AP016 — atanh odd slice — irrationality research

Exact named statement

forall d ab ac k. NatAtanhPrefix(d,ab,ac,S(2*k)) ->
  exists bb bc. NatAffineSlice(ab,ac,1,2,bb,bc,k) /\ ((forall j a. Lt(j,k) ->
  BetaAt(bb,bc,j,a) ->
  (S(2*j))*a=2*d) /\ (forall j a. Le(j,k) ->
  BetaAt(ab,ac,2*j,a) ->
  a=0))

PD0001 — Le · PD0002 — Lt · PD0013 — BetaAt · ND0411 — NatAffineSlice · ND0425 — NatAtanhPrefix

Fully expanded target AST

Complete certificate and independent checks

113 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: ebf68fd1ca1f37cd10b7e77ef28a69acf4aa4c4995cd8c215a6bc3d8a9f1d894
Bundle SHA-256: 6623977ef1c4aba8612a0450d2e0fb1484d6cb00f31a5b7d14b70187c5660c00

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

construct the actual odd index affine slice of a supplied atanh prefix and prove all odd quotient equations and all even zeros including empty slice and zero scale without analytic identification

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