AP065 — exp independent horizon — irrationality research

Exact named statement

forall d e x y L K n N ab ac bb bc h g s t r. ~d=0 ->
  ~e=0 ->
  x*e=y*d ->
  Le(y,L*e) ->
  Le(2*L,K) ->
  NatScaledExpRecurrence(d,x,ab,ac,K+(L*K+n)) ->
  NatScaledExpRecurrence(e,y,bb,bc,S(K+(L*K+n))+N) ->
  BetaAt(ab,ac,0,h) ->
  BetaAt(bb,bc,0,g) ->
  Sum(ab,ac,S(K+(L*K+n)),s) ->
  Sum(bb,bc,S(S(K+(L*K+n))+N),t) ->
  Pow(2,n,r) ->
  ~r=0 /\ (Le(g*s,h*t) /\ Le(r*(h*t),r*(g*s)+h*g))

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

Fully expanded target AST

Complete certificate and independent checks

179 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: 650e729c29cf242dce7af6b0b54b08b896036d8256a6ec458c80134305b3ee39
Bundle SHA-256: 2ad83c07ef353332351dba47fd70922980c533807a82e0ab7c479479d09f1e80

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.

AP051 · AP052 · AP053 · AP054 · AP055 · AP056 · AP057 · AP060 · AP062 · AP063 · CV009 · CV068

Scope

prove requested dyadic Cauchy accuracy across two independently supplied exponential codes denominators and heads at equal rational arguments and different finite horizons by constructing the actual fine short sum

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