AP069 — exp relative cross continuity

Exact named statement

forall d e x y g N ab ac bb bc a0 b0 s t. ~d=0 ->
  ~e=0 ->
  d*y=e*x+g ->
  NatScaledExpRecurrence(d,x,ab,ac,N) ->
  NatScaledExpRecurrence(e,y,bb,bc,N) ->
  BetaAt(ab,ac,0,a0) ->
  BetaAt(bb,bc,0,b0) ->
  Sum(ab,ac,S N,s) ->
  Sum(bb,bc,S N,t) ->
  Le(b0*s,a0*t) /\ Le((d*e)*(a0*t),(d*e)*(b0*s)+g*(a0*t))

PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · 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: bd0a751f36b51993e4a8a1c8d3802afe6e72a7304960b031618cbee1c6e66f62
Bundle SHA-256: 1f05df465a0a247f69b287823dcc92b3d2c728cb3808e5b3aa561dc6edcec249

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.

AP068 · CV009 · CV094 · CV095 · CV097

Scope

prove unrestricted relative finite exponential continuity across independent positive argument denominators arbitrary heads and actual codes by constructing rescaled common head tables

None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.