Exact named statement
forall a b M g k u v w. Le(a,M) ->
Le(b,M) ->
Le(b,a+g) ->
Le(a,b+g) ->
Pow(a,S k,u) ->
Pow(b,S k,v) ->
Pow(M,k,w) ->
Le(v,u+(S k)*(g*w)) /\ Le(u,v+(S k)*(g*w))Complete certificate and independent checks
41 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: 9f376fc95073195bee675f73105660651b69555fbeb652e7cd0ed1e8550cdc98
Bundle SHA-256: b720ef339bcbf9658387bf1a1dabbffa5358cdb0d304477734ed87996d1644aa
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
prove two sided error propagation for three actual bounded natural powers by decidable input order and the extracted gap without positive base assumptions or new induction
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.