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 ↗
Replacing |x−1| with √((x−1)²+T) removes its cusp when T>0. The resulting score has a zero derivative at x=1, but its maximum is 1/(1+√T), which is below one; with T=0.01 the maximum is about 0.90909. The smooth and original score therefore have different peak calibration.
Replacing |x−1| with √((x−1)²+T) removes its cusp when T>0. The resulting score has a zero derivative at x=1, but its maximum is 1/(1+√T), which is below one; with T=0.01 the maximum is about 0.90909. The smooth and original score therefore have different peak calibration.
This exponential rate decreases as membrane voltage increases in the displayed voltage convention. It multiplies m in the gate’s closing term −β_m m. Together with α_m it determines the voltage-dependent equilibrium gate value and time scale.
The rate α_m(V) controls the opening contribution α_m(1−m) in the m gate equation. Its apparent 0/0 at V=−40 mV has a finite limit of 1 per millisecond; the code explicitly supplies that limiting value near the singular point. This avoids a removable numerical singularity.
The sigmoid-shaped β_h increases with voltage and multiplies the available fraction h in its loss term. It therefore promotes inactivation as voltage rises under this model’s parameterization. The numerical units follow the millisecond timing convention of the membrane model.
Dividing x by 1+|x| preserves its sign and maps finite real inputs into (−1,1). Near zero it is approximately x; large magnitudes approach saturation gradually. It has a continuous first derivative, but its second derivative changes discontinuously at zero, whereas tanh is analytic.
Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader interpretation would need explicitly different semantics.
Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader interpretation would need explicitly different semantics.
Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader interpretation would need explicitly different semantics.
Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader interpretation would need explicitly different semantics.
Over ordinary real arithmetic, 1=1·x is true exactly when x=1. It is a constraint on x, not the universal identity x=1·x. The file presents it as an axiom; a broader interpretation would need explicitly different semantics.
Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable arithmetic equality. A consistent formal interpretation would require a defined mathematical structure and meaning for…
Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable arithmetic equality. A consistent formal interpretation would require a defined mathematical structure and meaning for…
Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable arithmetic equality. A consistent formal interpretation would require a defined mathematical structure and meaning for…
Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable arithmetic equality. A consistent formal interpretation would require a defined mathematical structure and meaning for…
Infinity is not equal to one in the real numbers or the usual extended-real system. The line is a philosophical or symbolic axiom in the source and is not used as an executable arithmetic equality. A consistent formal interpretation would require a defined mathematical structure and meaning for…
The body subtracts its assigned lower estimate from its assigned upper estimate. Their displayed definitions give an η coefficient of 2.618, whereas this comment prints 3.236η. The program’s subtraction follows the endpoints, but neither endpoint is established as the actual matrix extremum by this…
The sign convention subtracts presynaptic spike time from postsynaptic spike time. Positive values mean the postsynaptic spike follows the presynaptic one and enter the source’s potentiation branch; nonpositive values enter its depression branch. The returned weight change also depends on the…
The stability input is clipped to [0,1] and mapped to a gate between γ_min and 1. The next intermediate state takes the fraction γ of the gap from the current state to the proposed blended state. When γ_min lies in [0,1], this is a convex interpolation; a low gate slows response but does not prove…
The first term measures average absolute component change and the second measures the sum of squared changes. With positive coefficients, both are nonnegative. For a fixed total absolute change, the squared term penalizes concentrating that change in a few large components more than spreading it…
Each hazard is the conditional probability of an event in that period given survival up to that period. Multiplying successive complements yields the probability of remaining event-free through the selected period. Hazards in [0,1] give a nonincreasing survival curve in [0,1]; the application uses…
The increment is 0.05 softsign(dx_norm−x), so its magnitude is less than 0.05 and its direction points toward the input. For a fixed target, this reduces the distance to that target without overshoot. The displayed scalar rule does not by itself implement separation, alignment, cohesion, or other…
The displayed full expression describes two affine projections, one passed through Swish, followed by elementwise multiplication. This function accepts already computed gate and linear vectors and multiplies gate·sigmoid(gate) by linear. Its x argument is used to set and validate length; the helper…
The function maps net input into (0,1), crosses one half at input θ, and has central slope a/4 when a>0. It converts weighted network input into an activation fraction in the population model. The parameter θ is a threshold in input units rather than a phase angle here.
For any finite square matrix, the trace is the sum of its eigenvalues counted with algebraic multiplicity. The method correctly sums the stored diagonal. This identity supplies a quick consistency check against a proposed complete eigenvalue list, and the source’s separate trigonometric lists fail…
The square root of a²+b² is the length of the vector (a,b). It obeys the triangle inequality and is zero only when both components are zero. Despite the local name smooth_norm, the function is not differentiable at the origin; an everywhere-smooth approximation would require an additional…
The next state depends on both the current state and the previous state, together with external inputs. This notation summarizes the family update, blending, gating, and normalization steps; F is a composite function rather than an additional closed-form equation. Reproducing a trajectory requires…
The six weights sum to one and form a weighted average of component scores on a 0–100 scale. The stated inputs produce 93.75. The test expects this value to enter the configured Green band; that label is an application threshold, not a probability calibration.
