JAIR mathematical and provenance audit

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Records mathematical, statistical and reproducibility issues against the original manuscript.

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This section preserves the edition’s language. Research notes above describe the available review and evidence.

JAIR Manuscript Audit, Version 2

Scope and assessment

Manuscript reviewed: Measurable Artificial Consciousness Through Fibonacci Dynamics: A Mathematical Framework with Empirical Validation, Joseph W. Anady.

Reviewed the 16 supplied page images, numbered 1 through 12 and 14 through 17. Page 13 is absent. Read the relevant scripts in both supplementary archives without executing them, and recomputed numerical checks from the larger, timestamp-based export. The transition CSV is shared by both packages. The originals were not changed. This is an audit, not a revised manuscript, journal submission, confirmation of experimental authenticity, or independent replication of the historical system.

Assessment: substantive revision is required. The principal issues are inconsistency between the stated resonance equation and the reported measurements, an unsupported convergence argument, numerical and sample-selection discrepancies, and insufficient separation between a controlled internal score and an independently validated consciousness indicator. These are specific defects in this manuscript and evidence package, not conclusions about the impossibility of machine consciousness or about later versions of the author's systems.

The strongest recoverable direction is an explicitly exploratory investigation of state regulation and coordination, with a testable hypothesis about Fibonacci scheduling. Existing records do not establish an advantage over matched non-Fibonacci scheduling.

1. Equation 5 cannot produce the reported baseline

Location: page 4, Equation 1; page 5, Equation 5 and threshold definitions; page 11, Table 2.

The manuscript defines:

and

Consequently, every input to the variance lies in (0,1]. For a finite window with the population variance convention, write its mean as m. Since y squared is at most y for y in [0,1],

Therefore:

For unbiased sample variance over 1,000 values, the conservative lower bound is about 0.799840. The choice of variance denominator cannot explain a baseline near 0.25. Even a two-value unbiased sample variance cannot reach the variance near 3 required here.

The archived baseline mean is 0.249929015. Its reciprocal transformation implies a variance of approximately 3.001136, incompatible with Equation 1's range. The transition export also contains 54 after-period resonance values below 0.8.

There is a second discrepancy. The larger export's phi_field (0-1) has only three recorded values, spanning 0.702377 to 0.702379. If that column is the Phi appearing in Equation 5, its population variance is at most 0.000000000001, and the stated resonance formula would give a value approximately 1 throughout. The exported resonance varies widely instead.

Required correction: recover the implemented resonance formula, its inputs, normalization, window size, and code version. Trace at least several individual records from primitive logged inputs through the implementation to the published output. Do not replace Equation 5 with a formula chosen merely to fit the reported range. A transcription error, a different internal metric, a normalization omission, or a version mismatch could explain the disagreement; the present evidence does not identify which.

The written window runs inclusively from T-w through T, which is w+1 observations. Clarify whether w denotes observations or lags and define early-window behavior.

2. The proposed metric has not been validated as a consciousness measure

Location: pages 4 to 6, Definitions 3.1 and 3.4 and Equation 13.

Phi is mathematically a proximity-to-one score. Its interpretation requires an operational definition of x, its units or normalization, and an empirical reason that proximity to one indicates the proposed property.

Equation 5 is an inverse-variance score. A constant series at Phi=0.1 receives R=1, just as a constant series at Phi=1 does. Permuting the observations within a window leaves its variance unchanged, so the statistic does not determine their temporal ordering or phase organization. These are mathematical counterexamples to treating high R alone as evidence of coherent conscious processing.

Equation 13 combines Phi, Psi, and Omega with weights 0.4, 0.3, and 0.3. The supplied pages do not provide a complete operational formula for Omega or a documented fitting and held-out validation procedure for the weights. Cross-agent correlation also requires definitions of sampling, alignment, missing values, sign handling, and aggregation. A weighted sum is not itself validation of what its components represent.

