Exact named statement
forall d x ab ac m N a0 s t p. ~d=0 ->
Le(x,d) ->
NatScaledExpRecurrence(d,x,ab,ac,(S m)+N) ->
BetaAt(ab,ac,0,a0) ->
Sum(ab,ac,S m,s) ->
Sum(ab,ac,S((S m)+N),t) ->
Pow(2,m,p) ->
Le(s,t) /\ Le(p*t,p*s+2*a0)PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · PD0020 — Pow · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
155 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: 38cc1a427fdb362d86fb580c3b3a939ae9e62900f35876de3390a804f26294b2
Bundle SHA-256: a8288777d6ca50ce713634fdda4f018996ec8ff25566bf936657bfb3630e1e5d
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
supplied exponential recurrence head prefix and longer sum and actual cutoff power obey uniform finite truncation bound via constructed tail and actual affine sum uniqueness no infinite remainder assumption
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.