Exact named statement
forall k d x L tb tc N h a b. ~d=0 ->
Le(x,L*d) ->
Le(k,N) ->
NatScaledExpRecurrence(d,x,tb,tc,N) ->
BetaAt(tb,tc,0,h) ->
BetaAt(tb,tc,k,a) ->
Pow(L,k,b) ->
Le(a,b*h)PD0001 — Le · PD0013 — BetaAt · PD0020 — Pow · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
44 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: e86ad6b58635a4c4ece5af53c0cf336a09fc69caf323c09e6c79fea863077e79
Bundle SHA-256: 6d40a0ff19af1e096df1647183ec59ca894502ec46e796c50b4652362eb3ee33
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
prove every bounded actual exponential term is at most the actual natural argument bound power times its original head by one ordinary induction and positive denominator cancellation including zero argument bound
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.