HA + independent Lean evidence · Research, not Alpha admission

CV035 — horner linearity

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

Exact named statement

forall alpha beta gamma ab ac bb bc cb cc t N. NatLinearTriple(alpha,beta,gamma,ab,ac,bb,bc,cb,cc,N) ->
  exists ub uc vb vc wb wc u v w. NatScaledHornerTrace(ab,ac,t,N,ub,uc) /\ (NatScaledHornerTrace(bb,bc,t,N,vb,vc) /\ (NatScaledHornerTrace(cb,cc,t,N,wb,wc) /\ (BetaAt(ub,uc,N,u) /\ (BetaAt(vb,vc,N,v) /\ (BetaAt(wb,wc,N,w) /\ gamma*w=alpha*u+beta*v)))))

PD0013 — BetaAt · ND0409 — NatLinearTriple · ND0427 — NatScaledHornerTrace

Fully expanded target AST

Complete certificate and independent checks

111 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: ad3d9e7f204d9e713be5a888404827c60c7a6e4a2ceca04adb2deb516e9682df
Bundle SHA-256: 77477ae2e7d646455c9401f03bef0c0e798ef50fd7286954b938c74074793b65

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.

CV032

Scope

constructed three horner evaluations with weighted linearity from pointwise relation not multiplication 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.