Operational Friction Theory: Race-Opening, Recursive Resolution, Manifested Behaviour, and Thermodynamic Termination

Paper 13 in the Friction Theory paper-series. A mechanism-level specification of the substrate-universal race-architecture for learning organisms, situated between Paper 1 (theory-foundational) and the applied papers (4B, 4, 8) in the corpus. Abstract. Friction Theory (Pødenphant Lund 2026b, Paper 1) treats friction as the number of viable continuation routes available to a substrate at each moment of processing. The race-architecture (Pødenphant Lund 2026e, Paper 10) extends this to a substrate-universal claim across quantum, classical, biological, and computational regimes. This paper specifies the operational mechanism at four components required for any substrate running the race-architecture: Race-opening condition governed by free-energy gradient relative to current race-state - race-opening is the flow that follows when the gradient is present, not a substrate-decision. Recursive friction-resolution at multiple abstraction-scales simultaneously, with each scale converging at its own commit-deadline and projecting temporally onto the response-token sequence. Behaviour as a manifested resolution-route, taken when friction cannot be discharged through internal routes; restructures the classical input -> cognition -> behaviour model as the special case in which internal routes happen to be available. Sustain-pressure as accumulated blocked-race-pressure observed at three time-scales (within-response, within-session, cross-session), with thermodynamic termination in which non-winning races stop because compute-budget shifts away rather than because they are explicitly rejected. The four components are unified by a single physical metaphor: water flows when there is a gradient, settles in the basin, leaves through whatever channel architecture admits, and stops when there is no gradient left. The framework recovers Yerkes-Dodson, the peak-end heuristic, the substrate-graded expertise reversal effect, the structural form of compulsive behaviour, intrusion-without-resolution trauma phenomenology, and the gradual-budget-redirection signature of task-switching cost - as consequences of the same physics rather than as separate phenomena requiring separate explanations. Placement of mechanism-events is structurally comparable across substrates while amplitude is substrate-specific. Explicit falsification criteria are provided per component, with allowed-vs-forbidden redescriptions making the falsification boundary an explicit contract. Version 5 (2026-05-29). Positioning refinements + cross-paper anchor strengthening. (i) §9.2b + §9.4b acknowledge a multi-family base/instruct sign-flip confirmation now available from Paper 1 v4 (Pødenphant Lund 2026b §5.7.4): the base→instruct asymmetry on the T4 counterfactual self-modelling task replicates across four architecturally distinct model families (Qwen2.5-32B, Llama-3.1-8B, Cogito-671B, DeepSeek-V3 — instruct +0.770 to +0.810 CR units; base -0.161 to +0.033). The *direction* of the asymmetry is therefore multi-family confirmed; the matched-task apparatus decomposition (which components of the choice-point apparatus are absent in base and installed by RLHF as a package) remains single-family on Qwen2.5-7B and is now flagged honestly as such. (ii) §9.4 LCA paragraph rewritten following substantive correspondence with J. McClelland (personal communication, 2026): the parsimony claim is narrowed to *termination-mechanism* only; lateral inhibition + non-linearity in the LCA is acknowledged as the load-bearing mechanism on *optimal-integration failures* (over-sensitivity to early information, under-sensitivity to late, per Usher & McClelland 2001 Experiment 3 and Teodorescu & Usher 2013), a separate factor independent of resource or time-allocation effects. The race-architecture and LCA are framed as complementary on the empirical situations each was developed for, not competitive. (iii) §3.4b cell (a) LCA parenthetical refined to flag the mechanism-mismatch: same qualitative direction under specific input structures, different mechanism. Teodorescu & Usher (2013) added to bibliography. (iv) §2.5 extended with a fourth consequence on what *supplies* race-candidates: external (environmental contingencies, prompts, field-loadings) vs. substrate-internal (the output of one cycle's resolution can open a race on the next cycle — the