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 chain rule gives a factor of −(x−1), divided by the smoothing square root and the squared score denominator. For T>0 it is finite everywhere and equals zero at the target. This matches the C++ helper’s body and avoids the original score’s cusp.
For x≠1, differentiating the reciprocal score gives the displayed signed expression. At x=1 the left derivative is +1 and the right derivative is −1, so there is no ordinary derivative. The implementation uses Copysign and returns −1 at its positive-zero difference case; that is a selected branch…
Inputs equally far below and above one have the same absolute difference from one. Therefore Φ(1−ε)=Φ(1+ε) whenever both inputs lie in the stated domain. The score records distance from its target and discards which side of the target the input lies on.
The notation collects the score values from the first sample through sample T. Statistics such as a mean or variance act on a chosen subset of this sequence. A collection of values alone does not specify sample timing or independence.
Substituting φ>1 into 1/(1+|x−1|) makes the denominator φ, so Φ(φ)=1/φ exactly. This is a correct algebraic evaluation. It states what the score would be at that input and does not prove that a model reaches the input.
Substituting φ>1 into 1/(1+|x−1|) makes the denominator φ, so Φ(φ)=1/φ exactly. This is a correct algebraic evaluation. It states what the score would be at that input and does not prove that a model reaches the input.
The argmax operator returns the candidate source p whose AI_VIS score is largest for the specified query, claim, user context, time, and location. The starred p* denotes the selected source; it is not the numerical maximum score or the selection probability shown elsewhere on the poster. The…
With zero initial state, retention 0.9, and input 0.1, the exact value is 1−0.9ⁿ. It remains below one at every finite nonnegative n and converges to one. A finite threshold crossing depends on the chosen threshold, even though exact equality is never reached in ideal arithmetic.
Adding 0.1 to the full previous value gives Aₙ=A₀+0.1n. Unlike the leaky example, this state has no finite equilibrium and grows linearly. This comparison shows why retention coefficients materially determine the claimed accumulation behavior.
The center now receives an increment G(cₜ,ℓₜ). Its dependence on the outer state creates a possible causal path, but only if changing ℓ can actually change G and the update is executed. The magnitude, stability, and persistence of resulting changes depend on the defined function G.
Averaging all seven operators at the same input gives (5z+1+1/z)/7. This parallel average differs from applying the operators sequentially. The recurrence is undefined at zero and has two real fixed points; its behavior depends on the starting domain.
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.
Induction on cₜ₊₁=cₜ gives cₜ=c₀ at every later step. The center retains its starting value regardless of what happens in the separately evolving outer process. Changing this conclusion requires changing the center’s update law or its inputs.
State five is reset to one on every tick; state six copies its previous value, and state seven takes the reciprocal of the previous state six. The constant eventually propagates through these states. Initial state six must be nonzero wherever its reciprocal is evaluated.
Subtracting each reported refusal percentage from 100 gives its complementary compliance percentage, assuming refusal and compliance exhaust the outcome categories. The rounded inputs yield 14.2% and 2.8%. These are conversions of the source’s reported marginals, not newly observed outcomes.
The sum counts times at which the declaration indicator is one and the selected discrepancy exceeds ε, starting at the candidate onset. It is a count of coincident conditions under the chosen definitions. It does not become a validated cognition measure merely because the count grows.
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…
At equilibrium, the constant reset fixes states five and six at one, the reciprocal fixes state seven at one, and the increment sets state one to two. The decrement and identity links then set states two through four to one. This yields the vector (2,1,1,1,1,1,1), not seven identical values.
The first difference shows whether an update raises or lowers the current state; the second shows whether it lies above or below one. For 1/5≤z<1, both expressions imply z<F(z)≤1. These sign relations support a monotone convergence argument within that invariant positive interval.
The infimum selects the earliest time at which the declaration indicator is one. On a discrete record it is simply the first qualifying sample index. If the qualifying set is empty, the event is unobserved and requires an explicit missing or censoring convention.
