CV068 — ratio sum bound — irrationality research

Exact named statement

forall ab ac r N a0. NatRatioBoundPrefix(ab,ac,r,N) ->
  BetaAt(ab,ac,0,a0) ->
  exists s. Sum(ab,ac,N,s) /\ Le(s,(S r)*a0)

PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0441 — NatRatioBoundPrefix

Fully expanded target AST

Complete certificate and independent checks

112 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: fd9dbb392a8f45725f090de43a5e13f1e269a2e0b79293eeef87a1464dcd8f28
Bundle SHA-256: 88d9a3d159a222530ecfb17ba3316739ad965970ac80dd427f3bbd98c8e94638

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.

Scope

constructed actual finite sum bounded by ratio head with empty prefix and zero ratio cases from explicit separate adjacent entry bounds not an analytic limit

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