AP008 — exp two sided horizons — irrationality research

Exact named statement

forall d e x y C R H m N ab ac bb bc a0 b0 s t p. ~d=0 ->
  ~e=0 ->
  Le(x,d) ->
  Le(y,e) ->
  Le(C*(d*y),C*(e*x)+R) ->
  Le(C*(e*x),C*(d*y)+H) ->
  NatScaledExpRecurrence(d,x,ab,ac,m) ->
  NatScaledExpRecurrence(e,y,bb,bc,(S m)+N) ->
  BetaAt(ab,ac,0,a0) ->
  BetaAt(bb,bc,0,b0) ->
  Sum(ab,ac,S m,s) ->
  Sum(bb,bc,S((S m)+N),t) ->
  Pow(2,m,p) ->
  Le(p*(C*((d*e)*(a0*t))),p*(C*((d*e)*(b0*s)))+(9*(p*R)+2*(C*(d*e)))*(a0*b0)) /\ Le(C*((d*e)*(b0*s)),C*((d*e)*(a0*t))+9*(H*(a0*b0)))

PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · PD0020 — Pow · ND0443 — NatScaledExpRecurrence

Fully expanded target AST

Complete certificate and independent checks

197 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: 345ef6c15b5813f3423a35a13c658fa76dd43b9bc8fc56f2aed0330e254c788a
Bundle SHA-256: bc30f35fc3fbab167f5bd5d629e8cc410adc89a0b3f0300f74702335b96ef99e

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.

AP007 · CV009 · CV068 · CV087 · CV088 · CV094 · CV095 · CV096 · CV097 · CV098 · CV100

Scope

supplied finite exponential sums at unequal horizons have two sided scaled error bounds from actual constructed prefix and supplied cutoff power without input monotonicity or analytic limit assumptions

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