Exact named statement
forall ab ac a b r. Le(a,b) ->
exists p q x y. NatHornerValue(ab,ac,b,S r,x) /\ (NatHornerValue(ab,ac,a,S r,y) /\ (Pow(a,r,p) /\ (Pow(b,r,q) /\ (Le(p,q) /\ Le(p*x,q*y)))))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: 9427a92cb26d4fcfea9d3160585b295d542e0c343f466f0326c7f8acbf25bbe0
Bundle SHA-256: de7052c68bfe61d50e1ecc04b1833a5040b0f84ed2385c881e5666c954485c4f
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 actual horner values and powers for ordered bases with power order and exact length minus one scaled comparison including zero bases not an analytic limit
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.