The first operator adds one, the second subtracts one, and the third leaves its input unchanged. Applying the first two in sequence restores any ordinary finite real input. Their names do not alter these elementary operations.
Each next-state value is calculated from a previous-time neighbor: state one increments state seven, and state two decrements state one. Because updates are synchronous, a value must travel across ticks. This is a different system from both sequentially composing seven functions in one tick and…
At a nonzero fixed point, multiplying z=F(z) by 7z yields 2z²−z−1=0. Factoring gives (2z+1)(z−1)=0. This algebra identifies all finite real fixed points of the displayed recurrence.
State three receives the previous value of state two, and state four receives the previous value of state three. These equations create a two-stage delay with no numerical transformation. In-place sequential updates would change that delay and would be a different implementation.
This model splits an onset time into an architecture-level mean μ_A and a residual ε_i. It would describe timing variation only if actual onset events were defined and observed. Prompt sensitivity or a distribution of output responses does not, by itself, supply such an event-time dataset.
For discrete random variables, H(item)−H(item|state) equals mutual information and is nonnegative when conditional entropy is averaged over the joint distribution. A single realized item can have negative pointwise information gain, so the phrase at each tick is stronger than that theorem. A…
Each update retains a fraction λ or ρ of the previous value and adds q. With initial value zero and 0≤λ<1, past inputs decay and the state approaches q/(1−λ). This is a standard finite-capacity accumulation example whose long-term behavior follows from a geometric series.
Differentiating the average recurrence gives (5−z⁻²)/7. Its values at one and minus one half are 4/7 and 1/7, both with magnitude below one, so both fixed points are locally attracting for the scalar iteration. Local attraction does not prove global convergence across the singularity at zero.
The map ϕ converts sₜ into a representation that can be compared with zₜ. The map’s choice establishes units and which properties are preserved. Here ϕ is an extraction map, distinct from both the golden ratio φ and the project’s scalar score Φ.
The inequality means the next iterate is larger than the current one but no larger than the fixed point one. Repeatedly applying it gives a monotone bounded sequence within the specified interval. Identifying its limit then uses continuity and the fixed-point equation.
Multiplying the stated standard error 2.1 by 1.96 and adding and subtracting it from 11.3 yields [7.184,15.416] percentage points. The calculation is a conventional approximate 95% interval under a normal sampling approximation. Its coverage depends on the reported standard error and study design…
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,…
The ratio 45/32768 is about 0.001373291, or 0.137329%. It is the observed sample proportion for the event counted in the source. Converting it into a population probability or comparing it across conditions requires the trial design and uncertainty model.
Under N independent Bernoulli trials with a common event probability p, zero observed events have probability (1−p)ᴺ. Setting this probability to 0.05 and solving gives the exact one-sided 95% upper bound 1−0.05^(1/N). For N=100000 it is about 0.0000299569, or 0.00299569%.
The outer process can depend on its previous value and input, while the center’s update simply copies its old value. The center therefore stays constant even if the outer process is complex or changing. This explicitly demonstrates that surrounding activity cannot affect a stored component without…
The next parameter state is produced by an update operator using the current parameters, training batch, and reward signal. This makes explicit the mechanism by which training can persistently change a model. A prompt-driven output change does not imply this parameter-update operation occurred.
The process state evolves through F, a readout H extracts the representation z, and a detector D uses the declared inputs to score a declaration. These are distinct operations even when they share model parameters. Reproduction requires their actual implementations, and the detector’s use of future…
The predicted and represented values agree, so their difference is zero; the represented value still differs from the independently specified reference by one. This demonstrates why minimizing self-prediction error alone does not prove agreement with reality. The reference comparison is a separate…
If each of N checks independently has the same reversion probability p, the chance of observing no reversion is (1−p)ᴺ. A finite record without a return therefore remains compatible with small positive reversion probabilities. The formula quantifies a sampling model; correlated or unequal checks…