Ideal ignition windows for p-11B in a 0-D power balance: no window at Te = Ti and thresholds on Te/Ti, with two reactivity fits

In an ideal 0-D power-balance model of the Wurzel–Hsu type (arXiv:2105.10954), with two proton–boron-11 reactivity fits — Nevins–Swain as transcribed from the Wurzel–Hsu public code (MIT licence, commit 4ae563bf) and the updated S-factor of Wang et al. (arXiv:2601.00241) — in the box Ti ∈ [50, 500] keV, boron fraction x ∈ [0.05, 0.5], we report interval-arithmetic enclosures (Arb ball arithmetic, Tier C, not replayed in Lean). There is no ignition window at Te = Ti: the certified maximum of Pc/PB is in [0.4214, 0.4256] (Nevins–Swain) and [0.4287, 0.4326] (Wang). A window needs Te/Ti below thresholds θ* certified only for θ ≤ 1: Nevins–Swain [0.4223, 0.4308] over the box and [0.3753, 0.3828] at x = 1/6; Wang [0.4381, 0.4470] and [0.396, 0.402]. These thresholds hold for these fits and this bremsstrahlung only: a uniform reactivity factor of 1.1/1.2/1.32 moves the threshold to 0.477/0.524/0.579 (auditor, float). Positive control. The D-T ideal-ignition temperature of Wurzel–Hsu is reproduced ([4.2989514, 4.2989523] keV) together with their Table II/III values, for the model the authors' code ran; the gate model was chosen after a float run, and the most literal reading of the text prints 3.0×1021 instead of 2.9×1021 for the triple-product minimum (Tign in [4.3071225, 4.3071227] keV; auditor, Tier X). The D-T gate does not discriminate for the p-11B conclusion; the p-11B pipeline's discrimination is shown by the θ* witnesses, a check at θ = 1/3 and a no-bremsstrahlung control. A remark on their Fig. 28: the certified threshold at their own mix is 0.375–0.383, so Pc exceeds PB by about 11% at Te = Ti/3 (float check, 1.113 Nevins–Swain, 1.161 Wang); this sharpens a figure reading and does not contradict their conclusions. Tier split. Tier A pending a statement lock (Lean 4.34.1, Mathlib; axioms within propext, Classical.choice, Quot.sound): 20x(1−x) ≤ (1+4x)2 and 1 + 2.2t + 3t2 − 4.375t2.5 > 0 on [0, 1], kernel-checked, independently recompiled and replayed with leanchecker (rc 0) by the auditor, with kernel-rejected planted controls; no statement-lock entry exists. Tier L: the model and the fits as cited. Tier C: all enclosures. Tier X: float checks, including the auditor's Wang-side numbers. What this is NOT. Every statement concerns an idealised 0-D power-balance model with the stated fitted formulas. It makes no claim about any reactor, device, feasibility, climate or economics, does not say that p-11B fusion is possible or impossible, and does not say that Te < Ti can be maintained. Not in the model: synchrotron radiation, transport and conduction, ion–electron coupling mechanisms, alpha heating of electrons, ash, non-Maxwellian or kinetic effects, and the uncertainties of the fits. Limitations. Independently audited by a different AI agent instance (AUDIT.md, ACCEPT_WITH_CORRECTIONS, nine corrections applied); the auditor's Wang-side and D-T minimiser values are float only; no human audit and no statement lock (owed). The Bosch–Hale (1992) and Nevins–Swain (2000) coefficients could not be obtained from the primary papers by the producer or the auditor and are not verified; this matters most for θ*. result.json, logs/sha256.json and RESULT.md list data/papers and data/downloads files that are no longer in the repository (third-party material moved out). The Elenchus ledger gate exits with code 1 (0 blocking findings, 2 flags LEDGER_UNAUDITED_TIER_A, one per Tier A row).