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 signatures of conscious access are fixed by what a system computes, or also by the substrate that implements it, is usually argued conceptually: empirical purchase requires the same computation examined in two different substrates, with the same signature sought in both. The unfolding argument sharpens the difficulty, since for any recurrent network there is a feedforward network with the same behaviour, so behaviour alone cannot settle claims resting on internal dynamics, which must be tested directly. A dynamics demix separating input-driven change from change generated by a population’s own recurrence — validated on synthetic systems before any recorded data — was applied to two substrates on matched cognitive work: cortical populations in perceptual and value-based decisions, and language models constructing multi-step answers. Every neural dataset was autonomous-dominated; five language models were input-dominated, a categorical regime difference. At commitment to a perceptual decision the cortical autonomous component strengthened, locked to commitment, not the stimulus; the models showed no such attractor and committed only at their output layer. In a pre-registered control varying only architecture at matched accuracy, the eigenvalue measure separated recurrent from feedforward networks — architecture, not task. Pre-registered negative tests show the cortical effect is invisible to trial-averaged and scalar read-outs. A dynamical property used to reach a commitment is present in cortex but absent from a feedforward model on an analogous task. Nothing is claimed about phenomenal experience or machine sentience; the gap between decision commitment and conscious access is the central limitation.
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.