AP070 — exp absolute continuity — irrationality research

Exact named statement

forall d e x y g N ab ac bb bc a0 b0 s t C r. ~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(t,C*b0) ->
  Le((r*g)*C,d*e) ->
  Le(b0*s,a0*t) /\ Le(r*(a0*t),r*(b0*s)+a0*b0)

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

Fully expanded target AST

Complete certificate and independent checks

146 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: a085e6805bd448394a0ee2f1cd547da010b34b51bebbfe4b683fe338d87aeba9
Bundle SHA-256: 1804aac88411201a7aba240f21ec51eb677f7c532748c43fd7c5ae9bd547a9a8

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 · AP069 · CV009 · CV094 · CV095 · CV097

Scope

prove requested absolute finite exponential continuity from two actual independent computations an explicit sum majorant and symbolic precision budget without assuming the majorant or precision power as an analytic axiom

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