nx_ncf_quad_gate.nx

nx_ncf_quad_gate.nx -- X-AUT-NCF-001 RUNG 3: SYNTHESIZE AN AFFINE-INDEX LOOP (acc += c1*i + c0), the construct that covers x^2 and the quadratic/arithmetic-series family -- exactly the case rung 2's wiring honestly REFUSED (T4 boundary). Escalation: rung 2 simple loop (acc+c/acc*c/acc+i/acc*i) PROVABLY FAILS on x^2; the affine-index loop SUCCEEDS. Uses the shared lib nx_ncf_synth (the DRY core), so landing this rung AUTO-WIDENS the wiring (nx_ncf_route_gate now routes x^2). Construct ladder: linear < conditional < simple-loop < AFFINE-INDEX-LOOP, each with its own proving negative control. T1 linear FAILS on x^2. T2 simple-loop (rung 2) FAILS on x^2 -> the new construct is necessary. T3 affine-index loop SYNTHESIZES x^2 = acc=0; for i { acc += 2i-1 }. T4 MATERIALIZE+GOD-BUILD+run HELD-OUT {5->25, 6->36} -> 25036. T5 unified ncf_synth routes x^2 (kind=3). expect_exit: 0 license_tier: ORIGINAL