Exact named statement
forall n. exists r s. Pow(2,n,r) /\ (~r=0 /\ (DyadicSqrt2(n,r,s) /\ (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) /\ ((~(2*(d*p))=0) /\ ((NatExpWeightTable(2*(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(2*(d*p),S(S k),q)) /\ ((h=f*q) /\ ((Sum(tb,tc,S(S(S k)),y)) /\ ((NatScaledExpRecurrence(2*(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(2*(d*p),j,dj) ->
Pow(3*x,j,xj) ->
(a*fj)*dj=h*xj) /\ ((Le(r*y,s*h+8*h)) /\ (Le(s*h,r*y+h))))))))))))))))))))))PD0001 — Le · PD0013 — BetaAt · PD0020 — Pow · ND0446 — DyadicSqrt2 · ND0425 — NatAtanhPrefix · ND0437 — NatHornerValue · ND0443 — NatScaledExpRecurrence · PD0015 — Sum · ND0423 — NatExpWeightTable · ND0442 — NatPowerWeightedPrefix · PD0023 — Factorial
Complete certificate and independent checks
586 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: 9fba277808e08f9fc794a636d0be0242f1a8498dbd631870d0f88440174b708a
Bundle SHA-256: ca771f818bb607d30de80c5bc19a15ee2d05a0932355fc71c7800b0ef096d67b
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 · AP089 · AP090 · 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
construct positive fixed schedule half logarithm exponential tables after one chosen dyadic root and retain every actual factorial normalization and both checked cross errors
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.