CV029 — composition coefficients — irrationality research

Exact named statement

forall N. Lt(1,N) ->
  exists d ab ac wb wc db dc pb pc qb qc tb tc vb vc cb cc z. (~d=0 /\ (NatAtanhPrefix(d,ab,ac,N) /\ (NatExpWeightTable(d,N,wb,wc) /\ ((forall j a. Le(j,N) ->
  BetaAt(wb,wc,j,a) ->
  ~d=0 ->
  ~a=0) /\ (NatEulerPrefix(ab,ac,db,dc,N) /\ (NatPowerTrace(ab,ac,N,N,pb,pc,qb,qc,N) /\ (NatWeightedSeriesTrace(N,wb,wc,pb,pc,qb,qc,tb,tc,vb,vc,S N) /\ (NatPowerRow(tb,tc,vb,vc,S N,cb,cc) /\ ((forall j x y. Lt(j,N) ->
  BetaAt(cb,cc,j,x) ->
  NatConvolutionCoefficient(db,dc,N,cb,cc,N,j,y) ->
  d*(j*x)=y) /\ ((forall i a b c. Lt(S(S i),N) ->
  BetaAt(cb,cc,i,a) ->
  BetaAt(cb,cc,S i,b) ->
  BetaAt(cb,cc,S(S i),c) ->
  (S(S i))*c=i*a+2*b))))))))))) /\ (BetaAt(wb,wc,0,z) /\ (~z=0 /\ (NatExpAtanhRecurrence(cb,cc,N,z) /\ (forall i a. Lt(i,N) ->
  BetaAt(cb,cc,i,a) ->
  ((i=0 /\ a=z) \/ (exists k. i=S k /\ a=2*z))))))

PD0001 — Le · PD0002 — Lt · PD0013 — BetaAt · ND0401 — NatConvolutionCoefficient · ND0405 — NatPowerRow · ND0407 — NatPowerTrace · ND0421 — NatWeightedSeriesTrace · ND0410 — NatEulerPrefix · ND0423 — NatExpWeightTable · ND0425 — NatAtanhPrefix · ND0400 — NatExpAtanhRecurrence

Fully expanded target AST

Complete certificate and independent checks

252 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: 88f055686ab9620a1835d315530f9884d4bbd0626a5b97d2524141ff1701f83b
Bundle SHA-256: 401c29b8458ca2615288aa3d695825d8ecc57b021ecce5e677c0920c4df360d9

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.

CV001 · CV002 · CV004 · CV008 · CV009 · CV011 · CV012 · CV019 · CV020 · CV021 · CV022 · CV024 · CV025 · CV027 · CV028

Scope

constructed actual finite composition initial and all coefficients not factorial 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.