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 formula sums all 16×16 state coordinates, divides by 256, and takes tanh. It is therefore a monotone transform of their arithmetic mean, with range (−1,1) for finite inputs. It does not compare partitions, measure component variance, or establish a causal-integration property; the aggregate…
The formula sums all 16×16 state coordinates, divides by 256, and takes tanh. It is therefore a monotone transform of their arithmetic mean, with range (−1,1) for finite inputs. It does not compare partitions, measure component variance, or establish a causal-integration property; the aggregate…
The formula sums all 16×16 state coordinates, divides by 256, and takes tanh. It is therefore a monotone transform of their arithmetic mean, with range (−1,1) for finite inputs. It does not compare partitions, measure component variance, or establish a causal-integration property; the aggregate…
The formula sums all 16×16 state coordinates, divides by 256, and takes tanh. It is therefore a monotone transform of their arithmetic mean, with range (−1,1) for finite inputs. It does not compare partitions, measure component variance, or establish a causal-integration property; the aggregate…
The radian angle 2π/φ² equals approximately 2.39996323 radians, or 137.507764 degrees. The displayed degree value is obtained by converting the radian expression. Its presence in a model specifies an angular spacing; it does not establish an optimal architecture without an objective and comparison.
The radian angle 2π/φ² equals approximately 2.39996323 radians, or 137.507764 degrees. The displayed degree value is obtained by converting the radian expression. Its presence in a model specifies an angular spacing; it does not establish an optimal architecture without an objective and comparison.
This defines the golden ratio as the positive root of φ²=φ+1. It is approximately 1.618033988749895. The manuscript uses it as a frequency, coefficient scale, and proposed limiting value; those uses require their own dynamical justification.
The golden ratio is the positive root of φ²=φ+1, approximately 1.618033988749895. This source uses it to organize frequencies, weights, and scales. That choice is distinct from IIT’s symbol Φ and does not automatically confer stability, harmony, or an empirically validated cognitive property.
The golden ratio is the positive root of φ²=φ+1, approximately 1.618033988749895. This source uses it to organize frequencies, weights, and scales. That choice is distinct from IIT’s symbol Φ and does not automatically confer stability, harmony, or an empirically validated cognitive property.
The event time is the first eligible window in the full observation record whose persistence indicator is one. Because the search does not start at the declaration time, it can detect a change that precedes, coincides with, or follows a declaration. Eligibility T_W must specify missing-data…
The source chooses the constant input to be γφ. Substituting this choice into C*=I*/γ makes C*=φ. This is a parameter choice that targets a value, not an independent derivation that arbitrary inputs generate the same value.
Setting the C derivative to zero produces this relation between E*, C*, L*, and time. If those starred values are constants, the oscillatory term generally still changes with time, so a single constant balance cannot hold for all times unless its amplitude vanishes or another term compensates. It…
A candidate constant energy state requires the consumption γC* to match the modulated input at every instant. With fixed nonzero I*, the cosine varies, so averaging this relation is different from solving the original nonautonomous equation. The distinction matters for the claimed convergence…
Subtracting declaration time from the independently detected change time gives a signed lag. Positive lag means change follows declaration; negative lag means it precedes declaration; zero means coincidence at the observation resolution. When either event is unobserved, a numerical lag is not…
The state retains 99% of its previous energy value and takes 1% of the absolute sum of the current components. Opposite-sign components can cancel before the absolute value, so this is not the Euclidean norm or sum of absolute activities. With nonnegative initialization it stays nonnegative and…
The state retains 99% of its previous energy value and takes 1% of the absolute sum of the current components. Opposite-sign components can cancel before the absolute value, so this is not the Euclidean norm or sum of absolute activities. With nonnegative initialization it stays nonnegative and…
The state retains 99% of its previous energy value and takes 1% of the absolute sum of the current components. Opposite-sign components can cancel before the absolute value, so this is not the Euclidean norm or sum of absolute activities. With nonnegative initialization it stays nonnegative and…
The state retains 99% of its previous energy value and takes 1% of the absolute sum of the current components. Opposite-sign components can cancel before the absolute value, so this is not the Euclidean norm or sum of absolute activities. With nonnegative initialization it stays nonnegative and…
With δ>0 and a positive Fibonacci denominator, L relaxes toward C at a rate scaled by Fₙ/(Fₙ+Fₙ₋₁). For a fixed C and fixed n, its exact solution is an exponential approach to C. If C changes, the equation acts as a lagging filter of that trajectory rather than an independent proof of learning…
The next state is a linear transformation of the current state plus independent zero-mean Gaussian noise with identity covariance. At stationarity, the covariance solves the discrete Lyapunov equation shown alongside it. The benchmark scales W to spectral radius 0.9, which ensures a unique finite…
Both displacement vectors point outward from the center checkpoint: one toward t−k and the other toward t+k. Their normalized inner product measures the angle between those directions. Straight passage through the center gives −1, a right-angle turn gives 0, and return along the same side can give…
This version transforms its nonnegative activity accumulator through tanh, increasing from zero toward one as the accumulator grows. It differs from the older reciprocal-norm local score, which decreases with activity magnitude. Neither name can replace the actual formula when comparing generations.
