AP068 — exp relative continuity — irrationality research

Exact named statement

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

PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0443 — NatScaledExpRecurrence

Fully expanded target AST

Complete certificate and independent checks

137 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: 44c446356566e235233dd3597393197285525996f1312f828627e5f6c621ea1d
Bundle SHA-256: 0fa098dd5ca136b1341a37b5c0e3ef5211e1d8316588a5601d47c9d8d43f68df

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.

CV009 · CV094 · CV095

Scope

prove relative finite exponential sum continuity for arbitrary nonnegative arguments from actual tail slices without any small argument 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.