# Scientific and mathematical content review

## Scope

This review supplies source-specific mathematical interpretation for the consciousness atlas. It distinguishes recovered code, a mathematical definition, a historical author claim, a saved experiment artifact, an independent arithmetic check, and a fresh runtime experiment. No recovered project engine, archived notebook, downloaded model code, or donor-model inference was executed during the review.

The main deliverables are `content_package.json`, `equation_overrides.json`, `saved_research_verification.json`, `eigenvalue_counterexample.json`, and `donor_dossier_review.json`. The content package includes seven research articles, a glossary, primary scientific references, and memory leads. The final equation override map contains 560 individual authored interpretations, including 56 donor-model expressions, for the priority manuscript and code formulas; it is not a claim that every automatically recovered expression received independent theorem-level verification.

## What was independently checked

The saved normalized-MIP benchmark contains sixty linear-Gaussian networks, 163,140 cut-objective records and 2,400 stochastic-trial rows. All 141 checksum entries match. The reviewer independently reconstructed 227 selected Gaussian partition calculations spanning every network; maximum component disagreement was approximately 5.16×10⁻¹⁴. The stored covariance equations and objective ratios are internally consistent. These checks are numerical reconstruction and saved-data validation, not a fresh optimizer run.

The archived success counts are Queyranne 11/60, simulated annealing 515/600, simulated QAOA depth one 410/600, simulated QAOA depth two 457/600, and uniform sampling 214/600. The QAOA trials use classical statevector simulation and an already exhaustive cost table. Readout batches are not independent circuit-optimization repetitions. Of 360 saved QAOA optimizer restarts, 356 reached MAXFUN. The normalized objectives fail the tested submodularity condition; Queyranne’s general correctness guarantee does not apply to an arbitrary normalized objective. The unnormalized comparison and normalization-induced changes are explained separately in the article.

The declaration/state-change archive passes all forty-five checksum entries. Its 792 gradient records, seventy-nine evaluation-loss records, and 158 PCA-coordinate records are consistent with the saved tables. The evaluation-loss decrease is 63.6935429588%; the highest recorded gradient norm occurs at step 169. The metric, threshold, eligibility filter, and change-point definition alter the resulting onset and lag. These parameter-trajectory data do not measure declaration behavior or subjective experience.

## Manuscript interpretation

The Fibonacci manuscript’s unity proximity score, 1/(1+|x−1|), is a defined scalar score with a nondifferentiable cusp at one. It is distinct from IIT quantities also called Phi. Its variance-based coherence statistic is bounded below by 0.8 for inputs in [0,1], making a purported 0.25 baseline incompatible with that definition. Its proposed golden-ratio fixed point depends on an explicitly chosen driving term and is not a universal attractor theorem. Reported arithmetic corrections, later audits, and original claims remain versioned rather than silently replacing the old manuscript.

The later declaration study describes states, state representations, metrics, declarations, persistence, and onset as separate objects. Its saved LoRA analysis can be read as an operator-space parameter-change study. Reciprocal factor rescaling preserves a low-rank update operator while changing its factors; the operator and its factor coordinates should not be conflated. Centered bend uses outward displacements, so a straight trajectory has cosine minus one under that convention.

## Implementation-specific findings

The G16 numerical increment 0.013618 is not approximately phi⁻³. The rational decimal rotation has ideal period 500,000, while modulo-13 and modulo-17 counters repeat jointly after 221 steps. Trigonometric carriers, norm contractions, clamping, utility smoothing, and hashed feature accumulators have their actual numerical roles explained. A family label such as Bayesian, memory, free energy, or consciousness is not automatically the probability model, lossless memory, variational objective, or measurement implied by that label.

The Go and C++ branch uses some standard formulas directly and some restricted substitutes. The review names differences between a quadratic utility maximum and an argmax, a scalar exponential attention surrogate and normalized attention, a mean projection and phase-invariant synchronization, and a positive-definite metric and its incorrectly substituted geometric tensors. The real Go/C++ empty-input and variance behavior is described by version.

The independently reconstructed default sixteen-dimensional DNA matrices disagree with their claimed analytic spectra. Maximum sorted eigenvalue discrepancies are 0.0606289296 and 0.0345430856. The claimed eigenvalue sums also differ from the matrix traces. This is a direct finite-dimensional counterexample to those spectral lists, without running the larger project engine.

The recovered generator source has other static defects recorded by the GitHub audit, including vocabulary slicing beyond a 256-dimensional returned vector and Train methods that return loss without applying the available weight updater. These are source findings; the review does not claim a successful or failed execution that was never performed.

## August donor-model dossiers

The Kimi K2.5 dossier includes custom exact-integer hooks inside a file described by its header as official. Its overview denies a quantization configuration that appears in its nested text configuration. Its patch-merger tensor-pattern table conflicts with the output width implied by the constructor. Integer accumulation can be exact for represented integer inputs within range, while the full model can still incur quantization, scaling, nonlinear, and floating-point error. The embedded approximately 950-fold precision statement remains an attributed source claim.

The DeepSeek-R1 dossier attributes a latent-only cache to its embedded eager implementation, but that code caches reconstructed per-head keys and values. Its FlashAttention path pads values before caching. At two bytes per component, the displayed eager and padded caches require 81,920 and 98,304 bytes per token per layer; a separate 512+64 latent layout requires 1,152 bytes. Official DeepSeek source confirms distinct naive and absorbed implementations. The YaRN overview reverses the increasing ramp relative to the embedded code; the source-specific explanation corrects the orientation and retains the original formula.

## Assembled-atlas review

The reviewed intermediate atlas with 2,554 mathematical records had no blank explanation fields, and all 490 matching overrides at that snapshot were applied without stale interpretation text. The other overrides correspond to source instances absent from that snapshot or superseded during filtering. Generic reading-step heuristics incorrectly treated QAOA ket bars as absolute values and prose claims as substitution formulas; the review now explicitly supplies authored steps where available and an empty step list elsewhere, preserving the detailed explanatory paragraph. The coverage wording has been corrected from “token-array records” to “PCA coordinate records.”

Final import remains the parent’s responsibility. The review does not edit the website implementation. Priority checks after import are the donor article/source references, donor equation annotations, explicit reading-step override propagation, and the distinction between accepted mathematical records and the retained source-candidate ledger.

## Rebuilding this review package

Run `build_content_package.py`, then `build_equation_overrides.py`, then `augment_content_package.py`, then `augment_donor_review.py`, followed by the donor-equation annotation script if present. These scripts create editorial content and inspect source records; none should execute the recovered project engines. `verify_saved_research.py` is the separate numerical and checksum inspection tool. Primary references are stored with direct URLs and the claims they support inside the content package.