HA + independent Lean evidence · Research, not Alpha admission

AP001 — log root argument

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

Exact named statement

forall k. exists d s D ab ac x p. (NatSqrt2LogArgument(k,d,s,D,ab,ac,x,p)) /\ ((~d=0) /\ ((~s=0) /\ ((~D=0) /\ ((~p=0) /\ ((~((D*p)*s)=0) /\ (Le((3*x)*d,(D*p)*s)))))))

PD0001 — Le · ND0447 — NatSqrt2LogArgument

Fully expanded target AST

Complete certificate and independent checks

161 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: 2b80a217cebb668c94e88b3a849c0738ad80d20aee1014489d6b8561839e89df
Bundle SHA-256: 8097cee51aafd444321e288943d96cc527f06ab8e4f5dd4fd3b06e8366c9dd10

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.

CV025 · CV032 · CV086 · SQ001 · SQ002 · SQ003 · SQ004

Scope

construct actual dyadic root and finite odd reciprocal table horner value and power prove positive quotient denominator and upper bound one no analytic logarithm or accuracy assumption

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