AP064 — exp requested product — irrationality research

Exact named statement

forall d x y L ab ac bb bc cb cc K n a0 b0 c0 u v w r. ~d=0 ->
  Le(x+y,L*d) ->
  Le(2*L,K) ->
  NatScaledExpRecurrence(d,x,ab,ac,S(K+(L*K+n))+(K+(L*K+n))) ->
  NatScaledExpRecurrence(d,y,bb,bc,S(K+(L*K+n))+(K+(L*K+n))) ->
  NatScaledExpRecurrence(d,x+y,cb,cc,K+(L*K+n)) ->
  BetaAt(ab,ac,0,a0) ->
  BetaAt(bb,bc,0,b0) ->
  BetaAt(cb,cc,0,c0) ->
  Sum(ab,ac,S(K+(L*K+n)),u) ->
  Sum(bb,bc,S(K+(L*K+n)),v) ->
  Sum(cb,cc,S(K+(L*K+n)),w) ->
  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 · PD0020 — Pow · ND0443 — NatScaledExpRecurrence

Fully expanded target AST

Complete certificate and independent checks

266 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: f0434acec36b8372e936d5c8e5f08cb7bacbc68bca03a222d3af6dfa45e2d636
Bundle SHA-256: cd072e20381973dfe744997e4f8b40cfb61735f27a0be2bd40f78caa95769495

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 · CV008 · CV009 · CV011 · CV043 · CV044 · CV046 · CV047 · CV048 · CV068 · CV095

Scope

prove requested dyadic accuracy for the product of two independently supplied finite exponential sums against a third supplied sum at the added argument with explicit symbolic cutoffs and no 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.