HA + independent Lean evidence · Research, not Alpha admission

AP046 — half log precision

Full irrationality (IR072/G121) remains open. Stable: 432. Alpha v35: 4,318. This checkpoint changes neither catalogue.

Exact named statement

forall r p. Pow(2,S(S(18*r)),p) ->
  ~p=0 /\ Le(r,p)

PD0020 — Pow · PD0001 — Le

Fully expanded target AST

Complete certificate and independent checks

37 actual local proof nodes. Each node carries its complete ordinary HA proof body.

Full canonical proof bundle · Original HA receipt · Independent Lean receipt

Target SHA-256: 936a988b2a6fae61ebb3206a2a33746d5c8ad2e23501f642b0528b6b9e0e7877
Bundle SHA-256: 96815002d9cbada491bb67202df76d032ac56ed7b8f0c85b32d92a1406e3368a

Checked statement containment

These exact targets occur inside this certificate. These links summarize containment, not direct dependency arrows; the downloadable bundle records every private lemma and ordered edge.

Scope

prove generic binary growth n plus one at most two to n by ordinary induction then bound the actual two to eighteen r plus two cutoff power below by r without materializing large ground powers

None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.