Race All the Way Down, Race All the Way Up: A Unifying Vocabulary for Bounded-Commit Dynamics Across Quantum, Classical, Biological, and Computational Substrates

TL;DR

Scope note: Friction Theory (Paper 1) is established for biological, cognitive, and computational substrates. This paper investigates whether FT's mathematical scaffolding extends to physics-scope substrates (quantum measurement, classical mechanics, thermodynamics). This is open research, not established FT content; Papers 1–6 do not depend on its results.

"Decision" in resource-bounded probabilistic systems is treated not as a mental or agentive primitive but as a recurring structural phenomenon described in shared vocabulary: the resolution of competing processes racing toward commit under a finite-time budget. The central structural prediction is kernel-conditional: a system satisfying R1 (parallel candidates) + R2 (bounded resources) + R3 (irreversible commit) with a monotone-survival kernel exhibits a single-peaked inverted U on its evaluation-to-commit rate; non-monotone kernels can instead yield bimodal or U-shaped profiles (the Wallace counterexample, treated as a scope-condition rather than a refutation). In the monotone case: too low a rate yields no information processing; too high a rate yields noise-dominated commit; only the intermediate rate maximises information throughput.

Seven apparently independent physical and cognitive phenomena are conjectured to be organisable under this single race-structural vocabulary, spanning forty orders of magnitude in characteristic timescale:

1. Qubit decoherence-window
2. Ohm's law / Drude electron transport
3. Chemistry / biochemistry molecular kinetics
4. Stochastic resonance
5. Margolus-Levitin energy-density trade-off
6. Encoding-friction in learning
7. Yerkes-Dodson arousal-performance curve

"Race all the way down, race all the way up" is offered as a shared structural vocabulary across scales, not a claim that the substrates are identical: the same bounded-commit description recurs across different observables.

The paper then refines the three race-rules R1–R3 to a five-axiom formulation (A1–A5), and shows that the Schwinger-Keldysh formalism admits this race-axiomatisation under three assumptions: A1–A5 can be read onto the closed-time-path generating functional of a bipartite quantum system with einselected pointer basis and Markovian environment. Within the same formalism the following are exhibited as parameter-regimes:

• The Feynman path integral (quantum coherent limit)
• Onsager-Machlup stochastic dynamics (classical thermal limit)

...as parameter-regimes of one formalism. The CR-signal in large language models is treated separately as a substrate-mapping that provides empirical access to the race description, an empirical anchor rather than a regime of the formalism. The organisational point is that classical and quantum "decisions" can be described in the same bounded-commit vocabulary, not that they are metaphysically the same.

Substrate-agnostic clock-rate is bounded by Margolus-Levitin (maximum commit-rate) and commit-cost by Landauer (minimum energy per bit). Three hard problems (interference, linearity vs. nonlinearity, reversibility) are engaged honestly: the framework relocates rather than solves the measurement problem, from "why does superposition collapse?" to "why does race resolve?", the same problem in a new coordinate system, with potential tractability gains identified in §7.

The paper proposes no new physics; it presents existing mathematics (Martin-Siggia-Rose, Schwinger-Keldysh, Feynman-Vernon, Zurek einselection, Noether) organised under race as a lens, with concrete empirical anchor in LLM-substrate measurement and the kernel-conditional inverted-U pattern across seven substrate scales.

Falsification criterion: an identifiable system with R1+R2+R3 architecture and without an inverted U on its evaluation rate would falsify the structural core.