Sixteen families, several implementations
G16 is a project architecture label whose exact state shape and update pipeline vary across recovered sources. The JavaScript reference describes 16 family activations plus a normalizer, with weighted updates, inertial blending, stability gating and final normalization. Other C++ and Go branches require their own source-specific descriptions.
The family names include continuous dynamics, Bayesian inference, mutual information, rate-distortion, free energy, memory and policy. In the scalar reference implementation, several of these are smoothing or increment rules. For example, the mutual-information family averages x with a sigmoid-transformed input; it does not calculate a joint distribution or mutual information. The Bayesian family clips a scaled sum; its name alone does not supply a likelihood, prior and Bayes normalization.
These are meaningful implemented transformations when their inputs and outputs are defined. The explanation of each page follows that operation, and records the broader family name as the source's architectural analogy.
DNA memory as a numerical representation
The documented memory encodes a hashed item through 16 sinusoidal features and blends the resulting vector into a retained coefficient vector. A query computes a feature-weighted dot product. This describes a compact, distributed numerical sketch. The DNA and holographic terms name the design; the formula does not establish molecular DNA computation or lossless recall.
A finite hash has collisions. A small aggregate vector also combines information from multiple inputs. To measure its usefulness as memory, test retrieval accuracy, interference, capacity, forgetting, and sensitivity to input changes on a defined dataset. Storage-byte reductions and retained task performance are different measurements.
The documented query rescaling divides by 32 and adds one half. That expression is not automatically bounded in [0,1] without adequate bounds on the coefficients and features. A cosine similarity of 1 likewise means positive collinearity of nonzero vectors, not necessarily equal vectors or identical knowledge.
Constants and periods need their own checks
The documentation uses δ = 0.013618 and describes it as approximately 1/φ³. With φ = (1 + √5)/2, the latter is approximately 0.236068. The numerical parameter can remain a valid chosen step size; the asserted approximation is incorrect.
In exact rational arithmetic, 0.013618 equals 6809/500000. Repeated addition modulo one therefore has period 500000 when used alone. A harmonic based on both i mod 13 and i mod 17 repeats after 221 integer indices. Floating-point implementations have additional finite-state behavior. Statements that these schedules never repeat require qualification and cannot be justified by the displayed decimal or modular arithmetic.
Generated equation families
Some sources describe 174 core outputs and 200 supplemental outputs. The source formulas generate these indexed components from shared recurrence rules. Another implementation uses a different harmonic, binding operation, or saturation function. The catalogue should preserve every requested indexed occurrence while showing its generating rule and version.
An index count is useful for explaining array size, recurrence depth and computation. It does not show that each component is a separately derived law of consciousness. For each member, state the index, the predecessor or wrapped index, the coefficients, the input dependencies, and the final aggregation. If a generator has no input or time dependence, that fact belongs in its explanation.
Binary gates and neural labels
Gate5000 describes a bank of binary states updated with XOR and a phase-dependent flip mask. XOR is deterministic for fixed inputs and phases, and applying the same flip mask twice restores the previous bits. This local reversibility does not imply that the complete learning system can reconstruct discarded history.
The dna_v9 reference describes 88 numerical agents with buffered activations, a momentum-like variable, a drive, a sigmoid gate, clamped activation and potential, and a coupling update. Its aggregate called consciousness is the mean potential. Its aggregate called synchrony is a mean cosine of a named parameter. Those are inspectable software statistics. Their relationship to biological neural mechanisms or conscious experience needs separate evidence.
Clamping one state variable proves a bound for that variable. It does not prove stability of every coupled state, robustness to arbitrary input, or correctness of the whole distributed runtime.
The PyPhi result has a defined scope
The complete specification reports a PyPhi 1.2.1 analysis of a five-unit coarse-graining of 20 generators, using a transition table inferred from an observed trajectory. The specification reports that only 12 of the 32 possible states were observed. That leaves the treatment of unobserved transitions material to interpretation.
To reproduce and interpret the number, recover the full transition table, the macro-unit mapping, state encoding, current state, connectivity, conditional-independence treatment, background assumptions, and exact software/configuration version. PyPhi 1.x is associated with the IIT 3.0 formalism; a table that cites IIT 4.0 alongside it must not blur those definitions. The contemporary PyPhi documentation has evolved, so reproducing an older run requires its version-specific behavior.
