HA + independent Lean evidence · Research, not Alpha admission

CV080 — same table composition

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

Exact named statement

forall K. exists k N d ab ac wb wc z fn pn fpb fpc fqb fqc frb frc fsb fsc fs fv fub fuc hb hc r p3. (k=S K) /\ ((N=S k) /\ ((~d=0) /\ ((NatAtanhPrefix(d,ab,ac,N)) /\ ((NatExpWeightTable(d,N,wb,wc)) /\ ((BetaAt(wb,wc,0,z)) /\ ((~z=0) /\ ((Factorial(N,fn)) /\ ((Pow(d,N,pn)) /\ ((z=fn*pn) /\ ((forall j w f p. Le(j,N) ->
  BetaAt(wb,wc,j,w) ->
  Factorial(j,f) ->
  Pow(d,j,p) ->
  (w*f)*p=z) /\ ((NatPowerTrace(ab,ac,S k,S ((S N)*(S k)),fpb,fpc,fqb,fqc,S N)) /\ ((NatWeightedSeriesTrace(S ((S N)*(S k)),wb,wc,fpb,fpc,fqb,fqc,frb,frc,fsb,fsc,S N)) /\ ((NatPowerRow(frb,frc,fsb,fsc,S N,fub,fuc)) /\ ((Pow(2,((S N)*(S k)),fv)) /\ ((NatHornerValue(fub,fuc,2,S ((S N)*(S k)),fs)) /\ ((Le(fs,9*(z*fv))) /\ ((Le(N,((S N)*(S k)))) /\ ((Le(N,S ((S N)*(S k)))) /\ ((forall i a. Lt(i,N) ->
  BetaAt(fub,fuc,i,a) ->
  ((i=0 /\ a=z) \/ (exists j. i=S j /\ a=2*z))) /\ ((NatScaledHornerTrace(fub,fuc,3,N,hb,hc)) /\ ((BetaAt(hb,hc,N,r)) /\ ((Pow(3,k,p3)) /\ ((~p3=0) /\ ((r+z=(2*z)*p3) /\ ((~(z*p3)=0) /\ ((forall M. Le(M,((S N)*(S k))) ->
  exists r tb tc u p0 q0 h. (((S N)*(S k))=M+r) /\ ((NatAffineSlice(fub,fuc,M,1,tb,tc,S r)) /\ ((NatHornerValue(tb,tc,3,S r,u)) /\ ((Pow(2,M,p0)) /\ ((Pow(3,M,q0)) /\ ((Pow(3,((S N)*(S k)),h)) /\ ((~p0=0) /\ ((~q0=0) /\ ((~h=0) /\ ((~(z*h)=0) /\ ((Le(u*q0,(9*p0)*(z*h))) /\ (IRatLe(u,0,z*h,9*p0,0,q0))))))))))))) /\ (exists r tb tc u p0 q0 h. (((S N)*(S k))=N+r) /\ ((NatAffineSlice(fub,fuc,N,1,tb,tc,S r)) /\ ((NatHornerValue(tb,tc,3,S r,u)) /\ ((Pow(2,N,p0)) /\ ((Pow(3,N,q0)) /\ ((Pow(3,((S N)*(S k)),h)) /\ ((~p0=0) /\ ((~q0=0) /\ ((~h=0) /\ ((~(z*h)=0) /\ ((Le(u*q0,(9*p0)*(z*h))) /\ (IRatLe(u,0,z*h,9*p0,0,q0)))))))))))))))))))))))))))))))))))))))

PD0001 — Le · PD0002 — Lt · PD0013 — BetaAt · ND0411 — NatAffineSlice · ND0423 — NatExpWeightTable · ND0427 — NatScaledHornerTrace · PD0020 — Pow · PD0023 — Factorial · ND0405 — NatPowerRow · ND0407 — NatPowerTrace · ND0437 — NatHornerValue · ND0421 — NatWeightedSeriesTrace · ND0425 — NatAtanhPrefix · ND0444 — IRatLe

Fully expanded target AST

Complete certificate and independent checks

426 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: e5ce4e46386b9c0aa0cde7db11202d410819547dc4b6b462458184f2871f9611
Bundle SHA-256: 739a6442d3cf4657fdb256c65867cd7b790f76676c457cd00f167d607a5b759c

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.

CV001 · CV002 · CV004 · CV008 · CV009 · CV011 · CV012 · CV019 · CV020 · CV021 · CV022 · CV024 · CV025 · CV027 · CV028 · CV029 · CV031 · CV032 · CV033 · CV037 · CV038 · CV039 · CV043 · CV044 · CV046 · CV047 · CV048 · CV049 · CV056 · CV057 · CV058 · CV059 · CV060 · CV061 · CV062 · CV063 · CV064 · CV065 · CV072 · CV073 · CV075 · CV077 · CV078 · CV079

Scope

same actual full composition has proved low coefficient pattern geometric low prefix value factorial normalization and rational omitted tail bound without replacing supplied inputs weights or assuming code equality not analytic limit

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