AP071 — exp submultiplicative — irrationality research

Exact named statement

forall d x y N ab ac bb bc cb cc a0 b0 c0 u v w. ~d=0 ->
  NatScaledExpRecurrence(d,x,ab,ac,N) ->
  NatScaledExpRecurrence(d,y,bb,bc,N) ->
  NatScaledExpRecurrence(d,x+y,cb,cc,N) ->
  BetaAt(ab,ac,0,a0) ->
  BetaAt(bb,bc,0,b0) ->
  BetaAt(cb,cc,0,c0) ->
  Sum(ab,ac,S N,u) ->
  Sum(bb,bc,S N,v) ->
  Sum(cb,cc,S N,w) ->
  Le((a0*b0)*w,c0*(u*v))

PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0443 — NatScaledExpRecurrence

Fully expanded target AST

Complete certificate and independent checks

216 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: 172dd2d034e151140ec0f7866fbfea14a1de644c3bc4f01e38d61a48f66c9873
Bundle SHA-256: 9e82458eb38f49caf7d705ed9f288ba9de5be9b6e3884670b80be8a2c1b61d11

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.

AP037 · AP038 · AP040 · AP041 · AP060 · CV008 · CV009 · CV011 · CV043 · CV044 · CV046 · CV047 · CV048 · CV095

Scope

prove unrestricted submultiplicativity for three actual finite exponential sums at the same degree by constructing a Cauchy table and identifying its cross normalized value without extra horizons or analytic addition

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