Exact named statement
forall d x L tb tc K m N. ~d=0 ->
Le(x,L*d) ->
Le(2*L,K) ->
NatScaledExpRecurrence(d,x,tb,tc,(K+m)+N) ->
exists p ub uc a0 a s. (Pow(2,m,p)) /\ ((BetaAt(tb,tc,K,a0)) /\ ((BetaAt(tb,tc,K+m,a)) /\ ((NatAffineSlice(tb,tc,K+m,1,ub,uc,S N)) /\ ((NatRatioBoundPrefix(ub,uc,1,S N)) /\ ((BetaAt(ub,uc,0,a)) /\ ((Sum(ub,uc,S N,s)) /\ ((Le(p*a,a0)) /\ (Le(p*s,2*a0)))))))))PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0411 — NatAffineSlice · PD0020 — Pow · ND0441 — NatRatioBoundPrefix · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
138 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: a11bcab301bcc1baa600ebeb7741038a4ddea68d8a679317bf9afb96a127d859
Bundle SHA-256: 1390d3a7c2b97fdc38e34ee664d4941d9aa338b669daa1d77b5e68f7e22d6fe5
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.
Scope
construct actual powers heads shifted slices and sums with dyadic decay after every extra cutoff beyond twice a general natural argument bound including all zero margins and without an infinite remainder claim
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.