A Wave-Substrate Computer: Phase-Coded Information, Settling as Computation, and a Layered Test of Functional General Intelligence

This whitepaper builds a clock-free wave-substrate computer and tests one bet: that the properties by which the brain reaches general intelligence on a wave medium — phase coding, resonance matching, one-shot learning, metastability, noise immunity, sum=information — are sufficient for at-least-human-level function. Information is a continuous phase θ, not a bit; computation is the physics relaxing to a fixed point, not arithmetic. Every quantity is reproduced bit-for-bit (2×sha256 identical) and graded honestly; nothing is tuned.

The program stacks nine layers (L0–L9), each mapping an inherited brain finding to a machine mechanism with a falsifiable milestone and a stress test built to break it. The crux was L4 — resonance inference without computation — and it passed: the gate derives itself, constraint satisfaction is settling, analogy is resonance, probabilistic inference is noisy settling. The capability ladder then reaches its end condition, and two post-program continuations harden and compress the result.

The wave substrate and its near-field coupling are inherited from the jamming foundation (c² = B/ρ, clock-free propagation, 1/r² near-field). The brain chain — ephaptic coupling, phase coupling, metastability, attractors, theta-gamma capacity — is inherited from Felt Cognition. Both are cited as principle, never as fitting targets.

Chapters

1. The wave-substrate thesis: compute by phase, match by physics settlingPhase carries information and settling is the computation; the bet that this suffices for general function was tested layer by layer.[O] open
2. Method: no tuning, a stress test for every claim, and bit-for-bit reproductionInherited numbers are principles not fitting targets; every claim survives a breaking test; all twelve sims reproduce bit-for-bit.[V] verified
3. L0 — the proven substrate: storage, computation, pattern, and communication by phaseThe substrate stores, computes, holds many patterns and communicates at negative SNR; the sum is the information, matching is O(1)-in-P, learning is one-shot.[V] verified
4. L1 — the representation algebra: bind, bundle, and permute on the wave fieldbind, bundle and permute form a closed wave algebra; a sequence of length L*≈32 is read back by position, but role-value trees are shallow (depth d*≈2-4).[V] verified
5. L2 — time and sequence: metastable trajectories and a working-memory capacity lawAsymmetric coupling makes the field walk a learned loop (replay 1.0 at λ≈2.5) and working-memory capacity = min(slots, precision), landing in the Miller range 4-9.[V] verified
6. L3 — hierarchy and abstraction: nested phase coupling breaks the flat ceilingA slow phase gates which fast sub-field is active: it selects the level (margin +0.92), recognizes categories from novel instances, composes with zero gap, and multiplies capacity ~6x.[V] verified
7. L4 — the pivot: resonance inference without computationThe gate derives itself from a raw cue; constraint satisfaction is settling (1.0 ≫ random 0.5), analogy is resonance, probabilistic inference is noisy settling — 4/5 [V].[V] verified
8. L5 — dual learning systems: a fast episodic store and a slow semantic storeOffline replay builds a separate persistent slow store that cuts catastrophic forgetting; as an independent context channel it closes L4's open limit (strict ≈ 1.0 ≫ content 0.68).[V] verified
9. L6 — a self-supervised world model: prediction is forward settling, error is the learning waveThe field predicts its own next state by forward settling and learns from the difference wave: held-out error falls 0.978→0.126, rollout is faithful to horizon 12, and a forward model beats reactive recall by directionality.[V] verified
10. L7 — embodiment and real-time control: control is continuous settling, end to end analogIn a clock-free analog loop, control is continuous settling: the forward model holds a moving target through delay, analog I/O beats ADC/DAC and the dimensional advantage scales (N×gap 4.6→42.1).[V] verified
11. L8 — global integration and functional access: a resonant hub broadcasts the dominant patternA global resonant hub selectively binds and broadcasts the dominant pattern (lock margin ≥0.92, non-source recall 1.0), routes any module flexibly, and shows a functional PCI inverted-U — the number R=0.39 not transferred.[V] verified
12. L9 — functional general intelligence: the capability ladder and the end conditionThe integrated L0-L8 machine clears 6/7 capability rungs with the minimal store and 7/7 with the proven dual store wired in; A3 real-time adaptation is the lone single-store [O], closed inline.[V] verified
13. The axiom-independence audit: eight inherited invariants compress to a minimal, irreducible fiveThe 8 inherited invariants compress structurally onto 5 operational L0 axioms; nulling each one (paired, 6 seeds, gated by a passing control) collapses a core capability — all five load-bearing, the set irreducible.[V] verified
14. Inheritance, methods, and provenance: what is inherited, what is not, and how to reproduceThe wave machine inherits five brain invariants (B1-B5) and three physics invariants (P1-P3) as cited principles, never fitting targets; everything reproduces bit-for-bit from twelve pinned digests.[L] calibrated

Headline results

• Information is a continuous phase θ, not a bit; computation is the physics settling — no clock, no fetch-execute.
• Matching is O(1)-in-P and learning is one-shot; phase + clean-up holds BER ≈ 0.03% at −2.3 dB (22% raw bit errors).
• The pivot holds: the gate derives itself, constraint satisfaction = settling (1.0 ≫ random 0.5), analogy = resonance, probabilistic = noisy settling (4/5 [V]).
• Control is continuous settling in an end-to-end analog loop; the analog interface beats ADC/DAC and the dimensional advantage scales (N×gap 4.6→42.1).
• The capability ladder reaches 6/7 rungs with the minimal store and 7/7 with the proven dual store; the eight inherited invariants compress to a minimal, irreducible five.

Reproduction

One harness reproduces and audits every section. From the package root run python3 repro/check_completeness.py: it verifies all files are present, re-runs all twelve deterministic simulations (L0 through the axiom audit), and compares each result against its pinned SHA-256 digest bit-for-bit (v0.1 e9fdd3bc… through v0.12 7f59ced6…). The canonical artifact is this HTML; numbers shown on each page are loaded from those verified results.

Scope and firewall. This program builds function (capability) only. Consciousness — felt quality, the hard problem — is an explicit, never-erased blank on every page (consciousness_claim = 0, hard_problem_open = 1); “at least human-level” is a capability claim, not a consciousness claim. The grading vocabulary ([V] verified · [L] calibrated/cited · [O] open with a stated obstacle) is what makes the program falsifiable, and every open [O] is recorded with its specific obstacle. This is an in-silico model and theory blueprint — not validated engineering, not a built device; physical realization is deferred.