Exact named statement
forall n. exists r. Pow(2,n,r) /\ (~r=0 /\ (forall k. Le(S(S(18*r)),k) ->
exists d ab ac x p wb wc tb tc h f q y. (~d=0) /\ ((NatAtanhPrefix(d,ab,ac,S(2*k))) /\ ((NatHornerValue(ab,ac,3,S(2*k),x)) /\ ((Pow(3,S(2*k),p)) /\ ((~p=0) /\ ((~(d*p)=0) /\ ((NatExpWeightTable(d*p,S(S k),wb,wc)) /\ ((NatPowerWeightedPrefix(3*x,wb,wc,tb,tc,S(S(S k)))) /\ ((BetaAt(wb,wc,0,h)) /\ ((BetaAt(tb,tc,0,h)) /\ ((~h=0) /\ ((Factorial(S(S k),f)) /\ ((Pow(d*p,S(S k),q)) /\ ((h=f*q) /\ ((Sum(tb,tc,S(S(S k)),y)) /\ ((NatScaledExpRecurrence(d*p,3*x,tb,tc,S(S k))) /\ ((forall j a fj dj xj. Le(j,S(S k)) ->
BetaAt(tb,tc,j,a) ->
Factorial(j,fj) ->
Pow(d*p,j,dj) ->
Pow(3*x,j,xj) ->
(a*fj)*dj=h*xj) /\ ((Le(r*y,(r*2)*h+2*h)) /\ (Le((r*2)*h,r*y+h)))))))))))))))))))))PD0001 — Le · PD0013 — BetaAt · ND0425 — NatAtanhPrefix · ND0437 — NatHornerValue · PD0020 — Pow · ND0443 — NatScaledExpRecurrence · PD0015 — Sum · ND0423 — NatExpWeightTable · ND0442 — NatPowerWeightedPrefix · PD0023 — Factorial
Complete certificate and independent checks
522 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: 3ff68dfaeccdb0e61f146f12e87cf0d13b773fc609d14b0ad64a489af6b11d33
Bundle SHA-256: 64101f309bab0e6494249ca21315df0e64d1a96bd905228e70a880181c50af25
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 · AP082 · AP083 · AP084 · AP085 · 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
Scope
construct positive actual logarithm and factorial normalized exponential computations at every eligible fixed schedule index after one uniform dyadic threshold preserving all index normalization and both near two bounds
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.