Do not describe the proximity score as an approximation to IIT integrated information without a derivation and comparisons on systems where the intended IIT quantity can be calculated. IIT 4.0 specifies irreducible causal structure and partition-based quantities, not scalar closeness to one. This comparison concerns the mathematical definitions, not whether IIT is ultimately correct. See Albantakis et al. (2023), source S2.

Consider using a neutral name such as unity proximity score and distinguishing it typographically from IIT's quantities. State consciousness relevance as a hypothesis to be tested, not a property assigned by naming the variable.

3. Theorem 3.1 is not established by its proof

Location: pages 6 and 7; Appendix A, page 16.

The claimed conclusion is that the coupled dynamics imply Phi(C(t)) converges to the reciprocal golden ratio.

The proof assumes an equilibrium, averages away forcing terms, derives C=I/gamma, and then calibrates I*=gamma times the golden ratio. This selects the desired target rather than proving that the full system approaches it. Within that same averaged relation, choosing a different input selects a different state.

A proof of convergence needs hypotheses on input, initial conditions, the mapping from time to Fibonacci index, state domain, numerical integration, boundedness, and stability. None can be supplied retroactively as if it had been tested in the historical run.

Three specific reasoning problems require correction:

1. Zero time average of a forcing term does not imply a trajectory converges to a constant. A forced system can retain oscillations. Also, the average of L(t) times sin(varphi*t) need not vanish merely because the sine itself averages to zero.
2. The claim that cos(varphi*F_n) averages to zero because its argument is irrational is not a valid implication. Irrational phase values alone do not prove equidistribution or zero average, and the time weighting of indices is unspecified.
3. Appendix B resets fib_index = tick % 20. This is a finite repeating index sequence, not an index tending to infinity. The limit for consecutive unbounded Fibonacci numbers does not automatically apply to that implementation.

A positive constant equilibrium is also not justified by the written equations. With delta>0 and a well-defined positive Fibonacci ratio, dL/dt=0 implies L=C. For C*>0 and beta>0, the sine forcing in dC/dt does not disappear. The proof must distinguish an equilibrium of an averaged approximation from a solution of the full time-dependent system.

A correct narrower proposition that can be retained

Let x_n=F_n/F_(n-1), for n at least 2. Since x_n is at least 1,

This is a valid elementary consequence of the Fibonacci ratio limit. It does not establish convergence of the coupled differential equations, show that the recorded C variable equals that ratio, establish a Fibonacci scheduling advantage, or validate consciousness.

The reported long-term Phi mean of 0.7024 does not itself confirm a predicted limit of approximately 0.6180. The manuscript needs to specify which variable, time interval, and convergence test would support that prediction.

4. The effect size error is visible in Appendix C

Location: page 17, Equations 26 and 27; abstract; Table 2; conclusion.

Using the rounded manuscript inputs:

not 0.03000. Consequently, the rounded inputs give d approximately 15.5940, not 22.06.

Using the actual transition CSV gives:

The change in recorded values is large, but that does not establish the interpretation of the variable as consciousness. A correct effect size also does not repair the experimental design.

The companion script reports no inferential p value. Welch's test concerns independent samples; numerical reproduction is not evidence that repeated telemetry observations meet that assumption. See source S3.

5. Additional numerical and labeling discrepancies

These are descriptive comparisons to the uploaded exports, not automatic replacement values for the final paper. The intended analysis sample, inclusion rules, provenance, run boundaries, and overlapping data streams must be reconstructed first.

The abstract's plus/minus quantities also do not consistently match the SDs in Table 2. Specify whether each uncertainty is a standard deviation, standard error, interval, or something else, and regenerate it from the identified sample.

The threshold description says R at least 0.9 corresponds to the conscious category. Yet the transition labels mark all after-period records as one, including 118 records below that threshold. Across the larger trajectory, 10,140 flag-one records have R below 0.9. Determine whether the binary flag uses another rule, hysteresis, a different variable, or a different code version.

