CV084 — supplied geometric error — irrationality research

Exact named statement

forall ub uc tb tc k r z x y u p h q a. ~z=0 ->
  NatHornerValue(ub,uc,3,S k,x) ->
  x+z=(2*z)*p ->
  Pow(3,k,p) ->
  NatAffineSlice(ub,uc,S k,1,tb,tc,S r) ->
  NatHornerValue(tb,tc,3,S r,u) ->
  NatHornerValue(ub,uc,3,S ((S k)+r),y) ->
  Pow(3,((S k)+r),h) ->
  Pow(3,S k,q) ->
  Pow(2,S k,a) ->
  Le(u*q,(9*a)*(z*h)) ->
  exists b. (Pow(3,S r,b)) /\ ((h=p*b) /\ ((y=b*x+u) /\ ((~p=0) /\ ((~q=0) /\ ((~h=0) /\ ((~(z*h)=0) /\ ((~((z*h)*p)=0) /\ ((y+z*b=(2*z)*h+u) /\ ((Le(y*q,(2*q+9*a)*(z*h))) /\ ((Le((2*p)*(z*h),y*p+z*h)) /\ ((IRatLe(y,0,z*h,2*q+9*a,0,q)) /\ (IRatLe(2,0,1,y*p+z*h,0,(z*h)*p)))))))))))))

PD0001 — Le · ND0411 — NatAffineSlice · PD0020 — Pow · ND0437 — NatHornerValue · ND0444 — IRatLe

Fully expanded target AST

Complete certificate and independent checks

134 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: 4ee4edb3a27c63810499bc48918c92c504253b783efa6e306acf9c98ba79f558
Bundle SHA-256: a503bbe03a5d157fc56e871be761c191ffd3f399c409968b955e31a4e5b6e300

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.

CV082 · CV083

Scope

supplied actual prefix tail and full Horner values with actual power alignment and geometric tail premises give both valid rational error bounds with all denominators proved nonzero not computation existence or analytic limit

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