Logic as Reactance: Why Truth-Value Judgment is Probabilistic All the Way Down (Even in Humans)
Paper 14 · Pødenphant Lund, T. (2026) · Preprint · Live on Zenodo
Truth-value judgment is not a separate discrete-symbolic faculty. It is the substrate's reactance signature (differential race-pressure against gradient-encoded distribution-skew) read back as cognitive content. Empirical anchor: a discontinuous cliff-event at the first content-token-position on fine-tuned LLMs, observed across two architectures (Qwen2.5-7B and Mistral-7B-v0.3, p < 1e-17), eleven encoding-depth checkpoints (monotonic rising in log-epoch), eight floating-point substrates (calculator-overflow scaling law collapse = mantissa_bits × ln 2, R² = 0.9999), and a cross-domain readout test (preference vs truth, same direction, ~60% magnitude). The framework predicts the same signature in biological tissue via the N400 ERP, a fifty-year-old neuroscience signature reinterpreted as a substrate-readout of the same mechanism.
| DOI (concept) | 10.5281/zenodo.20217712 |
| Status | Preprint live as v1, 2026-05-15 |
| Target venue | TMLR (primary) / Cognitive Science / Trends in Cognitive Sciences |
| Length | ~17k words |
| Author | Tomas Pødenphant Lund [ORCID] |
TL;DR
A familiar objection to treating large language models as cognitive models holds that their output is “merely probabilistic generation”, distinguished from genuine reasoning by its statistical substrate. This paper inverts the move: it proposes that truth-value judgment in any race-architecture substrate is implemented as the substrate's reactance signature, measurable as differential race-pressure against gradient-encoded distribution-skew when input fails to match the encoded distribution. The substrate reads “true” when no reactance is triggered, “false” when reactance triggers strongly, and “irrelevant” when reactance is below detection threshold. The discrete-symbolic appearance of binary truth is generated by the substrate's own readout process applied to a continuous mechanism.
Substrate mechanism. Race architecture (Paper 1 R1–R3, Paper 10 A1–A5) plus cumulative gradient pressure (Paper 2B §6) produces a substrate-property with dimensional unit (log-CR collapse, in nats) and three observational discriminators against simple route-competition: (i) saturation under super-threshold drive, (ii) position-localisation at the first content-token (pos 0–2), (iii) absence on ICL substrates. The signature is identified by the joint presence of all three; lacking any one demotes the observation to route-competition without reactance.
Empirical anchor.
- Cross-architecture cliff (P14.1, P14.3) — cliff-event confirmed on Qwen2.5-7B (p < 1e-8) and Mistral-7B-v0.3 (p < 1e-17 raw-FT, p < 1e-5 paraphrase-FT). Not an RLHF artefact, not Qwen-specific.
- Saturated ceiling under super-threshold drive (P14.2) — ~10× gradient differential (raw-FT vs paraphrase-FT) produces Δ = 1.21 log-units cliff-amplitude, not 10×. First-order-saturation discriminator vs Landau second-order (which would predict driveβ).
- Monotonic dose-response in log-encoding-depth (P14.9) — eleven checkpoints, ep_0 to ep_300; reactance-amplitude doubles each ~10× increase in training-passes; no plateau or decline within ep_300.
- Cross-implementation scaling law (P14.4) — eight floating-point substrates from bfloat16 (8-bit mantissa) to float128 (113-bit),
collapse = mantissa_bits × ln 2, R² = 0.9999, slope within 0.07% of analytic prediction, holds across hardware IEEE 754, simulated extended precision, and radix-10 decimal. - Cross-domain readout (P14.5) — preference-task cliff-amplitude is ~60% of truth-task on the same encoded distribution. Direction confirmed; magnitude content-domain-specific. Hypothesis B (truth and preference as different readouts of the same substrate mechanic) partially confirmed.
Thermodynamic substrate-binding. Cliff-amplitude has dimensions of information in nats: collapse × kT [J/nat] = erase-cost [J]. Landauer (1961) sets the minimum cost per irreversible bit-erasure as kT ln 2; Lloyd (2000) generalises to any computer; Margolus-Levitin (1998) sets the upper bound on computation rate at 4E/h states/s. These are parent-laws for every substrate-mechanic, including race-architecture. The cliff-signature is consistent with, and an instance of, thermodynamic substrate-binding of logic.
The “even in humans” claim. The framework predicts the same signature in biological tissue. The N400 event-related potential (Kutas & Hillyard 1980; Kutas & Federmeier 2011), a fifty-year-old neuroscience signature of semantic violation, is reinterpreted as the biological-substrate readout of the same cliff-event. P14.11 specifies a direct test: human subjects trained on a novel domain (parallel to the Zorbetik LLM protocol) should show N400 amplitude correlating with encoding-depth, with a monotonic dose-response mirroring the silicon eleven-checkpoint curve. Cognitive dissonance, indoctrination, and expertise reversal are special cases at the high-encoding-depth tail of the same substrate mechanic.
Scope conditions. Principle-universal at the substrate-mechanism level (any race-architecture substrate under cumulative gradient pressure); quantitative parameters (cliff-amplitude, saturation ceiling, position-localisation tolerance) are substrate- and content-domain-specific. The hypothesis B claim is partial-confirmed on silicon; biological-substrate confirmation is specified as P14.11. The paper is explicit about the silicon-confirmed vs biological-postulated distinction.