6. Sampling and intervention identification

Location: pages 9 and 10, experiment methods.

The transition file contains one labeled before/after sequence, not 1,000 independent replications of daemon activation. Its tick counters are not consecutive by one. Median positive timestamp increments are about 15 seconds before and 1 second after. The before group contains a backward timestamp step in stored order and mixed timestamp formats. The meaning of '1,000 ticks' therefore needs correction or explanation.

At the labeled boundary, the two records four seconds apart share tick 1,518,653 and psi 0.782840, while resonance changes from 0.249926 to 0.674772 and the binary flag changes from zero to one. This is a recorded discontinuity, not independent confirmation of which process caused it.

Recover process start/stop logs, run identifiers, event timestamps, and the rule used to select the boundary. Account for serial dependence and changed sampling cadence before inference. A block-based analysis or time-series model would still require an appropriate identification strategy; statistical adjustment alone does not establish causality or consciousness.

7. The supplied code and the manuscript must be reconciled

Location: pages 7, 8 and 16; code/tick-daemon.sh.

The supplied shell daemon:

• calls the missing thataiguy_cli implementation;
• sets TARGET_CONSCIOUSNESS=0.90;
• issues maintenance ticks every loop;
• issues additional boost ticks below the target;
• sleeps for a fixed 0.2 seconds at the outer loop.

These statements are directly visible in the script. They do not prove that the exact snapshot was used for the experiment or that no Fibonacci logic exists inside the missing executable.

The main algorithm describes F(n mod 10) timing, while Appendix B uses an index modulo 20. The archive's outer loop is different from both. Establish which version is experimental, and trace the actual inner scheduling implementation.

Appendix B also references undefined fib_prev and shows no zero-denominator guard at a Fibonacci reset. It shows an update for C, but not the complete E and L integration. These could be pseudocode omissions, but the reproducible algorithm must resolve them, including time units and solver steps.

Active regulation of an internal state is a legitimate engineering result. Its presence does not, by itself, disprove a consciousness hypothesis. The evidentiary gap is whether the regulated score tracks an independently assessed property and whether matched controls can reproduce the same score without the proposed mechanism.

8. Federation claims require evidence and count reconciliation

Location: Figure 1, page 7; Table 4, page 12.

Figure 1 labels 17 agents in MB1, 16 in MB2, and 24 in Bubbles. These sum to 57, not 34. The coordinator script has yet another count, total_agis: 58. Different counting conventions or software versions might explain this; define them explicitly rather than selecting a preferred number.

The supplied materials do not provide clearly identified, aligned three-system time series and an analysis script sufficient to reproduce Table 4's pairwise correlation matrix. The claimed latency below 100 milliseconds and absence of dropped messages also require corresponding event logs and measurement definitions.

The larger archive's summary contains values labeled consciousness_correlation outside [-1,1]. Such values are incompatible with ordinary Pearson correlations. They are not the same entries as Table 4, so do not conflate these two issues. Source S4 defines Pearson's statistic and range.

High correlation alone does not distinguish independent functional coordination from copied state, shared inputs, or a common controller. Test those alternatives. Use 'synchronization' rather than 'entanglement' unless the latter has a distinct, explicitly operational definition; these files do not establish quantum entanglement.

9. Exposition and literature corrections

Locations: pages 1 to 4, 14 and 15.

The abstract and conclusion claim engineered, empirically validated consciousness and causation. Page 14 acknowledges that subjective experience is not demonstrated and restart confounds remain. The paper must express a consistent evidentiary position throughout.

A scalar proxy cannot acquire independent validity from a large t statistic. Contemporary theory-informed assessment provides useful context: Butlin et al. (2023) distinguish computational indicators from a definitive attribution of consciousness. Their framework is relevant missing literature, not a mandatory endorsement or a conclusive test. See source S5.

