Open-access preprints by Nathan M. Thornhill. Every paper below carries a DOI and a downloadable PDF.
The collected volume. Four open-access papers — The Existence Threshold, the 86% Scaling Law, the Dimensional Loss Theorem, and the Dynamic Existence Threshold — joined by three original bridge essays and front matter that trace the framework from binary discrete systems through dimensional embedding to dynamic Phi. 100 pages, 7×10 trade paperback. ISBN 979-8-9958925-0-2 · LCCN 2026941912.
Whether the dynamics that carry a decision to commitment differ between the recurrent circuits of the brain and the transformer networks of large language models is a question about internal dynamics. For any recurrent network there is a feedforward network with matched behavior, so claims resting on internal dynamics must be tested directly. A dynamics demix separates input-driven change from change generated by a population’s own dynamics. Validated first on synthetic systems and checked against the mean-field variance theory of driven echo-state networks, it was applied to cortical populations in perceptual and value-based decisions and to five feedforward transformer language models constructing multi-step answers. Every neural dataset was autonomous-dominated and the five language models were input-dominated; under inference, orbitofrontal cortex recruited its autonomous component on both read-outs (24 of 31 rats on the variance partition), whereas four of the five models did not. For the two models and the cortical dataset re-examined at a matched input dimension of eight, the direction of that difference held. The models’ regime label, however, depends on the dimension of the input basis, so the difference is reported as one of regime at matched input dimension rather than as categorical. After commitment to a perceptual decision the cortical autonomous dynamics became more persistent, more sharply when aligned to the inferred commitment time than to stimulus onset (a specificity supported rather than established); this recovers a transition already reported for these recordings. In the two language models probed layer by layer the correct answer, when detected, first became top-ranked before the output layer, under the read-out used; across generated tokens, no commitment-locked rise in autonomous persistence was found in any model. In a pre-registered control varying only architecture at matched accuracy, the eigenvalue measure separated recurrent from feedforward networks, most cleanly when no input followed the evidence; that control, not the cortex–model comparison, carries the architectural claim. Pre-specified negative tests in orbitofrontal cortex found no commitment signal of the predicted sign in trial-averaged or scalar read-outs. Conclusions are limited to the systems tested. No claim is made about phenomenal experience or machine sentience.
The substrate-neutral scalar that keeps getting proposed as a sufficiency index for consciousness is provably content-blind by construction: a photograph, white noise, and the word “TRUE” can be matched on density, lose the same organization scalar, and keep an identical 4/13 of their connectivity. So where does the information live that the scalar throws away? One pre-registered test, three substrates, three answers. In a transformer, factual truth is linearly decodable from the residual stream (AUC 0.83) while the scalar stays blind across all 29 layers. In the anaesthetized brain, which individual a recording belongs to decodes from leakage-controlled connectivity where the scalar sits at chance. In sleep, a recurrence measure survives residualizing the scalar out across five stage contrasts. A sufficiency predicate for consciousness cannot be a single global scalar — what it leaves out is multiply-realizable relational structure that a transformer’s residual stream and the brain’s thalamocortical loops both carry.
Two Parallel Lines of Evidence. A synthesis note recording the chronology of two independent lines of evidence that converge on architecture-independent geometric fixed points as the principal explanatory mechanism for representational memory failure: the 86% Scaling Law (Thornhill 2026b) and the Dimensional Loss Theorem with GPT-2/Gemma-2 validation (Thornhill 2026c) from January 2026, and the Sentra production-embedding study (Barman, Starenky, Bodnar, Narasimhan, Gopinath, March 2026) reporting variance concentration to ~16 effective dimensions via participation-ratio methodology. The two bodies of work use different metrics and report different specific quantities, but converge on the same architecture-independent geometric explanation.
Integration-Differentiation Balance Predicts System State Across Substrates. A cross-domain framework for detecting organizational dissolution. Demonstrates that a structural coupling metric (Integration-Differentiation balance) separates consciousness states at AUC 0.91 across 136,394 EEG recordings, convergent with a simpler spectral baseline on the same task and has been applied to financial markets, space weather, and neural data.
A physicalist framework for understanding consciousness through information thermodynamics. Establishes the theoretical conditions that define the boundary between existence and non-existence, exploring how systems maintain coherence against entropy.
The first quantitative measurement of information loss at dimensional boundaries. Measures a consistent 86.01% ± 2.39% information loss across the tested cellular automata systems, with weak scale-dependence across grid sizes.
A formal mathematical theorem describing the mechanisms underlying information loss during dimensional reduction. Provides the theoretical foundation for understanding how patterns persist—or fail to persist—across dimensional boundaries.
The July 2026 release of the OpenCitations Index joined to the Retraction Watch database, with the scripts that built the join. 12 files, CC BY 4.0. It reports 999,842 citations pointing at 46,425 retracted papers, of which 330,834 were made after the retraction date. This is a dataset, not a paper; cite it as a dataset. Retraction Watch data is used with credit under their stated terms; Retraction Watch does not endorse or comment on work built on it, and no affiliation is implied.