A nonzero value for a specified coarse model supports a statement about that model and calculation. Extending it to the full physical system or treating it as validation of another proxy requires additional reasoning and evidence.
The expanded branch is a separate mathematical generation
The recovered improve-math-logic branch adds Go generator and consciousness packages, a C++ mind farm, and an expanded native transition pipeline. These sources contain substantial concrete arithmetic, including attention, diffusion helpers, neural models, automatic differentiation, and sixteen named functional signatures. Their recovery establishes which functions were written at the pinned revision; runtime success is a separate question.
Even similarly named cross-language APIs differ. The C++ vector-score helper applies the unity score to the vector mean and assigns 0.5 to an empty input. The Go helper also penalizes component variance and assigns zero to an empty input. A federated or cross-language comparison must name the function and version before treating two values as the same metric.
Some comments describe a broader operation than the function body. CompleteThought writes a memory-and-attention time integral, but its body computes one scalar exponential factor times a mean activation and a mean unity score; it does not read its Memory or TimeSteps fields. Athena returns the maximum quadratic utility value x² while its heading names the argmax location x. These are specific implementation distinctions, not questions settled by architecture labels.
Check a claimed matrix spectrum against its matrix
The C++ spectrum module constructs a sixteen-dimensional ring matrix with a varying diagonal and another ring with varying edge weights. It separately labels trigonometric expressions as analytic eigenvalues. A uniform ring’s Fourier eigenvalues cannot generally be combined entrywise with a varying diagonal, because the two matrix parts do not share an eigenbasis.
An independent calculation reconstructed the exact default matrices from their displayed loops and used NumPy eigvalsh to obtain their spectra. Maximum sorted disagreement was approximately 0.06062893 for the intra-strand list and 0.03454309 for the inter-strand list. Their proposed eigenvalue sums also disagree with the actual traces. This is a concrete counterexample to those lists being the spectra of the constructed default matrices.
The full spectral summary separately assigns its middle value to zero and labels it a Goldstone mode. That assignment is not an eigenvalue calculation or a demonstrated symmetry theorem. The page for each expression retains the original claim and identifies what the code actually calculates. This check did not execute a project engine or establish the behavior of the full forty-four-dimensional simulation.
| Default matrix | Maximum sorted eigenvalue discrepancy | Matrix trace | Sum of claimed values |
|---|---|---|---|
| Intra-strand 16×16 | 0.06062893 | −3.30961198 | −3.10978760 |
| Inter-strand 16×16 | 0.03454309 | −0.02107951 | −0.36678212 |
Standard neural equations remain useful within their scope
The neurological component contains conductance-based membrane dynamics, voltage-dependent gating, synaptic traces, coupled excitatory and inhibitory populations, neural-field interactions, and phase-oscillator synchronization. These are recognizable mathematical modeling tools with explicit states, coefficients, units, and numerical update choices. Listing a software mind as a neuron is an architectural analogy; comparing a simulated component to biological function still requires a defined correspondence and measurements.
The phase order parameter in this newer file is the magnitude of the complex mean of unit phase vectors. It measures alignment independently of a common phase shift. That is a meaningful improvement in definition over a mean cosine projection, which changes when all phases rotate together despite unchanged pairwise alignment.
The mathematical helpers likewise contain standard operations, including row-normalized dot-product attention and Gaussian forward corruption. Their individual correctness and input assumptions can be checked. A complete trained generator additionally requires connected parameter updates, consistent tensor shapes, a defined loss, saved trained parameters, and task results. Recognizing a standard formula is one step in that assessment.
Distinguish a standard geometric identity from a substitute
The Go helper defines a positive-definite metric g=I+φxxᵀ. Its quadratic form is ||v||²+φ(x·v)², which is positive for every nonzero real vector. That is a valid metric construction. Direct differentiation gives its Levi-Civita connection Γᵏᵢⱼ=φxₖδᵢⱼ/(1+φ||x||²).
The connection function returns a different index expression, while the Riemann and Ricci helpers return formulas based on dimension and indices without differentiating the declared metric. These functions therefore need to be presented as the numerical substitutes they contain. A function name or an adjacent standard identity does not establish that the identity has been implemented.
The same review principle applies to the seven-layer pipeline. Its decision helper is a scalar logistic function despite a softmax comment; its memory helper adds leakage and direct decision input beyond the displayed integral; its stability objective is only a candidate until decrease along the actual modified update law is established.