This version transforms its nonnegative activity accumulator through tanh, increasing from zero toward one as the accumulator grows. It differs from the older reciprocal-norm local score, which decreases with activity magnitude. Neither name can replace the actual formula when comparing generations.
This version transforms its nonnegative activity accumulator through tanh, increasing from zero toward one as the accumulator grows. It differs from the older reciprocal-norm local score, which decreases with activity magnitude. Neither name can replace the actual formula when comparing generations.
This version transforms its nonnegative activity accumulator through tanh, increasing from zero toward one as the accumulator grows. It differs from the older reciprocal-norm local score, which decreases with activity magnitude. Neither name can replace the actual formula when comparing generations.
A pure sine has zero average over a whole number of periods and zero limiting time average over arbitrarily long intervals. The averaging interval and convention matter for a finite sample. Multiplying the sine by a changing, correlated amplitude can give a product with a nonzero average.
If two interpretations assign exactly the same probability to every observation in the study, the likelihood ratio for any observed record is one. Those data therefore supply no likelihood evidence favoring one interpretation over the other. Distinguishing them requires an additional observable,…
This choice takes Zₜ to be the effective update matrix Uₜ. It makes path geometry insensitive to reciprocal scaling of its two rank-one factors. It still describes parameter-operator change and does not by itself measure behavior or a declaration.
Each sample variance is weighted by its degrees of freedom, the weighted variances are averaged, and the square root returns the original measurement units. This is the conventional equal-variance pooled estimator used in Cohen’s d. Both groups require more than one observation for the displayed…
The formula shown is the pooled standard deviation, but substituting the written values gives approximately 0.0424265, not 0.0300. The denominator 1998 correctly adds the two degrees of freedom; the final square root was evaluated incorrectly in the source. The recovered CSV audit, using unrounded…
Dividing φ²=φ+1 by φ gives 1/φ=φ−1. Both sides are approximately 0.618033988749895. A rounded value such as 0.618 represents this constant, not a universal threshold for a measured system.
Multiplying one factor by a nonzero scalar and dividing the other by that scalar cancels in their outer product. The individual vectors can therefore move in magnitude while the effective weight update remains identical. This is why an operator-based distance avoids a basic ambiguity in factor-only…
The final logged evaluation loss is compared with the first logged value through 100(1−final/initial). The supplied values give 63.6935429588%, consistent with the recovered saved arrays. This describes the recorded loss series from the one inspected training run.
Dividing the rounded mean difference 0.6616 by the source’s incorrect 0.0300 yields the reported value near 22.06. Using the correctly pooled standard deviation changes the standardized effect substantially. The recovered CSV audit gives d≈15.5983482 from the unrounded sample summaries.
The mean difference is divided by its estimated standard error, using the sum of the two sample-mean variances. The source’s value near 348.79 agrees with the recovered descriptive calculation. Its magnitude does not remove the need to account for serial dependence, changing sample cadence, and the…