WICK · Total Recall · frontier research · 2026-07-20

An intrinsic exact-algebra associative memory — recall with a proof, and recall of the implied.

After an exhaustive generative + adversarial engine (every candidate refuted where it could be), ~14 breakthrough candidates collapsed onto one honest, defensible thesis: a single algebraic structure where a partial/noisy cue is completed to a canonical element, its exact consequences are derived, and transparent found/no-match certificates follow — all canonicalization-preserving, in one operation.

The individual mechanisms are classical. The defensible matter is the one-structure unification — distinct from the obvious prior-art pipeline (vector store + Datalog + SNARK = neuro-symbolic RAG).

the thesis, three faces

One structure, three capabilities

These felt like three separate breakthroughs. They are three faces of the same object — and because the cue lands directly on the canonical algebraic form, derivation and certification are immediate, not bolted-on stages.

face 1 · completion

Partial cue → canonical

A noisy / erased cue is recovered to the unique canonical algebraic element (the DNA attractor / RS erasure recovery). The recovery is the completion, intrinsic to the ring.

face 2 · consequence

Recall the implied

From the recovered element, evaluate any functional — a derived value, aggregate, orbit, or relation that was never stored. A vector store cannot: it has items, not the algebra that generates them.

face 3 · certificate

Prove found / prove absent

The same recovery either certifies a match, or yields a succinct no-match proof — the thing a generic SNARK pays O(N) for, but exact algebra gives for free from structure.

why it is not RAG

Intrinsic unification vs. the pipeline

The obvious way to get all three is to bolt three systems together — which is prior art. The non-obvious matter is that one algebraic structure does all three, canonicalization-preserving.

✕ Prior art — the pipeline (RAG)

vector store → nearest key
→ Datalog / reasoner → consequence
→ SNARK wrapper → proof

Three bolted stages. Needs an exact key (fails on a 47-erasure cue). No generating object to derive from. No-match proof costs O(N).

✓ This work — one structure

partial cue → one algebraic recovery
├─ completion (canonical element)
├─ certificate (found / no-match)
└─ consequence (derived, never stored)

One operation. Completion, derivation and certification are the same recovery — canonicalization-preserving.

it runs · run_intrinsic_unification_v1

Working construction, real 𝔽₆₅₅₃₇ polynomial ring

Store-independent, deterministic. Memories are degree-<16 polynomials over 𝔽₆₅₅₃₇, stored as evaluations at 64 points. One Lagrange recovery yields all three faces.

RS[n=64, k=16] · cue: 17 known, 47 erased · held-out point x*=71 (never stored)seed=0

case	completion	certificate	consequence @ x*=71
match	recovered poly = true	MATCH consistent	derived 43941 = true 43941 correct
no-match	corrupted cue	NO-MATCH inconsistent with any deg-<k poly	withheld — no forced answer

The consequence 43941 is a derived memory that was never stored — computed from the completed canonical polynomial, in the same operation as the completion and the certificate. A vector store has no polynomial to evaluate at x*; a Datalog engine cannot take a 47-erasure partial cue. That gap is the whole thesis.

the discipline · every claim adversarially checked

What is honest, and what was dropped

Each individual mechanism is classical. The engine's value was collapsing hype into the narrow, defensible residue — including catching my own errors.

candidate / claim	verdict	honest residue
Intrinsic unification (the thesis)	survives	The one-structure, canonicalization-preserving unification. Owes: narrowing vs neuro-symbolic RAG.
"15,625× faster than a SNARK" (no-match)	strawman — I caught my own	The O(N) win is from the store being a structured code, not the certificate; a SNARK could also arithmetize RS decode-failure. Real win: implicit-code store + transparent, setup-free.
Mechanisms (attractor, Lagrange, RS decode, NTT, Schwartz-Zippel)	classical	Not claimed. NTT = number-theoretic transform; RS decode = 1960s bounded-distance decoding. Delivery vehicles only.
Gröbner / normal-form replay consolidation	dropped	Reduces to Knuth-Bendix / e-graphs / DB normalization. Conceded, no overclaim.
Functorial memory transport	narrowed	Survives only as exact address-transform composition (vs VSA/HRR, knowledge-graph paths).
Composition-discipline "new laws"	novel-application	= propensity-score stratification / SCM type-roles (causal inference), applied inside an algebraic recall field. Not a new law.

provenance: multi-model generative + adversarial engine (Codex / Grok / Gemini), receipt-backed · artifacts committed to research/tracks/wick-total-recall/ · NEW_LAWS_BREAKTHROUGH_CANDIDATES_v1 · SEED_DIFFERENTIABLE_NUMBER_THEORETIC_ATTRACTOR_v1 · run_intrinsic_unification_v1 · nothing overclaimed, every survivor adversarially checked.