AP092 — fixed half log fine root — irrationality research

Exact named statement

forall n. exists r. Pow(2,n,r) /\ (~r=0 /\ (forall l e t. DyadicSqrt2(n+l,e,t) ->
  Le(S(S(18*r)),n+l) ->
  exists d ab ac x p wb wc tb tc h f q y. (~d=0) /\ ((NatAtanhPrefix(d,ab,ac,S(2*(n+l)))) /\ ((NatHornerValue(ab,ac,3,S(2*(n+l)),x)) /\ ((Pow(3,S(2*(n+l)),p)) /\ ((~p=0) /\ ((~(2*(d*p))=0) /\ ((NatExpWeightTable(2*(d*p),S(S (n+l)),wb,wc)) /\ ((NatPowerWeightedPrefix(3*x,wb,wc,tb,tc,S(S(S (n+l))))) /\ ((BetaAt(wb,wc,0,h)) /\ ((BetaAt(tb,tc,0,h)) /\ ((~h=0) /\ ((Factorial(S(S (n+l)),f)) /\ ((Pow(2*(d*p),S(S (n+l)),q)) /\ ((h=f*q) /\ ((Sum(tb,tc,S(S(S (n+l))),y)) /\ ((NatScaledExpRecurrence(2*(d*p),3*x,tb,tc,S(S (n+l)))) /\ ((forall j a fj dj xj. Le(j,S(S (n+l))) ->
  BetaAt(tb,tc,j,a) ->
  Factorial(j,fj) ->
  Pow(2*(d*p),j,dj) ->
  Pow(3*x,j,xj) ->
  (a*fj)*dj=h*xj) /\ ((~e=0) /\ ((~t=0) /\ ((Le(e,t)) /\ ((Lt(t,2*e)) /\ ((Le(r*(e*y),r*(t*h)+8*(e*h))) /\ (Le(r*(t*h),r*(e*y)+2*(e*h))))))))))))))))))))))))))

PD0001 — Le · PD0002 — Lt · PD0013 — BetaAt · PD0020 — Pow · ND0446 — DyadicSqrt2 · ND0425 — NatAtanhPrefix · ND0437 — NatHornerValue · ND0443 — NatScaledExpRecurrence · PD0015 — Sum · ND0423 — NatExpWeightTable · ND0442 — NatPowerWeightedPrefix · PD0023 — Factorial

Fully expanded target AST

Complete certificate and independent checks

595 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: 6d4b5804c59942bc029957cbb384a3a6d2235616d7c0e1cf4c0af32be3e12771
Bundle SHA-256: c9cabc5640c33f87f1fe31817ab71b04bfb0b43896488e79b8da6b69d62e232c

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 · AP091 · 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 · SQ005 · SQ006 · SQ007 · SQ008 · SQ009

Scope

transfer constructed fixed schedule half logarithm samples to any supplied finer dyadic root at the same index preserving all positive normalizations and both finite errors

None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.