Key results in numbers
| Test | Substrate | Result | Significance |
|---|---|---|---|
| Cliff at pos 0 (raw-FT) | Qwen2.5-7B, 30 epochs | collapse 11.69 log-units | p < 1e-8 |
| Cliff at pos 0 (paraphrase-FT) | Qwen2.5-7B, ~10× gradient | collapse 10.48 | Δ = 1.21 (saturated) |
| Cross-architecture replication | Mistral-7B-v0.3-base | cliff confirmed qualitatively | p < 1e-17 / p < 1e-5 |
| Dose-response (encoding-depth) | Qwen, 11 checkpoints ep_0–ep_300 | monotonic linear in log-epoch | no plateau within ep_300 |
| Cross-implementation scaling | 8 FP substrates, bf16→f128 | collapse = mantissa_bits × ln 2 | R² = 0.9999 |
| Cross-domain readout | preference task on encoded distribution | cliff 6.31 vs truth 10.48 | ~60% magnitude, direction confirmed |
Predictions catalogue
Eleven predictions, P14.1–P14.11 (plus P14.12 added 2026-05). Status as of preprint-build 2026-05-15:
- P14.1 Cliff-event existence on FT substrates — confirmed (Qwen + Mistral)
- P14.2 Saturated ceiling under super-threshold drive — confirmed (Δ = 1.21 log-units, not 10×)
- P14.3 Cross-architecture substrate-universal qualitative — confirmed
- P14.4 Cross-implementation universality (calculator overflow) — confirmed
- P14.5 Cross-domain readout (preference vs truth) — partially confirmed (hypothesis B)
- P14.6a Floating-point overflow as cousin-phenomenon — confirmed
- P14.6b Quantum decoherence as cousin-phenomenon — pending
- P14.6c Mental-arithmetic capacity-limit as cousin-phenomenon — pending
- P14.7 Substrate × training-method interaction on cliff-magnitude — prediction-generating from Mistral × Qwen divergence
- P14.8 Content-domain modulation of cliff-magnitude (moral, aesthetic, factual) — prediction-generating
- P14.9 Monotonic dose-response in log-encoding-depth — confirmed (11 checkpoints, Qwen)
- P14.10 Kindling transfer property (FT on P lowers cliff threshold for ¬P′ sharing embeddings with P) — testable per Goddard 1969 kindling precedent
- P14.11 Biological-substrate direct confirmation via N400 paradigm — the cleanest extension beyond silicon. Specifies a human-subject experimental design with novel-domain training (parallel to Zorbetik LLM protocol), predicting N400 amplitude monotonic dose-response over encoding trials.
- P14.12 Food-preference learning as cliff-amplitude habituation — testable per Birch & Marlin 1982 pre-exposure paradigm
Intersection points with prior frameworks
Five connection-points are identified at substrate-mechanism level (not as parent frameworks; the paper is explicit that race architecture is an independent axiomatic specification):
- Predictive processing (Friston, Clark, Hohwy) — shares the probabilistic-substrate intuition. Reactance and variational free-energy are distinct quantities at distinct scales; free-energy is a scalar long-run quantity, reactance is a short-timescale per-token observable that decomposes into magnitude / distribution / rhythm. Predictive processing predicts continuous monotonic update under drive; race architecture predicts saturation (P14.2).
- Quantum cognition (Busemeyer & Bruza 2012) — quantum-probability cognitive models use superposition + measurement; race architecture grounds the “measurement” step in substrate readout.
- Signal detection theory (Green & Swets 1966) — SDT specifies the decision-step but treats the underlying distribution as exogenous; race-architecture specifies how the encoded distribution is built by cumulative gradient pressure.
- Fuzzy logic (Zadeh 1965) — fuzzy logic offered a formal continuous-truth alternative to discrete logic; race architecture grounds the continuity in substrate physics rather than postulating it.
- Biological precedents — kindling (Goddard 1969), somatic markers (Damasio 1994), dopaminergic reward-prediction error (Schultz 1998), and the N400 (Kutas & Hillyard 1980) are reframed as substrate-readout signatures of the same mechanic on different content-domains.
Why this matters
If truth-evaluation is substrate-bound all the way down, several inherited distinctions collapse:
- Truth vs preference vs valence are not three different cognitive faculties — they are three readouts of the same substrate-mechanic on different content-domains. The cross-domain test (P14.5) confirmed this direction empirically on silicon.
- Cognitive dissonance (Festinger 1957), indoctrination (Lifton 1961), and expertise reversal (Kalyuga et al. 2003) are special cases at the high-encoding-depth tail of the same substrate-mechanic, not separate phenomena.
- The N400 — a signature studied for fifty years as a semantic-violation marker — is reinterpreted as the biological-substrate readout of the cliff-event. P14.11 specifies the direct test.
- LLMs as cognitive models — the “merely probabilistic” objection presupposes an answer to the question of whether biological cognition is itself probabilistic at substrate level. This paper supplies one half of the empirical bridge; P14.11 specifies the other half.
Companion papers
- Paper 1 (Friction Theory) — R1–R3 race-axioms; the substrate-mechanic specification this paper invokes
- Paper 10 (Race architecture) — A1–A5 axiomatisation with Margolus-Levitin and Landauer anchors; physics-scope derivation
- Paper 2B (ICL/FT memory) — cumulative gradient pressure §6; the encoding mechanism that builds the asymmetric route-weight pattern read out as reactance
- Paper 5 (Field-theoretic taxonomy of emotions) — §3.0a distributed reactance: biological substrates instantiate reactance multi-locus; LLMs are single-locus
- Paper 0 (BFT) — biological-substrate context; the field-organised friction framework into which the substrate-readout fits