Exact named statement
forall d x N. ~d=0 ->
Le(x,2*d) ->
exists wb wc tb tc w0 f p s. NatExpWeightTable(d,N,wb,wc) /\ (NatPowerWeightedPrefix(x,wb,wc,tb,tc,S N) /\ (BetaAt(wb,wc,0,w0) /\ (BetaAt(tb,tc,0,w0) /\ (~w0=0 /\ (Factorial(N,f) /\ (Pow(d,N,p) /\ (w0=f*p /\ (Sum(tb,tc,S N,s) /\ (NatScaledExpRecurrence(d,x,tb,tc,N) /\ ((forall j t f0 p0 q. Le(j,N) ->
BetaAt(tb,tc,j,t) ->
Factorial(j,f0) ->
Pow(d,j,p0) ->
Pow(x,j,q) ->
(t*f0)*p0=w0*q) /\ (Le(s,9*w0))))))))))))PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0423 — NatExpWeightTable · PD0020 — Pow · PD0023 — Factorial · ND0442 — NatPowerWeightedPrefix · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
163 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: 042906aaf5e07838dfb7be22391a4c26d6395af6e8d451e8c4322563fb810e26
Bundle SHA-256: 4d7e1dad4315320f229e167f800afa3ac7c13c3e5b338638e81bc06fb259ec32
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
all actual scaled exponential term data retained with finite sum at most nine times nonzero initial weight under x le twice nonzero denominator not rational division or analytic limit
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.