Exact named statement
forall n up ud rb rc. (NatSqrt2ApproxRecord(n,up,ud,rb,rc)) \/ ~(NatSqrt2ApproxRecord(n,up,ud,rb,rc))Complete certificate and independent checks
178 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: b08c1a483e177d9fa80cb2c787464ff0ad2f2a27dc52543517056b1184e2896e
Bundle SHA-256: e51a07de3eaf87cd53ec90045924966c992a365365a5643f872ffa483d7c78b7
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
constructively decide any supplied fifteen field approximation record by actual beta decoding complete sample decision and equality transport of all competing internal fields without unbounded search or classical axioms
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.