Exact named statement
forall k. exists d ab ac y p. ~d=0 /\ (NatAtanhPrefix(d,ab,ac,S k) /\ (NatZeroBefore(ab,ac,S k,1) /\ (BetaAt(ab,ac,0,0) /\ (NatBoundedPrefix(ab,ac,2*d,S k) /\ (NatHornerValue(ab,ac,2,S k,y) /\ (Pow(2,k,p) /\ Le(y+2*d,(2*d)*p)))))))PD0001 — Le · PD0013 — BetaAt · PD0020 — Pow · ND0437 — NatHornerValue · ND0440 — NatBoundedPrefix · ND0408 — NatZeroBefore · ND0425 — NatAtanhPrefix
Complete certificate and independent checks
136 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: b21b3f67a0aa28eb1456681cada027f47d5323c8f0b7e3c66defa64552756e5d
Bundle SHA-256: 775e8f82cf01abe8eecd1022c91ab0a44028d1b97d0beab802cb5f75c272f81e
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.
Scope
same actual atanh coefficient table nonzero denominator zero head and entry bounds with horner value power and integer majorant not logarithm or rational division transport
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.