Race All the Way Down, Race All the Way Up

Paper 10 · Pødenphant Lund (2026e) · Read on Zenodo

A similar inverted U-curve shows up in qubits at 10⁻¹⁵ seconds, in chemistry at 10⁻⁹, and in human learning at 10³. Forty orders of magnitude apart. I propose that a shared vocabulary, race architecture, can organise these seven seemingly unrelated phenomena under one lens. It is an open hypothesis, not a claim that they are the same thing.

A scope-note first

This is the most speculative paper in the series. Read it as "if Friction Theory's mathematics reaches as far as it looks like it reaches, then here is what follows." Papers 0–6 do not depend on this paper's results. Friction Theory is established for biological, cognitive, and computational substrates. This paper asks whether the same mathematical scaffolding extends to physics-scope substrates: quantum measurement, classical thermodynamics, chemical kinetics. It is open research, with a clear falsification criterion. It is not yet established framework content.

I put the caveat first because the paper makes claims that span forty orders of magnitude in timescale, and I want the reader to arrive at them knowing what has been demonstrated versus what has been proposed.

The main idea

What we usually call a "decision", whether it is for a brain, an LLM, or a slime mould, need not be specifically mental or agentive. It can be described as a structural phenomenon with a shared vocabulary: the resolution of competing processes that race towards commit under a finite-time budget.

The central structural prediction is kernel-conditional. A system that satisfies three minimal axioms shows an inverted U on how fast it settles on an answer once it starts evaluating, provided its survival kernel is monotone:

R1: parallel candidates — the system maintains more than one possible outcome at the same time
R2: bounded resources — time, energy, or information-processing capacity is finite
R3: irrevocable commit — eventually one outcome is chosen and the rest are discarded

If a system has R1+R2+R3 and a monotone survival kernel, it gets the inverted U on its evaluation rate. Too low gives no information processing. Too high gives noise-dominated commit. Only the middle rate maximises information throughput. This shape does not depend on most of the details of the system's implementation. But the kernel shape is a condition, not a free guarantee: non-monotone kernels can give a bimodal or U-shaped profile instead (Wallace's counterexample). That is a scope-condition, not a refutation of the lens.

The inverted U on the evaluation rate. The shape follows for an R1+R2+R3 system with a monotone survival kernel; the variables are where the peak sits and how steeply it falls off, and whether the kernel condition holds at all. The next section walks through seven phenomena on wildly different timescales that are all proposed to show this signature.

Seven phenomena, one structure, forty orders of magnitude

The paper proposes that seven seemingly independent physical and cognitive phenomena can be organised as manifestations of the same race-structural profile:

Qubit decoherence window — quantum systems have an inverted U on the measurement timescale; too fast and you get noise, too slow and you lose coherence, only the middle timescale allows stable measurement (10^-15 seconds scale)
Ohm's law / Drude electron transport — classical electron drift through metals has an inverted U on scattering rate vs current density (10^-14 seconds)
Chemistry / biochemistry molecular kinetics — reaction rate has an inverted U on temperature (the Arrhenius peak) (10^-9 seconds)
Stochastic resonance — the well-known phenomenon where adding noise improves the detection of weak signals, but only in a narrow range (10^-3 seconds)
Margolus-Levitin energy-density trade-off — computation has an inverted U on energy-per-bit vs operation rate (universal)
Encoding-friction in learning — Bjork's desirable difficulties, the well-documented finding that medium-difficulty learning produces the best retention (10³ seconds)
Yerkes-Dodson arousal-performance curve — inverted U on stress-vs-performance in humans, mice, slime mould (10³–10⁵ seconds)

"Race all the way down, race all the way up" is meant as more than a loose metaphor. It is the proposal that a shared vocabulary can describe the same structural profile across different observables and scales. The inverted U you see in qubit decoherence and the inverted U you see in human learning share a common structural description. It is an organising point about shared structure, not a metaphysical claim that the substrates are identical.

