is near one, the direct input term is suppressed. The scalar equation’s actual connection to other units depends on how c is…
The comment combines memory, an attention-like exponential, and a time integral. The body instead computes a mean unity score across family activations, builds Qᵢ=aᵢcos phaseᵢ and Kᵢ=aᵢsin phaseᵢ, and multiplies mean(V) by min(exp(Q·K/√d),10¹⁰) and that score. It never reads Memory or TimeSteps,…
The comment combines memory, an attention-like exponential, and a time integral. The body instead computes a mean unity score across family activations, builds Qᵢ=aᵢcos phaseᵢ and Kᵢ=aᵢsin phaseᵢ, and multiplies mean(V) by min(exp(Q·K/√d),10¹⁰) and that score. It never reads Memory or TimeSteps,…
The comment combines memory, an attention-like exponential, and a time integral. The body instead computes a mean unity score across family activations, builds Qᵢ=aᵢcos phaseᵢ and Kᵢ=aᵢsin phaseᵢ, and multiplies mean(V) by min(exp(Q·K/√d),10¹⁰) and that score. It never reads Memory or TimeSteps,…
The objective adds the project’s surprise, uncertainty, and penalty terms and subtracts value. If the system minimizes Ω, it therefore favors smaller changes and penalties and larger value, subject to the chosen coefficients. The labels express the project’s intended roles; the total is a…
This rule subtracts 0.05 times the absolute input. Applied in isolation, it never increases x and can decrease it without bound under a persistently nonzero input. It supplies a numerical penalty; an actual compression claim also needs an encoding, output size, decoding procedure, and fidelity…
Completing the square gives U(x,y)=x²−(y−x)². For a fixed x, the utility decreases with squared distance from y=x and has a unique maximum over real y at that point. This supplies the exact optimization problem used to explain the Athena signature.
The next state keeps 95% of x and incorporates 5% of dx_norm. It converges to a constant input with error factor 0.95 per update. It becomes a network consensus mechanism only if the supplied input is appropriately constructed from other agents and the resulting network weights satisfy the relevant…
The update is 0.9x+0.1d, with d=dx_norm. It retains 90% of the previous scalar state and moves 10% toward the supplied target. For a fixed d, the error after n updates is 0.9ⁿ(x₀−d), so the state converges geometrically to d.
The derivative x′ is the instantaneous rate of change, and F specifies how that rate depends on state and time. An Euler approximation would use x_next=x+dt·F(x,t). The neighboring project family is a particular scalar relaxation; this general ODE notation does not identify its physical meaning.
Each diagonal value is a cosine evaluated at a coordinate index divided by 10.6. The body uses indices i+1 from one through sixteen. Because those values vary by position, this diagonal matrix generally does not share eigenvectors with the cyclic neighbor matrix.
The dot product divided by both vector lengths measures directional alignment, producing a value in [−1,1] for nonzero real vectors. A value of 1 means positive collinearity, including vectors with different magnitudes; zero means orthogonality. It compares the stored numerical representations and…
Each agent loses activity at rate λSᵢ and receives weighted, bounded tanh contributions from other agents, modulated by their pairwise score. The decay competes with the network feedback. Stability requires assumptions about coupling strengths, λ, and the score dynamics; the existence of a decay…
The comment describes adding dt times the weighted state sum. The body actually uses a_next=a+dt(Ca−a), which is relaxation toward the row-weighted average. For nonnegative row-stochastic C and dt in [0,1], this preserves the convex range of the input activations.
Expanding the increment gives c_new=[1+0.01(0.8P−k_c)]c+0.01(0.8P+k_c). For fixed P and k_c, this is an affine scalar recurrence whose stability depends on the magnitude of its multiplier being less than one. The equation includes no clamp for c, so bounded P alone does not guarantee bounded…
The sum includes indices at distance at most three from m, excludes m itself, and clips the range at the ends of the array. It therefore includes fewer neighbors near a boundary than in the interior. This finite-range rule helps explain why row sums vary across the matrix.
The displayed candidate is the first line of a multiline expression that adds a damped diagonal term and a sum of nearby couplings. Such a row sum is not generally an eigenvalue of a nonuniform matrix. The body also uses index m in its estimate but m+1 in the actual diagonal construction, so even a…
The function assigns this combination of coupling parameters directly to lambda_1. It does not extract the smallest eigenvalue of the constructed full 44-by-44 matrix in this method. It should therefore be shown as a declared estimate rather than an independently solved spectral endpoint.
The method assigns a linear combination of coupling parameters to lambda_44. This is separate from calculating the actual largest eigenvalue of the full matrix. The parameter coefficients are part of the project’s estimate and require validation before use as spectral bounds.
The body uses carrying capacity K=1 and growth rate r=0.5, returning 0.5x(1−x). This is a rate-shaped scalar feature, positive between zero and one and zero at both endpoints. A growth trajectory would additionally apply a time integration or recurrence to that rate.
A gate flips when its index modulo 1000 falls below the threshold 1000×bias. The next bit is the XOR of its old value, its input bit, and that deterministic mask bit. With five groups of 1000 gates, the threshold mask repeats across the five groups; differences can still come from their old states…
The matrix places cos(θₖ) on its diagonal and 0.1sin(θₖ) on a cyclic neighbor diagonal, with zeros elsewhere. Multiplication combines each component with its cyclic neighbor. Although called a rotation in the source, this is generally not an orthogonal rotation: when cos(θₖ)=0, it scales a cyclic…
A narrow positive Gaussian models local excitation and a broader negative Gaussian models inhibition. The body places 2σ² in both exponential denominators, while the comment displays σ², so the code uses the usual Gaussian width convention. The sign and reach of the net kernel depend on both…
The intermediate value is exp(iωx)sin(x), and the function then takes its complex magnitude. Since the exponential has magnitude one, the returned result is exactly |sin(x)|. The phase factor is discarded, so this helper does not preserve the advertised complex oscillation in its output.
This family forms a weighted average of the current state and utility, with weights 0.9 and 0.1. A constant utility u is a stable fixed point, and deviations from it shrink by a factor 0.9 on each update. If both inputs lie in [0,1], the next state also lies in that interval.
For a nonzero denominator y, the sensitivities of x/y are 1/y and −x/y². The code directly uses these expressions and has no denominator regularization. A zero denominator therefore remains outside the mathematical domain and can produce nonfinite values.