CV042 — weighted convolution — irrationality research

Exact named statement

forall t L M ab ac bb bc lb lc mb mc nb nc ub uc vb vc k. NatGeometricWeightTable(t,L,lb,lc) ->
  NatGeometricWeightTable(t,M,mb,mc) ->
  NatGeometricWeightTable(t,L+M,nb,nc) ->
  NatHornerWeightedPrefix(ab,ac,lb,lc,ub,uc,L) ->
  NatHornerWeightedPrefix(bb,bc,mb,mc,vb,vc,M) ->
  exists u v w. NatConvolutionCoefficient(ab,ac,L,bb,bc,M,k,u) /\ (NatConvolutionCoefficient(ub,uc,L,vb,vc,M,k,v) /\ (BetaAt(nb,nc,S k,w) /\ u*w=t*v))

PD0013 — BetaAt · ND0401 — NatConvolutionCoefficient · ND0428 — NatGeometricWeightTable · ND0429 — NatHornerWeightedPrefix

Fully expanded target AST

Complete certificate and independent checks

148 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: 6537f190afaf524e595debbbbc01006bfd85ea9994906ff6b4aca84d7b4057af
Bundle SHA-256: fa0ff9d23182905616197f0cd573075710d2cd07a9c6f9fef7f31fe2bea7dc9f

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 coefficient weighting identity for all indices given three weight tables and two product prefixes not full evaluation or analytic identity

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