Exact named statement
forall n s a b. FloorSqrt(n,s) ->
Le(a*a,n) ->
Lt(n,b*b) ->
Le(a,s) /\ Lt(s,b)Complete certificate and independent checks
16 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: 87748e18b800d65594ab1288e0586b089302a29354fd0c34e978ab8a54a76e5a
Bundle SHA-256: ee5be134efec33276a298e8ac6119db809740d9fe595e3586e9c51d175e60f96
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 floor root lies between roots of supplied nonstrict lower and strict upper square bounds via replayed natural decidable order no real number or accuracy axiom
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.