Exact named statement
forall k l d s q t. DyadicSqrt2(k,d,s) ->
DyadicSqrt2(k+l,q,t) ->
IRatLe(s,0,d,t,0,q) /\ IRatLe(S t,0,q,S s,0,d)Complete certificate and independent checks
134 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: 13d665c846b9974b8406b7dbafd3d385a28847ea32ce289f7bf5caf79f2d8a32
Bundle SHA-256: 662b208170553daf44e743701543229b6fc24f7f1542c2fd68db47c81d1001f3
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
actual dyadic sqrt2 intervals at ordered precisions have valid rational nondecreasing lower and nonincreasing upper endpoints with proved denominator positivity no limit
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.