HA + independent Lean evidence · Research, not Alpha admission

CV045 — cauchy row sum

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

Exact named statement

forall ab ac L bb bc M N. exists gb gc. NatCauchyGrid(ab,ac,L,bb,bc,M,N,gb,gc) /\ (forall k. Lt(k,S N) ->
  exists u. NatConvolutionCoefficient(ab,ac,L,bb,bc,M,k,u) /\ NatAffineSum(gb,gc,(S N)*k,1,S N,u))

PD0002 — Lt · ND0401 — NatConvolutionCoefficient · ND0433 — NatCauchyGrid · ND0412 — NatAffineSum

Fully expanded target AST

Complete certificate and independent checks

136 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: 1e5bd50b1aebb4f3f9ccee2b1ed520e7c8faafdc3731a8285363a3811d4a23da
Bundle SHA-256: 0ca030a7524f9c287ebb556c1577d3b530d13d8d90e9f26e53c538ef10c1da6e

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.

CV009 · CV011 · CV044

Scope

constructed cauchy grid and all actual row sums identified with convolution coefficients using proved zero tail not column sums or evaluation identity

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