Exact named statement
forall n. exists r d ab ac x p tb tc h y. (Pow(2,n,r)) /\ ((~r=0) /\ ((~d=0) /\ ((NatAtanhPrefix(d,ab,ac,S(S(18*r)))) /\ ((NatHornerValue(ab,ac,3,S(S(18*r)),x)) /\ ((Pow(3,S(S(18*r)),p)) /\ ((~p=0) /\ ((~h=0) /\ ((~(d*p)=0) /\ ((Le(3*x,d*p)) /\ ((NatScaledExpRecurrence(d*p,3*x,tb,tc,S(S(18*r)))) /\ ((BetaAt(tb,tc,0,h)) /\ ((Sum(tb,tc,S(S(S(18*r))),y)) /\ ((Le(r*y,(r*2)*h+h)) /\ (Le((r*2)*h,r*y+h)))))))))))))))PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · PD0020 — Pow · ND0437 — NatHornerValue · ND0425 — NatAtanhPrefix · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
452 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: c7f28f686ec9b7eb26f152b6aed3eecb9aa4b32a686ba022e3ba80d363e5f620
Bundle SHA-256: 99ef8cd7a0cdd76a9c39d828620e1c8858565b70d202b79dfb36df034bddb63e
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.
AP032 · AP033 · 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 · CV086
Scope
construct actual two to n and the explicit finite log exponential computations with two integer error bounds at most two to minus n from two retained stage proofs and positive comparison powers without infinite analytic identification
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.