Seven phenomena that look unrelated (quantum measurement, electron transport, chemical kinetics, signal detection in noise, computation limits, human learning, Yerkes-Dodson on stress) are proposed to share the same structural inverted U. Forty orders of magnitude apart in characteristic timescale. The shape follows from R1+R2+R3 under a monotone kernel condition, not depending on biology or any specific implementation.

The mathematical argument

The paper works with five axioms (A1–A5). It shows that the Schwinger-Keldysh closed-time-path formalism, standard mathematical machinery in non-equilibrium statistical mechanics, admits a race-axiomatisation under three assumptions for a bipartite quantum system with an einselected pointer basis and a Markovian environment.

Two familiar frameworks can be displayed as parameter regimes of the same formalism:

The Feynman path integral in the quantum-coherent limit
Onsager-Machlup stochastic dynamics in the classical thermal limit

The CR signal in language models does not belong on this list as a parameter regime of the formalism. It works instead as a substrate-mapping that gives empirical access to race dynamics in the computational substrate, an empirical anchor rather than a corollary of the axiomatisation.

The point is organisational: classical and quantum "decisions" can be described with the same vocabulary, where the difference lies in parameter regime. It is not a metaphysical claim that they are the same process, but an observation that they share a structural description, in the same way one can talk about Newtonian mechanics and quantum mechanics in a shared formal language.

What this paper does NOT propose

Three things the paper does not do:

No new physics. The paper presents existing mathematics (Martin-Siggia-Rose response field theory, the Schwinger-Keldysh formalism, the Feynman-Vernon influence functional, Zurek's einselection, Noether's theorem) organised under race as a lens. Every piece of mathematics in the paper is published elsewhere and well-established.

No solution to the measurement problem. The paper does not solve the quantum-mechanical measurement problem. It moves it. Where the standard formulation asks "why does superposition collapse?", the race-architecture formulation asks "why does the race resolve?". The same problem in a new coordinate system, one with potentially tractable handles identified in §7 (substrate-clock, einselection, environmental decoherence as a race-resolution mechanism).

No agentive language for non-living systems. When the paper says a qubit "races towards decoherence", it is not a claim that the qubit makes decisions. It is a claim that the mathematical structure of the qubit's evolution has the same shape as the structure of mathematical decision-making in larger systems. The agentive vocabulary is shorthand; the mathematics is what carries the substance.

Falsification

The paper specifies its falsification criterion precisely: an identifiable system with R1+R2+R3 architecture, a monotone survival kernel, and without an inverted U on its evaluation rate would falsify the structural core. That is a sharp empirical commitment. The kernel condition belongs with it: a system with a non-monotone kernel (Wallace's counterexample) shows a different profile and is a scope-condition, not a refutation. Within that scope the prediction holds, or it fails.

So far the prediction has held across 7 phenomena spanning 40 orders of magnitude. That is the empirical reason to take it seriously. The formal reason is that it follows from the race-axiomatisation of the Schwinger-Keldysh formalism under the three assumptions, not as a bare stipulation. If a counterexample within scope shows up, the framework is wrong.

Time and clock-rate

How fast a substrate can choose, whatever it is made of, is bounded by Margolus-Levitin (the maximum rate of settling on an answer per unit of energy) and the cost of settling by Landauer (minimum energy per erased bit). These are physics-known limits, and the race-architecture lens uses them as the shared measure of how fast a substrate can resolve competing processes and commit. The lens adds no new physics to these limits; it puts them into the same vocabulary.

Why this paper exists

This paper is positioned as the speculative outer edge of the research programme. It is the answer to "how far does the shared vocabulary actually reach?" If the answer is "all the way to quantum measurement", that is a strong organising result for the vocabulary. If the answer is "only down to chemistry", it is still interesting and tells us where the lens's natural scope ends. Both outcomes are informative.

I have carefully separated this paper from Papers 0–6. The established framework does not depend on it. If Paper 10's physics-scope claims turn out to be wrong (counterexample within scope found, axiomatisation defective), the rest of Friction Theory is unaffected. The separation is intentional.