Race all the way down, race all the way up: A unifying vocabulary for bounded-commit dynamics across quantum, classical, biological, and computational substrates

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Original abstract

The same bounded-commit dynamics recur, unnamed, across quantum decoherence and einselection, classical Onsager–Machlup path integrals with Kramers escape, race-model accumulators in decision neuroscience, and autoregressive language models — literatures whose citation patterns leave the shared structure invisible. This paper proposes race-architecture as the vocabulary and empirical anchor that makes that common structure explicit. It is a synthesis, not new physics. The connected literatures include: quantum decoherence and einselection (Zurek 1981+); Onsager-Machlup classical path integrals + Kramers escape; race-model accumulators in cognitive psychology and decision-neuroscience (Vickers; Ratcliff; Usher-McClelland; Cisek-Kalaska); Wallace's biocognition rate-distortion / Yerkes-Dodson programme; 1/f noise across condensed matter, neural avalanches, and financial markets; large-language-model CR-signal dynamics (Pødenphant Lund 2026d). These literatures share an underlying structure - competing processes resolving under a finite-time budget - but use mutually incompatible vocabulary. Race-architecture is captured by R1+R2+R3 (parallel candidates with non-trivial competitive interference + bounded resources + irreversible commit), refined to five axioms A1-A5 for compatibility with Schwinger-Keldysh formalism. The Section 1.5 structural prediction is kernel-conditional (Wallace counterexample). The Schwinger-Keldysh formalism admits a race-axiomatisation under three assumptions; Feynman path integral and Onsager-Machlup are exhibited as parameter-regimes. The LLM CR-signal is a substrate-mapping providing empirical access. Companion papers in the friction-theory series: Paper 0 - Behavioural Friction Theory (concept DOI 10.5281/zenodo.19462499); Paper 1 - Friction as the cost of probabilistic computation (10.5281/zenodo.20012654); Paper 3 - Friction-guided inference (10.5281/zenodo.20014121); Paper 13 - Operational Friction Theory (10.5281/zenodo.20059876). v4.3 changelog (July 2026): a prior-art and positioning revision; no result is altered and no new empirical claim is made. (1) Section 8.1 previously surveyed adjacent unification programmes while omitting the two most prominent contemporary cross-substrate ones. Constructor theory (Deutsch 2013; Deutsch & Marletto 2015) and assembly theory (Sharma et al. 2023, Nature) are now cited and differentiated, and Wolpert (2019) is credited for the stochastic-thermodynamics bridge to computation. Because both added programmes are themselves cross-substrate, the section's closing differentiator is rewritten: cross-substrate scope alone no longer distinguishes this proposal, and the distinction is relocated to the organising primitive (modal / historical / dynamical) together with the consequences that follow from it. (2) Section 2.2 now states explicitly that a commit-event is, mathematically, a first-passage event, credits first-passage theory as already a substrate-agnostic cross-domain unification, and concedes that no new results in that formalism are claimed. The kernel-conditional non-monotone rate-shape is explicitly withdrawn from the paper's residual claims, since it has close antecedents in resonant activation, optimal stochastic resetting and hazard-shape effects; it is presented as a substrate-crossing synthesis only. (3) Section 4.3 anchors the computational substrate in the statistical-mechanics-of-learning literature (Gardner 1988; Engel & Van den Broeck 2001), with Shan, Li & Sompolinsky (PNAS 2025) cited as independent warrant rather than as a finding of this paper. (4) Abstract and scope statements tightened, and strawman disclaimers removed (the paper no longer disavows claims a reader would not attribute to a vocabulary proposal). Nine references added, all verified. Revisions made after external review. v5 (August 2026) — the abstract now leads with the measured result. The body is unchanged. What was buried is that the per-token count carries no detectable memory beyond the adjacent token: first-lag autocorrelation ratio at most 0.105 across five substrates, and 0.004 and −0.028 on the two ratio-instrumented ones. Memorylessness beyond one step is what a Markov process looks like, and the section reporting it had called this the stronger form of the reading all along while the abstract carried the exponential fit instead. The same sentence oversold the fit and undersold the finding; both halves are corrected. The structural mapping onto the equal-time Keldysh component is stated with the three assumptions that actually govern it — Gaussian approximation, discretization, Markovian modes — and as an analogy under those assumptions rather than a strict parameter-limit reduction. The cross-substrate predictions are stated with the tests that would bear on them, including the superconducting-qubit joint diagnostic and its falsifier, which had not appeared in the abstract at all. The operational-time claim now cites the point-process literature it had ceded in prose (Daley & Vere-Jones, 2003). A three-denial paragraph became one scope clause carrying the same content. Earlier versions remain in the version history.

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