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(2*(d*p),3*x,cb,cc,S(S(18*r))) ->
NatScaledExpRecurrence(2*(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 /\ (~(2*(d*p))=0 /\ (~(2*(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
Complete certificate and independent checks
240 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: da6645f80e599d951709a835b4f07996fb457ad7c848fe65a66fb2ed76dbf5b0
Bundle SHA-256: 2c3fe08cb08b747f0bfb835ea226855277aebb872f9f587736be3e74c22da8cc
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.
AP087 · CV009 · CV032 · CV062 · CV068 · CV086 · CV087 · CV088 · CV089 · CV090 · CV092 · CV093 · CV094 · CV095 · CV096 · CV097 · CV098 · CV100 · CV101
Scope
apply checked actual power cutoff budgets and positive cancellation to independent half logarithm exponential refinement without assuming the budgets changing the original logarithm computations or adding arithmetic helpers
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.