AP081 — exp joint error — irrationality research

Exact named statement

forall L K d e x y g n N ab ac bb bc a0 b0 s t r p. ~d=0 ->
  ~e=0 ->
  Le(x,L*d) ->
  Le(y,L*e) ->
  Le(2*L,K) ->
  Le(d*y,e*x+g) ->
  Le(e*x,d*y+g) ->
  NatScaledExpRecurrence(d,x,ab,ac,K+(L*K+n)) ->
  NatScaledExpRecurrence(e,y,bb,bc,S(K+(L*K+n))+N) ->
  BetaAt(ab,ac,0,a0) ->
  BetaAt(bb,bc,0,b0) ->
  Sum(ab,ac,S(K+(L*K+n)),s) ->
  Sum(bb,bc,S(S(K+(L*K+n))+N),t) ->
  Pow(2,n,r) ->
  Pow(2,S(9*(S L)+n),p) ->
  Le(p*g,d*e) ->
  ~r=0 /\ (~p=0 /\ (Le(r*(b0*s),r*(a0*t)+a0*b0) /\ Le(r*(a0*t),r*(b0*s)+2*(a0*b0))))

PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · PD0020 — Pow · ND0443 — NatScaledExpRecurrence

Fully expanded target AST

Complete certificate and independent checks

323 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: 7cd2d99c4a00cc142b8b0811c8a227ab0423f1aaad7a8f745af23c75e8b7b638
Bundle SHA-256: 59ca12ab08a8f656d9d6503f675d5d770dd16a330430746c7c00077f8aa32f25

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.

AP037 · AP038 · AP040 · AP041 · AP051 · AP052 · AP053 · AP054 · AP055 · AP056 · AP057 · AP060 · AP062 · AP063 · AP068 · AP069 · AP070 · AP071 · AP072 · AP073 · AP074 · AP075 · CV008 · CV009 · CV011 · CV022 · CV030 · CV043 · CV044 · CV046 · CV047 · CV048 · CV068 · CV069 · CV070 · CV094 · CV095 · CV097

Scope

prove explicit combined input and truncation errors for independent bounded finite exponential computations by constructing the actual middle prefix preserving the two error budgets without analytic limit assumptions

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