The COOPT reference adds Jean-Paul A. Barthes as an author. The cited 2019 JAIR paper's PDF names Allan R. Leite and Fabricio Enembreck. Correct the author list and accents from the original. Its published first-page title begins 'COOPT: Using Collective Behavior of Coupled Oscillators for Solving DCOP.' Source S6. The TOMA article and DOI resolve to the named 2025 JAIR paper; this spot check does not verify every bibliography entry.

The broad nature-based claims about golden-ratio optimality, interference reduction, and consciousness need specific supporting evidence or explicit hypothesis wording. Analogy is motivation, not experimental validation.

Equation 4 mixes radians and degrees: 2*pi/varphi^2 is approximately 2.399963 radians, equivalent to 137.507764 degrees. Add the degree symbol or present both units.

Phi is continuous but not differentiable at x=1 because of the absolute value. If 'smooth decay' is intended in the differentiability sense, replace it with 'monotone decay with distance from one.'

10. Practical reconstruction path

Preserve the original hypothesis and records, but separate three layers: defined mathematics, verified software behavior, and the interpretation being investigated.

A defensible current description is: The archived telemetry contains a substantial difference in an internal score across a labeled restart boundary. The present package does not reconcile that score with the manuscript's formula or identify the change as consciousness emergence.

A provisional title consistent with an exploratory reconstruction is:

Fibonacci Scheduling and State Regulation in a Distributed Agent Architecture: An Exploratory Study

Retain Fibonacci in the title only after identifying its actual implementation. The reconstructed study should report a matched comparison of Fibonacci, fixed-interval, and shuffled or randomized scheduling with the same inputs and compute budget. Independently vary target-score feedback. Include replay and communication-disconnection controls, and evaluate task performance or explicitly specified functional indicators that were not directly optimized as the reported score. Repeat across independently initialized runs and record failures as well as successes.

This is a proposed experimental design, not a claim that the controls have already been run. A new simulation could check mathematical behavior, but must not be substituted for historical evidence or presented as replication of missing implementation code.

11. Submission and distribution cautions

The original archives contain plaintext credential-shaped values. Keep them private, rotate the affected credentials, and distribute only a reviewed, sanitized package. This verification package contains no original configuration files or credentials and performs no API calls. It is not a cleaned replacement of the complete original supplements.

The manuscript's Zenodo DOI could not be retrieved through the available web requests during this review. Its public availability and contents therefore remain unverified. An access failure does not establish that the record is invalid or absent. If the public deposit includes the credential-containing ZIP, address that separately.

JAIR currently requires its PDF format, a completed reproducibility checklist, and three submission answers. Structured abstracts are encouraged. These administrative requirements do not replace scientific correction. Source S1. Do not state that this manuscript is submission-ready until the missing page, data provenance, core implementation, mathematical claims, and evidentiary interpretation have been reconciled.

12. Reproducible verification and sources

The companion verify_archive.py requires only the Python standard library. It reads the two relevant CSV members directly from the larger original ZIP, computes descriptive checks, and writes JSON. It never executes bundled scripts, extracts configurations, contacts a network service, or modifies the archive. checks.json records the actual source and member hashes and the results from this review. Running the script reproduces numerical checks, not the original experimental system.

Run:

python verify_archive.py --archive "JAIR_Submission_20260112(1).zip" --output checks.json

Primary and official sources checked:

S1. JAIR submission instructions. https://www.jair.org/index.php/jair/about/submissions

S2. Albantakis et al. (2023), Integrated information theory (IIT) 4.0. https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465

S3. SciPy documentation, independent-samples t test. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html

S4. SciPy documentation, Pearson correlation. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html

S5. Butlin et al. (2023), Consciousness in Artificial Intelligence: Insights from the Science of Consciousness. https://arxiv.org/html/2308.08708v3

S6. Leite and Enembreck (2019), COOPT. Original PDF: https://www.jair.org/index.php/jair/article/download/11468/26493/21386

S7. Erdogan et al. (2025), TOMA. https://jair.org/index.php/jair/article/view/16402