HA + independent Lean evidence · Research, not Alpha admission

CV049 — horner product

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

Exact named statement

forall ab ac L bb bc M t. exists cb cc ahb ahc x bhb bhc y chb chc z. NatConvolutionPrefix(ab,ac,L,bb,bc,M,cb,cc,L+M) /\ (NatScaledHornerTrace(ab,ac,t,L,ahb,ahc) /\ (BetaAt(ahb,ahc,L,x) /\ (NatScaledHornerTrace(bb,bc,t,M,bhb,bhc) /\ (BetaAt(bhb,bhc,M,y) /\ (NatScaledHornerTrace(cb,cc,t,L+M,chb,chc) /\ (BetaAt(chb,chc,L+M,z) /\ z=t*(x*y)))))))

PD0013 — BetaAt · ND0402 — NatConvolutionPrefix · ND0427 — NatScaledHornerTrace

Fully expanded target AST

Complete certificate and independent checks

218 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: 396f5d28929411112a14eafdfa700edebdae4db2f0d4669afc4dec841105c464
Bundle SHA-256: 07fee4d447429fe28b7c296c10327f9331046aef8d12be69574f73e21c1e09e6

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.

CV008 · CV009 · CV011 · CV032 · CV037 · CV038 · CV039 · CV043 · CV044 · CV046 · CV047 · CV048

Scope

constructed full length convolution and actual three horner traces with exact extra multiplier product law including zero multiplier not truncated evaluation or analytic identity

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