CV091 — atanh rational truncation — irrationality research

Exact named statement

forall d ab ac M N. ~d=0 ->
  NatAtanhPrefix(d,ab,ac,M+N) ->
  exists x z p h. NatHornerValue(ab,ac,3,M,x) /\ (NatHornerValue(ab,ac,3,M+N,z) /\ (Pow(3,M,p) /\ (Pow(3,M+N,h) /\ (~(d*p)=0 /\ (~(d*h)=0 /\ (IRatLe(3*x,0,d*p,3*z,0,d*h) /\ (IRatLe(3*z,0,d*h,3*x+3*d,0,d*p))))))))

PD0020 — Pow · ND0437 — NatHornerValue · ND0425 — NatAtanhPrefix · ND0444 — IRatLe

Fully expanded target AST

Complete certificate and independent checks

146 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: c1d96e8b045d76e79bd363c41f9562f92787aaef0867562246f3d89f06132418
Bundle SHA-256: d46e09d94d9ac0ad74bd6dc8082e3e5d09cd31addc63b89fa81d81b4b6c92522

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.

CV032 · CV062 · CV089 · CV090

Scope

supplied actual atanh table prefix and whole values with actual powers and all nonzero denominators give valid rational monotonicity and error at most three over three to cutoff not analytic limit

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