Exact named statement
forall alpha beta gamma ab ac bb bc cb cc L db dc M i. NatLinearTriple(alpha,beta,gamma,ab,ac,bb,bc,cb,cc,L) ->
exists u v w. NatConvolutionCoefficient(ab,ac,L,db,dc,M,i,u) /\ (NatConvolutionCoefficient(bb,bc,L,db,dc,M,i,v) /\ (NatConvolutionCoefficient(cb,cc,L,db,dc,M,i,w) /\ gamma*w=alpha*u+beta*v))ND0401 — NatConvolutionCoefficient · ND0409 — NatLinearTriple
Complete certificate and independent checks
123 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: 454dd9464f21bb867fd39a78eebb4d9eabe59aae256c134ab0624e05d8d17f91
Bundle SHA-256: 7f4a09006875aad735b0543e6386b8e508c35c8890e2a801ffaf91c14f6dbf84
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
constructed weighted natural convolution linearity not composition
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.