What survived: a claims register with falsifiers for a pre-registered AI research program

Top-level reconciliation of the two research arcs, plus a claims register: every surviving claim, its evidence, and what would falsify it. Written to be the single legible entry point. The project's real asset is its method — pre-register, run once, report failures, baseline at equal budget — so this document foregrounds status and falsifiers, not narrative.

Last updated after the 10-step roadmap (docs/ten-step-roadmap.md).

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STATE OF THE PROJECT — 2026-07-29 update (read this first; the body below is the older register)

The body of this register predates programs 3–4, the reckoning, the codesign campaign, and the 2026-07 foundations strands. It remains accurate for arcs 1–2 as far as it goes; this block is the current one-page state, with claims and falsifiers. Per-strand canonical docs are linked from README.md.

Alive (build on these):

1. Verifier exploitability (the lead thread). Best-of-N is bounded by verifier exploitability ε, not accuracy; N*(ε) shipped as verifier-budget; ε is pool-relative (two channels: exploit + coverage; swings 6.2× with candidate pool). Falsifier: a verifier whose selection survives adversarial pool shift without a clean prefilter. (verifier-bottleneck/FINDINGS.md)
2. Test-time recurrent depth. Real, parameter-efficient (1/8 params, +0.36 ± 0.13 OOD over N=10 seeds; the single-seed shipped figure was +0.28), extrapolating (8×) compute axis; domain governed by update contractivity — externally reproduced at LLM scale (STARS/FPRM). Verifier-gated halting beats best fixed depth (0.991 vs 0.960, ~2.3×±0.8 less compute, N=10). Patent line closed (ACT/PonderNet/DEQ own the wins). (TTC-recurrent-depth-synthesis.md)
3. The AIMC window law (ship-ready defensive publication). On hybrid LMs, the attention window policy — not the attention fraction — decides AIMC's decode win (sliding-window ~5.6–6.8× flat in context; full attention collapses to ~1.2× at long context); measured quality boundary on RecurrentGemma-2B (recall 1.0 within window, 0.0 beyond, effective range ~0.5·W at L=2·W). Lane = power-bound 1–8B edge + power-capped ≲8k disaggregated prefill (K-series all closed; produced KV portable at ≥5-bit). Falsifier: gain-cell analog attention maturing through the ITO+GQA+OSFET corner (quantified, three immaturities deep). (PAPER-aimc-window-codesign.md, DIRECTION-prefill-flank.md)
4. Optical interconnect, narrow. Bandwidth-density/capacity fabric for pooled KV at rack reach and extreme scale ONLY; energy case flips under honest laser wall-plug × utilization; the niche is incumbents' shipping thesis (Celestial) — our contribution is boundaries + negatives. (../codesign-analog-moe/MASTER-SYNTHESIS.md)
5. The method (the project's durable asset). Novelty gate (5 checks + meta-check), the soundness axis (not-novel ≠ false; landing on a named theorem = corroboration), floor arithmetic for registered thresholds, and gate-first same-day strand closure — calibrated on ~15 deflations and 5 independent reconvergences of "interconnect not compute; strong baseline beats clever structure." (NOVELTY-GATE.md, SOUNDNESS-AXIS.md)

Dead (do not reopen without new evidence): waves/complex as load-bearing substrate (equal-budget falsified everywhere; only real-OK non-commutativity survives in cognition); optical compute for inference (worse-PIM: AIMC beats it 11–20×); quantum/exotic substrates for learning or biology at equal budget; frontier-datacenter AIMC (watts-Amdahl cap ~1.4×); the ε "universality class" (Thurstone identity); all foundation-flavored metaphysics objects (grounding 5/5, ontogeny 14/14, eschatology 5/5, resolution=perennialism — each deflated or reduced to owned mathematics).

The 2026-07 foundations strands (all closed, gate-first, same-day): their durable residue is method plus a few measured facts — self-critique fails via shared error structure (same-context critic 12/12 misses; sign FLIPS in the dominated regime); creation/eschatology dissolve into certificate theory + the flux law (expansion manufactures the gap, the gap feeds the flux, the flux makes structure; relics invert the coupling — Layzer + Prigogine + Zel'dovich compose; arrow-capability of a law = recurrence + invariants, residue 0; IC ≡ post-selection = 0 bits).

