AP053 — halving prefix decay — irrationality research

Exact named statement

forall k ab ac N a0 a p. Le(k,N) ->
  NatRatioBoundPrefix(ab,ac,1,S N) ->
  BetaAt(ab,ac,0,a0) ->
  BetaAt(ab,ac,k,a) ->
  Pow(2,k,p) ->
  Le(p*a,a0)

PD0001 — Le · PD0013 — BetaAt · PD0020 — Pow · ND0441 — NatRatioBoundPrefix

Fully expanded target AST

Complete certificate and independent checks

36 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: 07ae73101d211aba3dfdb13a23c81410079b1c0ab2cde23e58d19ff2b5e0d6d8
Bundle SHA-256: 8ab91a86da1d7a0fb5ffb4d711d6723b98695277ef3042587d475462c3bf0bbf

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

prove symbolic binary decay at every bounded index of an actual supplied halving prefix by one ordinary HA induction including zero head index and horizon without division or an infinite sequence

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