Exact named statement
forall n. exists r s. Pow(2,n,r) /\ (~r=0 /\ (DyadicSqrt2(n,r,s) /\ (forall e bb bc l z q N eb ec b v. ~e=0 ->
NatAtanhPrefix(e,bb,bc,(S(S(18*r)))+l) ->
NatHornerValue(bb,bc,3,(S(S(18*r)))+l,z) ->
Pow(3,(S(S(18*r)))+l,q) ->
NatScaledExpRecurrence(2*(e*q),3*z,eb,ec,(S(S(S(18*r))))+N) ->
BetaAt(eb,ec,0,b) ->
Sum(eb,ec,S((S(S(S(18*r))))+N),v) ->
~q=0 /\ (~(2*(e*q))=0 /\ (Le(r*v,s*b+8*b) /\ Le(s*b,r*v+b))))))PD0001 — Le · PD0013 — BetaAt · PD0020 — Pow · ND0446 — DyadicSqrt2 · ND0425 — NatAtanhPrefix · ND0437 — NatHornerValue · ND0443 — NatScaledExpRecurrence · PD0015 — Sum
Complete certificate and independent checks
583 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: bdd05acec456f38c8dbd660093564668cdcb6a6207fd285396940740dcf42ff8
Bundle SHA-256: 40a9356ff0ed241d51a10a9948e73f850ff7b8cd979cb9ca1531a692fa238b49
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 · AP034 · AP037 · AP038 · AP040 · AP041 · AP042 · AP043 · AP044 · AP045 · AP046 · AP047 · AP048 · AP049 · AP050 · AP087 · AP088 · CV001 · CV002 · CV004 · CV008 · CV009 · CV011 · CV012 · CV019 · CV020 · CV021 · CV022 · CV024 · CV025 · CV027 · CV028 · CV029 · CV030 · CV031 · CV032 · CV033 · CV037 · CV038 · CV039 · CV043 · CV044 · CV046 · CV047 · CV048 · CV049 · CV056 · CV057 · CV058 · CV059 · CV060 · CV061 · CV062 · CV063 · CV064 · CV065 · CV068 · CV069 · CV070 · CV072 · CV073 · CV075 · CV077 · CV078 · CV079 · CV081 · CV082 · CV083 · CV084 · CV086 · CV087 · CV088 · CV089 · CV090 · CV092 · CV093 · CV094 · CV095 · CV096 · CV097 · CV098 · CV100 · CV101 · SQ002 · SQ009
Scope
choose one actual dyadic root before all later independent half logarithm exponential tables and prove both finite cross errors by checked reference restriction refinement and positive scale cancellation
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.