Exact named statement
forall d ab ac M N. NatAtanhPrefix(d,ab,ac,M+N) ->
exists bb bc x y z p q h. NatAffineSlice(ab,ac,M,1,bb,bc,N) /\ (NatHornerValue(ab,ac,3,M,x) /\ (NatHornerValue(bb,bc,3,N,y) /\ (NatHornerValue(ab,ac,3,M+N,z) /\ (Pow(3,M,p) /\ (Pow(3,N,q) /\ (Pow(3,M+N,h) /\ (h=p*q /\ (z=q*x+y /\ (Le(y+d,d*q) /\ (Le(h*x,p*z) /\ (Le(p*z,h*x+d*h))))))))))))PD0001 — Le · ND0411 — NatAffineSlice · PD0020 — Pow · ND0437 — NatHornerValue · ND0425 — NatAtanhPrefix
Complete certificate and independent checks
142 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: fe8e75a1b92914b876b3335a496085b7cea520d900aaedca8a40e6f31ac26fa6
Bundle SHA-256: 0fdb76e370b33e761b9fd995aafbdc8a6d9bb0db5819bb8216a9d6d4ca7760c3
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
supplied actual atanh table prefix tail whole values and powers constructed with exact scaled split tail bound and both cross multiplied truncation bounds including zero lengths no division or analytic limit
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.