Exact named statement
forall d x L K n. ~d=0 ->
Le(x,L*d) ->
Le(2*L,K) ->
exists wb wc ab ac h f q s r. (NatExpWeightTable(d,K+(L*K+n),wb,wc)) /\ ((NatPowerWeightedPrefix(x,wb,wc,ab,ac,S(K+(L*K+n)))) /\ ((BetaAt(wb,wc,0,h)) /\ ((BetaAt(ab,ac,0,h)) /\ ((~h=0) /\ ((Factorial(K+(L*K+n),f)) /\ ((Pow(d,K+(L*K+n),q)) /\ ((h=f*q) /\ ((Sum(ab,ac,S(K+(L*K+n)),s)) /\ ((NatScaledExpRecurrence(d,x,ab,ac,K+(L*K+n))) /\ ((forall j v fj dj xj. Le(j,K+(L*K+n)) ->
BetaAt(ab,ac,j,v) ->
Factorial(j,fj) ->
Pow(d,j,dj) ->
Pow(x,j,xj) ->
(v*fj)*dj=h*xj) /\ ((Pow(2,n,r)) /\ ((~r=0) /\ (forall N. exists vb vc bb bc g F Q t. (NatExpWeightTable(d,S(K+(L*K+n))+N,vb,vc)) /\ ((NatPowerWeightedPrefix(x,vb,vc,bb,bc,S(S(K+(L*K+n))+N))) /\ ((BetaAt(vb,vc,0,g)) /\ ((BetaAt(bb,bc,0,g)) /\ ((~g=0) /\ ((Factorial(S(K+(L*K+n))+N,F)) /\ ((Pow(d,S(K+(L*K+n))+N,Q)) /\ ((g=F*Q) /\ ((Sum(bb,bc,S(S(K+(L*K+n))+N),t)) /\ ((NatScaledExpRecurrence(d,x,bb,bc,S(K+(L*K+n))+N)) /\ ((forall j v fj dj xj. Le(j,S(K+(L*K+n))+N) ->
BetaAt(bb,bc,j,v) ->
Factorial(j,fj) ->
Pow(d,j,dj) ->
Pow(x,j,xj) ->
(v*fj)*dj=g*xj) /\ ((Le(g*s,h*t)) /\ (Le(r*(h*t),r*(g*s)+h*g))))))))))))))))))))))))))PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0423 — NatExpWeightTable · PD0020 — Pow · PD0023 — Factorial · ND0442 — NatPowerWeightedPrefix · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
202 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: 1271edf53171c0ca044ba475b8805112ebf82d4ac21ba32f38e69819c32da8c8
Bundle SHA-256: 21e999a7af380b2fa76fc861ba96979e5942ec7acfcb115ec655a9b91b167beb
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.
AP051 · AP052 · AP053 · AP054 · AP055 · AP056 · AP057 · AP060 · AP062 · AP063 · AP065 · CV009 · CV022 · CV030 · CV068 · CV069 · CV070
Scope
construct one positive factorial normalized coarse exponential table and precision power before the universal extra horizon then actual positive fine tables with requested dyadic error without an analytic limit
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.