L0 — the proven substrate: storage, computation, pattern, and communication by phase
The wave substrate is a phase-coupled oscillator field that provably does four things: store patterns as attractors (capacity αᴄ ≈ 0.06 of N), compute by relaxing a corrupted cue back to the stored pattern (clean recovery up to ~20% corruption), hold many coexisting patterns below full coherence, and communicate at negative SNR (bit-error rate ≈ 0.03% at −2.3 dB).
Beyond the four operations, four resonance properties make it a computer: the sum of waves is the information — one composite field holds K ≈ 96 items read by resonance; matching cost is independent of the number stored (O(1)-in-P); one exposure gives immediate recall with no catastrophic forgetting; and full parallelism is an inherited principle [O]. This layer is frozen and reused unchanged by every layer above.
L0 is the foundation the whole program stands on, and it is already proven (sessions v0.1–v0.2). The field is a near-field, phase-coupled oscillator network — the in-silico analog of the brain’s ephaptic coupling — and information is carried by phase θ, recovered from corruption by the field’s own relaxation.
The four operations
The substrate stores, computes, patterns, and communicates, each verified by a sweep.
| operation | result | condition |
|---|---|---|
| store (D1) | recall 0.989 at P=15 | capacity edge αᴄ ≈ 0.06 of N; collapses past it |
| compute (D2) | cue cleaned to overlap ≈ 0.96 | up to ~20% phase corruption; basin fails near 35–40% |
| pattern (D3) | many patterns coexist | below full coherence (low R); the metastable band |
| communicate (D4) | BER ≈ 0.03% | at −2.3 dB SNR (22% raw bit errors) — phase + clean-up |
The communication result is the end-to-end proof that phase beats bits under noise: even when a fifth of the raw bits flip, attractor clean-up recovers the message almost perfectly. This single property recurs as the I/O advantage at embodiment (L7).
The four resonance properties that make it a computer
Storage alone is memory; these four make the substrate compute.
- The sum is the information. One composite wave holds K ≈ 96 items, and any one is read back by resonance — superposition is the representation, not a side effect.
- Matching without computation. The number of settling steps is independent of how many patterns are stored (O(1)-in-P); on parallel hardware, P = 10⁵ would cost the same physical time as P = 1.
- One-shot learning. A single exposure yields immediate recall, with no catastrophic forgetting of earlier items.
- Parallelism [O]. The O(1) physical time claim is an inherited principle, not a measured wall-clock here — physical realization is deferred.
Why it is frozen
L0 is closed and read-only. Every higher layer — representation, time, hierarchy, inference, learning, world model, embodiment, access — reuses these exact primitives unchanged, so any capability shown later is a property of composition on this substrate, not of a new mechanism slipped in. The frozen-substrate discipline is what lets the program attribute its results honestly.