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The two arcs in one paragraph

The project has two independent arcs that share a substrate (complex/wave vectors) and a method. Arc 1 — continual learning & cognition asked whether representing information as waves yields continual learning without forgetting (it does not — that comes from a decorrelating rule, not waves) and whether the same substrate models human reasoning (it does, in one specific corner: non-commutativity). Arc 2 — photonic inference asked whether an optics-native SSM beats a GPU on latency (it does, but inside a now five-walled box). Both arcs have reached honest, defensible termini that are far narrower than the original ambitions — and correct.

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Arc 1 — continual learning & cognition

What's dead (project a — continual learning)

Three independent roads (capacity bake-off 5-i, online forgetting 5-★, weight-only 5-★b) reached the same place: continual learning is delivered by a decorrelating projection/pseudoinverse rule — a classic 1980s associative-memory result with nothing to do with waves — and a real-valued substrate does it at least as well at equal budget. "No backprop ≠ no forgetting." Terminus; nothing left to chase that isn't goalpost-moving.

What survived, then narrowed (the representational phase edge)

Exps 8/9/13 established a real representational edge: a complex/phase encoding separates amplitude-correlated concepts better than an equal-budget real encoding when the data has directional/asymmetric structure — but only with synthetic, injected asymmetry, and only above A≈0.3. Roadmap step 6 closed this thread negatively: on natural corpus directed co-occurrence (asymmetry ≈0.46, above the synthetic crossover) the complex encoding loses to equal-budget real at every discriminating noise level, and amplifying the corpus's own asymmetry up to 8× does not flip it. The edge is a property of the synthetic antisymmetric structure, not of natural directional data. Surviving claim, fully qualified: real on synthetic directional data, absent on natural corpus data.

Where the substrate is genuinely necessary (project b1 — non-commutativity)

This is the one corner where "build it as waves" is justified by evidence, not by the name. The substrate is the Busemeyer/Bruza quantum-cognition formalism, and the roadmap grounded it in our own concept-waves:

• Conjunction fallacy (exp 16): p(F∧B) > p(B) from incompatible concept-waves, 100% of seeds; vanishes at zero incompatibility (classical control).
• Disjunction fallacy (step 1): the bundled co-prediction, same geometry unchanged — under the same representativeness principle, p(F∨B) < max(p(F),p(B)), 100% of seeds.
• Feature-emergent (step 3): the effect survives with no hand-inserted axis — incompatibility emerges from genuinely shared features; null control (no shared features) kills it.
• Sure-thing violation (step 5): a decision error (second paradigm) — interference drops p(play|unknown) below both conditionals; requires the phase.
• QQ-equality on real survey content (step 4): the parameter-free invariant holds to machine precision on the Clinton/Gore pair.

What did not transfer cleanly (reported, not buried):

• Quantitative magnitude fit (step 2): the minimal 2-knob model is over-constrained — it gets the fallacy and the human ordering but cannot match a 3-value probability triple (one knob couples representativeness to incompatibility). Needs a richer geometry.
• Order-effect SIGN (step 4): the naive correlated geometry does not reproduce the Gallup assimilation direction (both ratings fall when asked second); matching the sign needs a fitted geometry, as Wang & Busemeyer did. The parameter-free QQ invariant is the strong result; the sign is geometry-dependent.

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Arc 2 — photonic inference

Verdict: SUPPORTED, but now five-walled (was four). An optics-native static-S4 SSM beats an H100 on decode latency (~55× at d=256, reproduced exactly in step 9) only inside:

1. decode-only (prefill loses ~500×),
2. low-precision (>10⁻⁴; the cliff voids it otherwise),
3. small d_model (55×→2.2× over d=256→2048; the size wall),
4. zero dynamic-weight matmuls (the static S4 structure),
5. NEW — task-gated (roadmap steps 7–9): the win requires a workload the static S4 can do at iso-accuracy. On position-selective recall the static SSM cannot reach attention accuracy at any width (step 7: ~16% vs 100%, flat in d), so on recall-heavy decode (the important LLM case) the win is void — no finite-d re-scoring recovers it. The free square-law gate is not the problem (step 8: D3 holds); the static mixing is. Recovering recall needs a selective (Mamba) SSM — the riskier photonic story the cost model deliberately avoided.

