HA + independent Lean evidence · Research, not Alpha admission

CV085 — constructed composition error

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 ex ep ev evb evc ezb ezc es p3 a2. (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) /\ ((NatHornerValue(ab,ac,3,N,ex)) /\ ((Pow(3,N,ep)) /\ ((Pow(3,((S N)*N),ev)) /\ ((NatPointwiseProductPrefix(wb,wc,evb,evc,ezb,ezc,S N)) /\ ((Sum(ezb,ezc,S N,es)) /\ ((forall j y a b c. Lt(j,S N) ->
  BetaAt(evb,evc,j,y) ->
  Pow(ep,j,a) ->
  Pow(3,j,b) ->
  Pow(ex,j,c) ->
  a*y=(ev*b)*c) /\ ((Pow(3,k,p3)) /\ ((Pow(2,N,a2)) /\ ((~ep=0) /\ ((~ev=0) /\ ((~p3=0) /\ ((~(z*ev)=0) /\ ((~((z*ev)*p3)=0) /\ ((IRatLe(es,0,z*ev,2*ep+9*a2,0,ep)) /\ (IRatLe(2,0,1,es*p3+z*ev,0,(z*ev)*p3))))))))))))))))))))))))))

PD0001 — Le · PD0002 — Lt · PD0013 — BetaAt · PD0015 — Sum · ND0423 — NatExpWeightTable · PD0020 — Pow · PD0023 — Factorial · ND0437 — NatHornerValue · ND0439 — NatPointwiseProductPrefix · ND0425 — NatAtanhPrefix · ND0444 — IRatLe

Fully expanded target AST

Complete certificate and independent checks

435 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: 390079559204a44746d65722e27b386315e6b9830542df520c3ed5acd50b4d58
Bundle SHA-256: c2e9f924a90d6c5c2580db4e5dc7d18a89a02f6936f3c0dff0ebc0d566b2d833

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 · CV081 · CV082 · CV083 · CV084

Scope

unconditional same actual atanh input factorial weights whole support composition and finite weighted sum with monomial normalization and both valid rational errors no geometric or tail premises no analytic limit

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