CV043 — shifted scaled sum — irrationality research

Exact named statement

forall ab ac ub uc s N q a. (forall i u. Lt(i,s) ->
  BetaAt(ub,uc,i,u) ->
  u=0) ->
  (forall j b c. Lt(j,N) ->
  BetaAt(ab,ac,j,b) ->
  BetaAt(ub,uc,s+j,c) ->
  c=a*b) ->
  (forall j. Lt(j,q) ->
  BetaAt(ub,uc,(s+N)+j,0)) ->
  exists x y. Sum(ab,ac,N,x) /\ (Sum(ub,uc,(s+N)+q,y) /\ y=a*x)

PD0002 — Lt · PD0013 — BetaAt · PD0015 — Sum

Fully expanded target AST

Complete certificate and independent checks

125 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: 6ee048a7b7670833a6caa1ec7172b086096264b73542ae00b8122a9ea9f004fa
Bundle SHA-256: 1568eaa83e40883b44bda2ac0fa02854792abb1da4e9f099e327e168e4fac1c1

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

Scope

constructed sum values for actual scaled shifted block with leading and trailing zeros not full convolution 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.