Exact named statement
forall K. exists d ab ac x p tb tc h y r a. (~d=0) /\ ((NatAtanhPrefix(d,ab,ac,S(S K))) /\ ((NatHornerValue(ab,ac,3,S(S K),x)) /\ ((Pow(3,S(S K),p)) /\ ((Pow(3,S K,r)) /\ ((Pow(2,S(S K),a)) /\ ((~p=0) /\ ((~r=0) /\ ((~h=0) /\ ((~(d*p)=0) /\ ((Le(3*x,d*p)) /\ ((NatScaledExpRecurrence(d*p,3*x,tb,tc,S(S K))) /\ ((BetaAt(tb,tc,0,h)) /\ ((Sum(tb,tc,S(S(S K)),y)) /\ ((IRatLe(y,0,h,2*p+9*a,0,p)) /\ (IRatLe(2,0,1,y*r+h,0,h*r))))))))))))))))PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · PD0020 — Pow · ND0437 — NatHornerValue · ND0425 — NatAtanhPrefix · ND0443 — NatScaledExpRecurrence · ND0444 — IRatLe
Complete certificate and independent checks
439 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: f184312da8aa97085684bf27c6b090fe30ff3df7d6afcd251bbc4309ddb1c715
Bundle SHA-256: 9762342212b1e76b6e2d3f640b5a1086fcd5ea3957daf4e257d97d987ef5923a
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 · CV086
Scope
construct actual finite logarithm coefficients and exponential terms and connect the same product table to its positive head recurrence sum and both errors near two without asserting the infinite logarithm identity
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.