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 ↗
Dividing 14.2 by 2.8 gives approximately 5.0714. This is a ratio of two rounded marginal percentages. It is distinct from a percentage-point difference, an odds ratio, or a paired-outcome effect, each of which uses a different calculation.
The baseline is set equal to the representation recorded at the declaration time. Distances from this baseline describe subsequent displacement from that specific state. Because the anchor depends on declaration timing, it should not be the only basis for an independent test of whether change…
Two of the operators are identities, one replaces every input by the constant one, and the last takes a reciprocal. The reciprocal requires a nonzero input when used alone. In the displayed sequential chain it receives the constant one, so its potential singularity is removed by the earlier reset.
The origin distance compares the present representation to a fixed historical baseline. The current distance compares it to the reference extracted from the present system state. A changing but accurately tracked system can have a large origin displacement and a small current mismatch, so the two…
Composition acts from right to left. The increment and decrement cancel, the identity operations preserve the current value, and f₅ then resets it to one; the following identity and reciprocal leave one unchanged. The final output is one for every ordinary finite real initial input, so the chain…
Applying softmax to [3,1,0.5,0.1] gives approximately [0.785890,0.106359,0.064510,0.043242]. The source’s [0.73,0.10,0.06,0.04] sums to 0.93 and is not a correctly normalized result. Its qualitative point that finite unmasked logits all receive positive probability is correct, but the displayed…
Subtracting one from both sides gives error_next=a×error. For 0<a<1, the positive error shrinks geometrically but remains nonzero at every finite step when initialized above one. This supplies an ordinary nonconscious dynamical example of persistent finite-time discrepancy with eventual convergence.
The average recurrence has fixed points at one and minus one half. Substituting either value into F(z) returns that value. The presence of two fixed points already rules out a single global destination for every allowed real starting state.
P names the existing program or codebase at the repair step under consideration. It stays fixed while different candidate programs P′ are compared, so the change-cost term C(P′−P) measures each proposal relative to the same starting code. In the recursive update P_(t+1)=R(P_t,D_t), P_t is this…
P′ names one proposed modified program considered by the repair objective. The prime distinguishes a candidate from the current program P; it does not denote a derivative. In the central formula, the search varies P′, measures its remaining bug loss B(P′,D), and penalizes its change from P through…
The fractional part of the phase sum lies in [0,1); subtracting one half centers the bias in [−0.5,0.5). This formula differs from the arithmetic mean of phases in the earlier SEFERIM document. It has a discontinuity when the sum crosses an integer and should be kept as a separate version.
The source associates δ=0.013618 with approximately 1/φ³. These numbers are not close: 1/φ³≈0.2360679775. Treating the decimal as the actual increment gives a rational rotation with exact period 500000 in ideal arithmetic, so both the approximation and an aperiodicity claim require correction.
This conditional returns one when the centered bias is positive and zero otherwise. The result is a single shared mask bit in this version’s gate update, unlike the earlier index-dependent mask. It is a deterministic threshold rule, not a probability of a gate flip.
The written DNA increment is rational, while 1/φ is irrational as an exact real number. Their ideal pair does not exactly repeat because of the irrational component, but the claim δ≈1/φ³ is wrong and any finite-precision deterministic computer state has only finitely many representable…
The expression computes one minus the ratio of the later window mean to the earlier window mean, then converts to percent. With the supplied means it gives about 46.52465%. This is a reduction in the selected average gradient norm, not a percentage gain in capability or a replicated effect across…
The expression computes one minus the ratio of the later window mean to the earlier window mean, then converts to percent. With the supplied means it gives about 46.52465%. This is a reduction in the selected average gradient norm, not a percentage gain in capability or a replicated effect across…
The filter is evaluated at zero and five positive thresholds ranging from 10⁻⁴ to 0.005. Increasing the threshold excludes more small-displacement comparisons. The selected peak can move as this eligibility rule changes, which is why the source reports the threshold alongside any preferred…
Bₜ names the behavior measured from the model saved at checkpoint t. To use it in the proposed study, the task, prompts, outcomes, and evaluation procedure must be fixed. A saved weight matrix by itself does not provide this behavioral observation.
The first transition allows the outer process L to depend on x, while the second allows x to depend on L. This notation makes the proposed two-way path explicit. Actual causal coupling requires those dependencies to be operative and testable; a function signature can include an argument that its…
The tuple separates four components of a model instance at time t: learned parameters, persistent memory, runtime state or context, and observation records. This is a bookkeeping convention that makes it possible to specify which component changed. It does not imply that every component is directly…
The average uses a symmetric window of w observations around time t. For odd w, there are (w−1)/2 samples on each side and one center sample. Because future samples enter the window, the smoothed series is a retrospective descriptive summary rather than an immediately available online detector.
