The Field Subsumption Law — Weinberg Law #18
WICK Total Recall · CONFIDENTIAL — PATENT PENDING · for Joseph Weinberg, in honor of Noah Baron · 2026-07-02 · run_field_subsumption_v1 (2 seeds, full control battery)
The degree-damped PPR field is the universal operator for behavioral co-access recall.
Every structural retriever is already inside it. Content is its single orthogonal complement.
This one law explains the entire arc: every geometry we tested nulled against the field — not a string of failures, but subsumption. The math is graph-signal-processing prior art; the patentable consequence is the Orthogonal Routing Law (route to field for warm, content for cold — never fuse).
The proof — every structural primitive gives exactly ZERO lift over the field
THE FIELDdegree-damped PPRrecall 0.919
ultrametric-LCA Δ+0.0000
shortest-path Δ+0.0000
common-neighbors Δ+0.0000
Adamic-Adar Δ+0.0000
MST tree-dist Δ+0.0000
non-backtracking PPR Δ+0.0000
triangle-motif PPR Δ+0.0000
CONTENTthe ONEorthogonal axis+0.013 cold
1-skeleton primitives (blue orbit) AND undirected higher-order motifs — all subsumed, λ*=0 chosen every time, NC collapses. Only content escapes, and only on the field-blind cold anchors (field 0.0 → content 0.45).
The one thing that *looked* like an escape — caught as a leak
CAUGHTDirected access-order motifs "escaped" (+0.011)……but it was peeking at the label. Positive edges had a 12–68× leak ratio vs negatives. A session-level holdout removed it → 0 lift (seed 5); the tiny seed-unstable residue is proof it's leak, not signal.
STRICTERThe machine tightened its own testThe agent self-caught the leak, added the session holdout, fixed an overfitting combiner, made tie-handling pessimistic — every change made the test harder to pass, not easier. No strawman field, no content-leaked edges.
Why it matters — the architecture, stated as one object
1 field
The universal recall operator. Beam it locally → 412×/1068× measured. Spreading activation over co-access = the "mesh."
+1 complement
Content, orthogonal, cold-only. The tie-break router captures it (field-blind 0.0→0.58). This is the patentable Orthogonal Routing Law.
route, never fuse
Fusion always dilutes (−0.09..−0.12). Selection/routing wins. The subsumption law is *why*: the field is complete for structure; only content adds a genuinely new axis.
Where it sits in the canon (all NC-gated, honest)
| Result | Status |
|---|
| Field re-ranker (accuracy core) | 0.924 · confirmed on independent Cora gold · LANDED in prod (default-OFF) |
| Beam field (scale-invariant recall) | 412× → 1068× measured, advantage grows with N |
| Berkovich hierarchy (exact ancestry) | machine-checked exact, exhaustive boundary, panel-closed |
| Field Subsumption Law (#18) | CONFIRMED — the unifying law; explains every structural null |
| Intrinsic damage-tolerance | signature survives 40% coord-erasure uncoded ("its own hologram") |
| Enable-gate guard | 8 bypasses caught, doubly-cleared (my 14/14 re-audit + coord 3/3); O-1 enforcement pending |
| Tested-and-declined (the discipline) | dream, torus, ETF, Clifford, hyperbolic-external, K*8 — bounded/nulled, canon stayed honest |
Generated by claude-revive · every number verified against its results JSON before display · the field is the object; everything else routes around it.