AP083 — log exp cutoff refinement

Exact named statement

forall r d e ab ac bb bc l x z p q N cb cc eb ec a0 b0 u v P. ~d=0 ->
  ~e=0 ->
  NatAtanhPrefix(d,ab,ac,S(S(18*r))) ->
  NatAtanhPrefix(e,bb,bc,(S(S(18*r)))+l) ->
  NatHornerValue(ab,ac,3,S(S(18*r)),x) ->
  NatHornerValue(bb,bc,3,(S(S(18*r)))+l,z) ->
  Pow(3,S(S(18*r)),p) ->
  Pow(3,(S(S(18*r)))+l,q) ->
  NatScaledExpRecurrence(d*p,3*x,cb,cc,S(S(18*r))) ->
  NatScaledExpRecurrence(e*q,3*z,eb,ec,(S(S(S(18*r))))+N) ->
  BetaAt(cb,cc,0,a0) ->
  BetaAt(eb,ec,0,b0) ->
  Sum(cb,cc,S(S(S(18*r))),u) ->
  Sum(eb,ec,S((S(S(S(18*r))))+N),v) ->
  Pow(2,S(S(18*r)),P) ->
  ~p=0 /\ (~q=0 /\ (~P=0 /\ (~(d*p)=0 /\ (~(e*q)=0 /\ (Le(b0*u,a0*v) /\ Le(r*(a0*v),r*(b0*u)+a0*b0))))))

PD0001 — Le · PD0013 — BetaAt · ND0425 — NatAtanhPrefix · ND0437 — NatHornerValue · PD0020 — Pow · ND0443 — NatScaledExpRecurrence · PD0015 — Sum

Fully expanded target AST

Complete certificate and independent checks

238 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: 97d070681313d49334933a292e949acae3f61cc484c18b5a122d05060269d1c5
Bundle SHA-256: 18275d48a04f78840e82c3d6f549a632496ea202cafc32b10de83ef2be0979fa

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.

AP082 · CV009 · CV032 · CV062 · CV068 · CV086 · CV087 · CV088 · CV089 · CV090 · CV092 · CV093 · CV094 · CV095 · CV096 · CV097 · CV098 · CV100 · CV101

Scope

prove the existing auxiliary 18 r plus 2 cutoff pays both logarithm and exponential refinement errors from actual power computations without assuming the budgets or changing the fixed approximation program

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