L4 — the pivot: resonance inference without computation
This is the program’s crux: does inference-without-computation hold on cognitive tasks? It does, on four of five forms. The slow gate is now derived from a raw, unlabeled cue (no oracle); constraint satisfaction is settling (a native anti-ferromagnet solves a planted graph at 1.000 ≫ random 0.5); analogy is resonance; and probabilistic inference is noisy settling. No hybrid was forced.
The substrate relaxation IS a constraint solver: an edge of coupling −1 makes the L0 field a 2-colouring / MAX-CUT machine that tracks the known frustration optimum 1/(1+f) with a tiny spurious gap (0.0014). The gate that L3 had to assume is resonance-read from a raw cue and then routes the fast field (derived == oracle, cost ~0). The one honest [O] is structural — strict capacity trades off directly against gate-derivability — with its resolution (an independent context channel) named for L5.
If “inference without computation” holds on cognitive tasks, the wave machine reaches general function as a different species of computer; if not, the program would have to adopt a digital–symbolic hybrid. L4 tested this and came back largely positive — 4 of 5 forms [V], one honest structural [O], hybrid branch not triggered (session v0.5, digest 2d3057bb…).
The gate derives itself
The debt L3 left — “assume the correct gate” — is paid here. The slow context is resonance-read from a raw, unlabeled cue in an upper field and then routes the fast field, composing H1 and H2 into one loop. Where the geometry is separable the loop closes: the gate is derived at 1.0 (for cue overlap ≤ 0.2), derivation costs about nothing, and the derived gate performs identically to an oracle (0.96–0.99) and far above a flat baseline (0.38–0.49).
The honest boundary: at heavier overlap (ρ = 0.4) the upper geometry stops being separable and gate inference falls to 0.71.
Three forms of inference, each as physics
| form | wave mechanism | result | grade |
|---|---|---|---|
| constraint satisfaction | relaxation of a signed phase field | planted graph 1.000 ≫ random 0.5; tracks 1/(1+f), spurious gap 0.0014 | [V] |
| analogy | structural resonance on L1 records | fill-a-factor robust to J=12; proportional A:B::C:? to J* = 4 | [V] |
| probabilistic inference | noisy settling = sampling | all three directional Bayes laws hold (prior, evidence, temperature) | [V] |
Constraint satisfaction is the headline: an edge weighted −1 turns the L0 relaxation itself into a 2-colouring / MAX-CUT solver — no clock, no tuned constant, the physics drops out the answer. Spurious minima did not dominate at the tested scale; the only shortfall tracks the genuine frustration optimum.