The average uses a symmetric window of w observations around time t. For odd w, there are (w−1)/2 samples on each side and one center sample. Because future samples enter the window, the smoothed series is a retrospective descriptive summary rather than an immediately available online detector.
The inequality says the recorded value at the next time differs from the current one. Whether that difference is meaningful depends on measurement precision, the distance or norm, and the components being compared. A difference alone does not establish persistence, causality, or a particular…
The bend statistic is evaluated with lags 5, 10, and 15 on each side of a center checkpoint. Larger lags compare broader segments of the path. These are sensitivity settings applied to the same training run, rather than separate runs.
Summing the retained contributions q, λq, λ²q, and so on gives q(1−λⁿ)/(1−λ). For |λ|<1 this tends to q/(1−λ). The denominator must be nonzero; at λ=1 the recurrence instead accumulates linearly.
The map ρ produces a reference measurement from the same system state. To make d(z,r) meaningful, r and z must be comparable in a declared common space. Independence here concerns the measurement definition and validation, rather than requiring r to be statistically unrelated to the model.
An independently specified detector is applied to the observations available up to time t. The indicator records whether its criterion is satisfied, and t_D is the first time this happens. If no qualifying event is observed, t_D is missing or censored; it should not silently be recorded as time…
This variable scores a grounded declaration concerning the independently evaluated behavior Bₜ. The declaration measurement and behavior measurement must refer to the same model instance and checkpoint. The notation proposes a target observable; it does not supply actual declaration observations.
The quantity measures how far a selected state or representation has moved from its declared baseline. Defining the baseline independently is essential if the same quantity will be used to locate a transition. The distance also needs a norm, scaling convention, and handling of parameterization…
This version compares zₜ with the current reference rₜ and separately with r at declaration time. The fixed-reference distance can remain large even when the current representation accurately tracks the current reference. The later manuscript revises the event-time design, so this earlier baseline…
This earlier definition searches only after t_D for the first window of persistent discrepancy. It therefore cannot discover a qualifying change that began before declaration and, by construction, makes every found lag positive. The final manuscript replaces that restriction with an independent…
The outer product bₜaₜᵀ forms a rank-at-most-one matrix, and the scalar s sets its contribution to the model weight update. The pinned study uses s=64. Comparing this effective matrix describes the implemented linear operator more directly than comparing one factor alone, because different factor…
The outer product bₜaₜᵀ forms a rank-at-most-one matrix, and the scalar s sets its contribution to the model weight update. The pinned study uses s=64. Comparing this effective matrix describes the implemented linear operator more directly than comparing one factor alone, because different factor…
Subtracting the current evaluation loss from the loss ten steps earlier gives a positive number when loss has fallen. It is an absolute change in loss units, not a percentage and not a derivative unless divided by elapsed time. Comparisons must use the same evaluation procedure at both checkpoints.
Subtracting the current evaluation loss from the loss ten steps earlier gives a positive number when loss has fallen. It is an absolute change in loss units, not a percentage and not a derivative unless divided by elapsed time. Comparisons must use the same evaluation procedure at both checkpoints.
H maps the model’s state into the representation z that will be measured. Its output could be a parameter-derived coordinate, activation summary, or another declared measurement. The chosen H, its units, and its invariances must be fixed before comparing z with a reference.
The minimum discrepancy across the next W observations must exceed ε for the indicator to equal one. This requires every observation in the window to clear the threshold, rather than merely its average. The window beginning at t can only be confirmed once its final observation is available.
The matrix inner product factorizes into an inner product of the output factors and an inner product of the input factors, multiplied by their scale coefficients. With one fixed s, that coefficient is s². This identity permits exact operator comparisons using small vector calculations without…
The matrix norm is the product of the two factor lengths multiplied by the absolute scale. The final manuscript writes s without absolute bars because the pinned coefficient is positive. If either factor is zero, the effective operator and its norm are zero regardless of the other factor.
The analysis compares four odd window lengths: 5, 11, 21, and 31 observations. Smaller windows preserve more local variation, while larger windows smooth it more strongly. Agreement across these choices is descriptive robustness to smoothing, not independent replication.
This proposed criterion requires a report to predict or describe an independently measured property of the same model instance. Its purpose is to tie the declaration to something that can be checked, rather than scoring wording alone. The measured property, scoring rule, and temporal availability…