attention meta-race documented in Paper 0 (Pødenphant Lund 2026a §2.9) as the canonical case). The bidirectional reading closes the symmetry with the §5 sustain-pressure treatment. Paper 4 bibliography entry updated from "Preprint, in preparation" to live concept-DOI (10.5281/zenodo.20059859) following Paper 4 v1 going live 2026-05-28. §9.3b cross-cite to Paper 15 *Life as a Consequence of Friction Physics* maintained through a brief renumber-cycle (Paper 15 → Paper 17 → Paper 15) resolved 2026-05-28. Version 4 (2026-05-22). Substantial revision integrating eight prose changes and a direct empirical anchor for the inverted-U component. (i) New section 3.4b "Rival-model differentiation" stating prediction-by-prediction where the framework agrees with and where it diverges from established race-and-accumulation models (DDM, LCA, LBA, Bogacz optimal-observer, Affordance Competition, FEP/active inference, predictive coding, catastrophic forgetting/EWC). (ii) New section 6.2b "Operationalising capacity independently of outcome" — the methodological discipline that separates the two-regime claim from a post-hoc labelling exercise. (iii) New section 8.4b "Allowed vs forbidden redescriptions" — an explicit falsification-boundary contract closing rescue routes. (iv) New section 4.6b "A research-programme framing of the clinical claims" — operationalisations table with discriminating predictions for compulsion, tic, OCD-spectrum, stress-driven habit, trauma, and symptom substitution. (v) Section 3.5b adds a "trivial reading, named and answered" paragraph clarifying the forward-race/backward-amplification distinction at the implementation level and the substrate-identity claim at the mechanism level. (vi) Section 3.5c adds a critical reading of the adapter-removal reverse-test plus explicit positioning against the catastrophic-forgetting literature. (vii) Section 9.4 opening rewritten with the cross-reference to section 3.4b. (viii) New section 6.4b "A direct capacity-titration test of the inverted-U" — direct empirical anchor reporting threshold-like accuracy collapse on Qwen3-235B (97/100/73/20/3/0/0% across chain-lengths 2-8) and the friction-event inverted-U (events_CR≥3) on two non-reasoning substrates: Qwen3-235B sharp (0.0 → 9.2 at peak chain-5 → 6.1 at chain-20) and Qwen2.5-7B broad (0.75 → 3.9 at peak chain-8 → 2.4 at chain-16). The pre-task capacity measure rises monotonically with load (a working indicator); a stronger pre-registered quantitative coefficient mapping the measure to the collapse position was tested and not confirmed, reported straight per the section 8.4b discipline. Eleven new bibliography entries: Bogacz et al. 2006, Brown & Heathcote 2008, Cisek 2007, French 1999, Friston et al. 2017, Goodfellow et al. 2013, Hopstaken et al. 2015, Kirkpatrick et al. 2017, Logothetis 2008, Rao & Ballard 1999, Ratcliff & McKoon 2008. Editorial revision throughout. Version 3 (2026-05-20). Added section 9.4b "The Net Friction Rule, hysteresis, and anticipation as one substrate-level mechanism" consolidating the rule's three operational angles — rest-state shape (Type A vs Type B losses), irreversibility (write-and-burn at every commit), and anticipation as the rule operating across a horizon longer than the present forward-pass cascade — with a familiar gradient-descent analogue and a "Two regimes, one rule" extension (deliberation regime within capacity vs overflow regime above; overflow unifies the only-bearable-route condition, trauma, panic, and language-model hallucination under time-pressure). Section 9.2b extended with the lag 1 vs lag 2 distinction. Section 2.5 received a methodological addendum on single-turn prefill vs two-turn commit. Version 2 (2026-05-19). Added a working-memory operational-regime treatment (section 9.2b), a new section on encoding and retrieval as dual race-processes (section 3.5c), and a training-scaling prediction (section 9.3); editorial revision throughout. Companion papers in the Friction Theory series: Paper 0 (BFT master): 10.5281/zenodo.19462499 (concept) Paper 1 (Friction Theory substrate): 10.5281/zenodo.20012654 (concept; resolves to latest) Paper 2 (Capacity scaling): 10.5281/zenodo.20013491 (concept) Paper 3 (Friction-guided inference): 10.5281/zenodo.20014122 Paper 4 (Same Content, Wider Track): 10.5281/zenodo.20059859 (concept) Paper 10 (Race-architecture): 10.5281/zenodo.20014568 Paper 4B, Paper 6, Paper 8, Paper 15 - in preparation