CV046 — cauchy column sum — irrationality research

Exact named statement

forall ab ac L bb bc M j a ub uc T q. BetaZeroExtend(ab,ac,L,j,a) ->
  NatCauchyColumn(ab,ac,L,bb,bc,M,j,ub,uc,T) ->
  (j+M)+q=T ->
  exists x y. Sum(bb,bc,M,x) /\ (Sum(ub,uc,T,y) /\ y=a*x)

PD0015 — Sum · ND0291 — BetaZeroExtend · ND0435 — NatCauchyColumn

Fully expanded target AST

Complete certificate and independent checks

133 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: 94eff8a4d0a0b19ee9a9c9a63604deabe5c06331fd7e9e1fd64593a4026f0b4f
Bundle SHA-256: 51a97eb9d305b9d355bd3f737745a5fb8736bf7c9d3423149e3f209882f7b742

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 · CV043

Scope

actual complete cauchy column sum equals padded left value times right sum under explicit span equality not unconditional grid columns or evaluation

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