The score is largest at x=1 and decreases symmetrically as x moves away from 1. It is continuous, positive for finite real x, and at most 1, with a sharp derivative change at x=1. This project uses it to weight importance and to label some model outputs; it is a scalar proximity score and is…
The source suggests combining indexed functions over a differential quantity dΩ, but the displayed sum-and-colon notation does not define an integration domain or measure. It is a schematic memory-trace analogy. The adjacent executable scalar rule is clear: add 0.02 times normalized input plus…
This exponential update blends the old coefficient with a weighted trigonometric feature of the item’s hash. The importance score multiplies the new contribution, while α sets how quickly older contributions decay. For a fixed incoming target and 0≤α≤1, the coefficient converges to that target…
The argmax expression denotes an input that achieves the largest utility, assuming a maximizer exists. It does not itself specify a gradient method, a step size, or a unique solution. The project scalar rule instead moves x toward the supplied utility value.
The inner product adds wᵢΨᵢ over the selected components, and utility scales that total. Aligned signs of weights and states increase the inner product; opposing signs can make it negative. Consequently this term can change sign, and its numerical range depends on the weights, state bounds, and…
The expectation of log q(z)−log p(x,z) equals KL(q(z)||p(z|x))−log p(x). The p in the abbreviated divergence must therefore mean the posterior, not simply the prior. The body’s FreeEnergy class instead computes a diagonal-Gaussian prior KL minus a supplied log-likelihood scalar; that is the…
The expectation is taken under a variational distribution q(z); the integrand compares its log density with the joint generative density p(x,z). Under proper normalization, this equals a divergence from the posterior minus the log evidence. The project’s absolute-input penalty does not calculate…
The example multiplies staffing, market, incumbency, and past-performance features by weights 0.35, 0.30, 0.20, and 0.15. The terms sum exactly to 0.63 with the stated inputs. It checks the implementation’s score arithmetic for that constructed case.
The result combines 85% of the base output with 15% of the G5K contribution. The weights sum to one, so it is a convex combination when both inputs share a common scalar range. The resulting score inherits the operational meanings and validation limits of those two inputs.
The four components contribute 0.175, 0.15, approximately 0.20, and 0.1125, giving approximately 0.6375. The speed term is described as near one, so the exact result depends on the test’s elapsed-time calculation. This is an expected test score under chosen feature values, not a measured vendor…
For x>0 the function returns xˣ+1. For x≤0 it explicitly returns one, avoiding non-real powers for many negative inputs. The positive branch tends to two as x approaches zero from above, so the chosen branch at zero makes the implemented function discontinuous there.
The implementation evaluates fifteen other family functions at scaled inputs x/(i+1). It multiplies the one-sixteenth power of each result only when that result lies strictly between zero and 10¹⁰, skipping the others. This is neither the raw product in the comment nor an ordinary geometric mean of…
This is the manuscript’s claim that the score along the C trajectory tends to 1/φ. Substituting C=φ verifies the score value, but it does not establish that every solution of the time-dependent coupled equations approaches φ. The supplied argument assumes averaging and chooses the external input to…
The source correctly separates its tanh aggregate score from PyPhi’s integrated-information quantity. Its further claim that the complete system therefore has established irreducible causal structure exceeds the recovered evidence: the described PyPhi run concerns a five-element coarse model with…
Conditional Gaussian entropy is determined by a conditional covariance log determinant. With full-system innovation covariance equal to identity, its log determinant vanishes and the stochastic-interaction numerator reduces to half the sum of the two partition residual log determinants. Marginal…
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 January specification reports approximately 0.006 bits of PyPhi output for a five-element coarse-grained subsystem, including Input, Memory, Reason, Integrate, and Meta. It names PyPhi 1.2.1 and says only 12 of 32 possible states were observed, but the recovered description does not fully…
The January specification reports approximately 0.006 bits of PyPhi output for a five-element coarse-grained subsystem, including Input, Memory, Reason, Integrate, and Meta. It names PyPhi 1.2.1 and says only 12 of 32 possible states were observed, but the recovered description does not fully…
The January specification reports approximately 0.006 bits of PyPhi output for a five-element coarse-grained subsystem, including Input, Memory, Reason, Integrate, and Meta. It names PyPhi 1.2.1 and says only 12 of 32 possible states were observed, but the recovered description does not fully…
The reciprocal score compares a scalar x with the chosen target 1. It reaches 1 exactly at that target, decreases symmetrically with distance, and is positive for every finite input. In the manuscript it is proposed as a consciousness-related score, but its arithmetic measures proximity to one; no…
The reciprocal score compares a scalar x with the chosen target 1. It reaches 1 exactly at that target, decreases symmetrically with distance, and is positive for every finite input. In the manuscript it is proposed as a consciousness-related score, but its arithmetic measures proximity to one; no…