HA + independent Lean evidence · Research, not Alpha admission

SQ001 — floor sqrt

Full irrationality (IR072/G121) remains open. Stable: 432. Alpha v35: 4,318. This checkpoint changes neither catalogue.

Exact named statement

forall n. exists s. FloorSqrt(n,s) /\ forall t. FloorSqrt(n,t) ->
  t=s

PD0051 — FloorSqrt

Fully expanded target AST

Complete certificate and independent checks

31 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: da6b93cc7d0f9f4458be509f5f2405cac0063f79ab70acfef60768c09a0f2d5c
Bundle SHA-256: c67e379ff1997694a46682d276a9f81661370a42a311190580828229450435de

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

unconditional floor square root totality and uniqueness from exact replayed Bertrand ancestor bodies and original conservative FloorSqrt definition not dyadic accuracy or real interpretation

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