Exact named statement
forall d x y L K n. ~d=0 ->
Le(x+y,L*d) ->
Le(2*L,K) ->
exists aw az ab ac a0 af aq aFull bw bz bb bc b0 bf bq bFull cw cz cb cc c0 cf cq w u v r. (NatExpWeightTable(d,S(K+(L*K+n))+(K+(L*K+n)),aw,az)) /\ ((NatPowerWeightedPrefix(x,aw,az,ab,ac,S(S(K+(L*K+n))+(K+(L*K+n))))) /\ ((BetaAt(aw,az,0,a0)) /\ ((BetaAt(ab,ac,0,a0)) /\ ((~a0=0) /\ ((Factorial(S(K+(L*K+n))+(K+(L*K+n)),af)) /\ ((Pow(d,S(K+(L*K+n))+(K+(L*K+n)),aq)) /\ ((a0=af*aq) /\ ((Sum(ab,ac,S(S(K+(L*K+n))+(K+(L*K+n))),aFull)) /\ ((NatScaledExpRecurrence(d,x,ab,ac,S(K+(L*K+n))+(K+(L*K+n)))) /\ ((forall j a fj dj xj. Le(j,S(K+(L*K+n))+(K+(L*K+n))) ->
BetaAt(ab,ac,j,a) ->
Factorial(j,fj) ->
Pow(d,j,dj) ->
Pow(x,j,xj) ->
(a*fj)*dj=a0*xj) /\ ((NatExpWeightTable(d,S(K+(L*K+n))+(K+(L*K+n)),bw,bz)) /\ ((NatPowerWeightedPrefix(y,bw,bz,bb,bc,S(S(K+(L*K+n))+(K+(L*K+n))))) /\ ((BetaAt(bw,bz,0,b0)) /\ ((BetaAt(bb,bc,0,b0)) /\ ((~b0=0) /\ ((Factorial(S(K+(L*K+n))+(K+(L*K+n)),bf)) /\ ((Pow(d,S(K+(L*K+n))+(K+(L*K+n)),bq)) /\ ((b0=bf*bq) /\ ((Sum(bb,bc,S(S(K+(L*K+n))+(K+(L*K+n))),bFull)) /\ ((NatScaledExpRecurrence(d,y,bb,bc,S(K+(L*K+n))+(K+(L*K+n)))) /\ ((forall j a fj dj xj. Le(j,S(K+(L*K+n))+(K+(L*K+n))) ->
BetaAt(bb,bc,j,a) ->
Factorial(j,fj) ->
Pow(d,j,dj) ->
Pow(y,j,xj) ->
(a*fj)*dj=b0*xj) /\ ((NatExpWeightTable(d,K+(L*K+n),cw,cz)) /\ ((NatPowerWeightedPrefix(x+y,cw,cz,cb,cc,S(K+(L*K+n)))) /\ ((BetaAt(cw,cz,0,c0)) /\ ((BetaAt(cb,cc,0,c0)) /\ ((~c0=0) /\ ((Factorial(K+(L*K+n),cf)) /\ ((Pow(d,K+(L*K+n),cq)) /\ ((c0=cf*cq) /\ ((Sum(cb,cc,S(K+(L*K+n)),w)) /\ ((NatScaledExpRecurrence(d,x+y,cb,cc,K+(L*K+n))) /\ ((forall j a fj dj xj. Le(j,K+(L*K+n)) ->
BetaAt(cb,cc,j,a) ->
Factorial(j,fj) ->
Pow(d,j,dj) ->
Pow(x+y,j,xj) ->
(a*fj)*dj=c0*xj) /\ ((Sum(ab,ac,S(K+(L*K+n)),u)) /\ ((Sum(bb,bc,S(K+(L*K+n)),v)) /\ ((Pow(2,n,r)) /\ ((~r=0) /\ ((Le((a0*b0)*w,c0*(u*v))) /\ (Le(r*(c0*(u*v)),r*((a0*b0)*w)+c0*(a0*b0))))))))))))))))))))))))))))))))))))))))PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0423 — NatExpWeightTable · PD0020 — Pow · PD0023 — Factorial · ND0442 — NatPowerWeightedPrefix · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
289 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: 90a7f53271dfd7883b4edc4850e14370009306488126a38310f44e94983de3fd
Bundle SHA-256: d685c940c575f292c72c45d963a0be7d367a9f6cc3be8e83e5bac6b8fdb71cb6
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 · AP059 · AP060 · AP061 · AP062 · AP064 · CV008 · CV009 · CV011 · CV022 · CV030 · CV043 · CV044 · CV046 · CV047 · CV048 · CV068 · CV069 · CV070 · CV095
Scope
construct three positive factorial normalized exponential tables and actual input prefix sums with requested dyadic product error retaining all indexwise normalizations without an analytic addition axiom
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.