The win's mechanism remains data-residency (weights resident, no per-token HBM traffic), not cheap multiplies (optical energy is ~0–1% everywhere). Cost model is calibrated to literature within an order of magnitude (Prompt 9). The whole 10-part build passes 164 tests.

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Claims register

Status: ✅ supported · ⚠️ partial/qualified · ❌ falsified · 🔒 closed terminus.

Roadmap #2 updates (see docs/ten-step-roadmap-2.md)

Status changes to the rows above, and new claims:

Two headline shifts from roadmap #2:

• Photonic arc UPGRADED. The roadmap-1 "fifth wall" (task-gating: static S4 can't recall) is navigable — a selective SSM recovers recall accuracy (C14′) while keeping zero dynamic-weight matmuls and a 45–60× decode win (C16, C17). The arc's verdict moves from "SUPPORTED, task-gated (recall = dead end)" to "SUPPORTED; recall reachable via a selective SSM that keeps the win."
• Cognition (b1) strengthened but contextualized. C11/C12 resolve once the geometry is decoupled / fitted (C11′, C12′), and a genuinely novel falsifiable prediction emerges (C18). BUT a literature cross-check (r2-step 10) surfaced Boyer-Kassem et al. 2016, "Quantum-like models cannot account for the conjunction fallacy" — the QP account is contested, and our own fitting strains (C11 original, C12) are consistent with that critique. The honest position: the substrate reproduces each signature cleanly, but jointly satisfying all constraints is genuinely hard and debated — cite the critique, don't overclaim.

One-line bottom line: waves earn their keep in exactly one place — non-commutativity in human judgment (b1) — where the conjunction/disjunction/sure-thing errors fall out of incompatible concept-waves; everywhere else (continual learning, natural-data representation, general photonic inference) the honest verdict is narrower than the name suggests, and now precisely bounded.

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What's genuinely open (worth doing; not goalpost-moving)

Both items previously listed here were CLOSED by Program 4 (docs/program4-closing-the-gates.md):

• Cognition magnitude fit (C11/C12) → CLOSED (P4 s6). A real-valued 2-D projective model fits the Moore-2002 Clinton/Gore order-effect magnitude (RMSE 0.052) and satisfies the parameter-free QQ-equality to 1e-15. Magnitude and sign are real-representable; complex adds nothing the QQ constraint doesn't already bind. The last clean cognition number is closed — complex decorative.
• Photonic selective/Mamba SSM relevance → CLOSED (P4 s1, decisive negative). The latency win needs zero dynamic-weight matmuls; only pure static/diagonal-SSM keeps it (≈0% of deployed decode), and attention breaks it outright. The photonic story does not extend to real LLM decode — structurally, calibration-independent.

The actually-open items now live on the surviving (substrate-agnostic) tracks — not photonics or cognition, both of which are closed:

• Does the TTC hybrid scheduler generalize off Kuramoto slow-dynamics? (Program 3: bounded so far.)
• A deployable verifier-ε estimator for real reward models (ε-budget CLI shipped; real-RM estimation open).
• Does "worse PIM" hold for large/high-precision models? (LightML, ISCA 2025, contests it at scale.)

Program 4 re-charter recommendation (the fork)

The founding premise (wave-based continual learning / Thesis B) is dead; the two applied bets resolved (photonic compute DEAD, interconnect ALIVE-but-bounded). Recommendation: PIVOT the project from "wave-based continual learning" to "inference-time compute + verifier reliability tooling" — the TTC hybrid scheduler and the verifier ε-budget tool are the only upward, substrate-agnostic survivors and depend on none of the dead theses. Carry optical interconnect as an optional hardware sidecar, and retire the wave/continual-learning thesis with a clear, well-evidenced obituary. See docs/program4-closing-the-gates.md step 10.