A priori estimates across the subcritical Lane–Emden hyperbola

This consequence note records the full strictly subcritical Lane–Emden estimate package for n at least 3 and p,q greater than 1: universal pointwise and gradient estimates on arbitrary proper domains, exterior decay, zero-Dirichlet half-space nonexistence without a growth assumption, and fixed bounded C2-domain Dirichlet bounds and strong compactness in exact spaces. It applies the OpenAI 2026 entire Liouville theorem to established Polacik–Quittner–Souplet and Quittner–Souplet reductions, with an explicit normalization and boundary blow-up account. The full-range conclusion is an immediate consequence; no independent solution of the base conjecture, new reduction, or first-priority claim is made.

The upstream unweighted analytic proof was independently audited. Actual Lean source semantics were inspected, but a complete kernel build and axiom audit were not reproduced; the follow-on theorem is not claimed formalized. AI tools were used extensively for research, drafting and verification. The preprint has not undergone conventional human peer review or refereeing at publication. The source archive contains dependency and priority audits, exact hashes, proof commentary and reproducible diagnostic checks; these diagnostics are not numerical proof certificates.