nx_ncf_cube_gate.nx

nx_ncf_cube_gate.nx -- X-AUT-NCF-001 RUNG 4: SYNTHESIZE A QUADRATIC-INDEX LOOP (acc += c2*i*i + c1*i + c0), covering x^3 and the cubic family -- exactly the case rung 3 (affine-index) honestly REFUSED. Escalation: the rung-3 affine-index loop PROVABLY FAILS on x^3 (its sum is quadratic-in-x); the quadratic-index loop SUCCEEDS (x^3 = sum(3i^2 - 3i + 1)). Uses the shared lib nx_ncf_synth, so the WIRING auto-widens (x^3 now routes). Construct ladder: linear < conditional < simple-loop < affine-index-loop < QUADRATIC-INDEX-LOOP. T1 linear FAILS. T2 affine-index loop (rung 3) FAILS on x^3 -> the quadratic-index body is necessary. T3 quadratic-index loop SYNTHESIZES x^3 = acc=0; for i { acc += 3i^2 - 3i + 1 }. T4 MATERIALIZE+GOD-BUILD+run HELD-OUT {5->125, 6->216} -> 125216. T5 unified ncf_synth routes x^3 (kind=4). expect_exit: 0 license_tier: ORIGINAL