CV070 — scaled exp terms — irrationality research

Exact named statement

forall d x N. ~d=0 ->
  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))))))))))

PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0423 — NatExpWeightTable · PD0020 — Pow · PD0023 — Factorial · ND0442 — NatPowerWeightedPrefix · ND0443 — NatScaledExpRecurrence

Fully expanded target AST

Complete certificate and independent checks

144 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: 7f9e9c6aa4b255463768b661ebe9736b133dd810525dfd27ff94dfbe3693bf1d
Bundle SHA-256: 2be0d10e36a67786ed5fd20800f6a2d52c10229fea219ea68edd70e832a8b075

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.

CV022 · CV030 · CV069

Scope

same actual factorial weights and power terms with nonzero initial value exact scaled exponential recurrence and factorial normalization not finite exp bound 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.