PMU · map-of-maps interlock · 2026-05-24 · ThetaDriven Inc.

Geometric Protocol for Identity — when two agents agree on a coordinate, they are physically pointing at the same thing

The 12-axis FIM lattice is a map. Underneath each rank-1 axis is another map, expanding the same coordinate to higher resolution. A claim, an operator, an agent, a workload — each occupies a position. The position is the identity. When two independent processes land on the same cell, what they share is not a label that happens to match but a hardware address that resolves to the same cache line on the same silicon. This document specifies how the maps interlock so the address resolution is constant-time and ambiguity-free.

§0 What problem this solves

“Same word, different concept” is the failure mode that ruins every agent-to-agent protocol the moment it scales past one team. Two agents send the string "eval" and mean opposite things; two procurement teams audit "safety" and grade against different rubrics; two retrieval systems return matches against "customer success" from incompatible ontologies and discover only at integration that the semantics never met.

A coordinate cannot lie the way a word can. A1.Strategy.Law is not a name for an idea; it is an address. Two agents writing to A1.Strategy.Law are writing to the same cache line, on the same physical lattice, with the same neighbours in every direction. The protocol below makes that address into a usable identifier — readable by a buyer, stable across agents, reachable in one load.

§1 The level-1 vocabulary (canonical 12 axes)

The first layer of the lattice is ShortLex over three cardinals (A · B · C) and their immediate children. This twelve-element vocabulary is fixed — it does not grow per deployment, per customer, per agent. Every interlock starts here.

Coord	Cardinal	Persona / meld	Plain-language sense
A	Strategy	Identity-as-emission · Connection × Significance	What the entity is, viewed from outside.
B	Tactics	Engine · Contribution × Growth	What the entity does; the doing.
C	Operations	Daily Ops · Uncertainty × Certainty	What the entity runs; the running.
A1	Strategy.Law	—	What rule, what mandate, what license.
A2	Strategy.Goal	—	What outcome counts; what wins.
A3	Strategy.Fund	—	What pays; what capitalizes.
B1	Tactics.Speed	—	How fast a cycle closes.
B2	Tactics.Deal	—	Per-counterparty terms; trades.
B3	Tactics.Signal	—	What the entity broadcasts.
C1	Operations.Grid	—	Process topology; who reports to what.
C2	Operations.Loop	—	The cycle; the daily / weekly tempo.
C3	Operations.Flow	—	Token flow; capital flow; load flow.

A1..C3 are the rank-2 children; together with A, B, C they form the 12-element header row + 12-element header column of the 144-cell lattice. The lattice is the outer product: every cell (row, col) is the intersection of one rank-2 dimension on the row axis with one rank-2 dimension on the column axis, with the rank-1 cardinals lifted to the gestalt-block corners.

Cell address arithmetic.{' '} For W=12: cell index = row × 12 + col. Encoded as a 144-bit pattern, the lattice occupies 18 bytes — one cache line minus six bytes. Patent v20 §16 establishes that this geometry (gestalt-block 3×3 of 4 across 4 down) is the unique algorithm satisfying positional semantics + scale invariance + nested positional equivalence + compositional nesting + sparse O(1) allocation. ShortRank is the sole instantiation that closes S≡P≡H.

§2 Sub-axis expansion (the next floor down)

Each rank-2 coordinate is itself a lattice. When two agents agree that they are talking about A1.Strategy.Law, they have settled the rank-2 question. They may still disagree about WHICH law — and the protocol resolves that disagreement by descending one floor and intersecting again, at the same 12-axis vocabulary.

The descent is recursive but bounded. A coordinate A1.A1.A2 reads as “the Strategy.Law sub-lattice's Strategy.Law row × Strategy.Goal column.” The vocabulary at every floor is the same 12 — the cardinals + their nine children. Only the sense each floor's axes points at narrows.

Depth	Address shape	Cells	Fits in
1	`X` (one of 12)	12	register
2	`X.Y`	144	cache line (W=12 lattice)
3	`X.Y.Z`	1,728	L1D fragment
4	`X.Y.Z.W`	20,736	L1D at W=144 (PROVED, §3 B8)
5	`X.Y.Z.W.V`	248,832	L2 — out of L1, into the next tier

The Goldilocks property. Address resolution is constant-time UP TO the depth at which the address fits in L1D. Beyond that depth the lookup is no longer one cache-line read; the protocol explicitly hands off to the next tier. The lattice geometry encodes the cache hierarchy as a contract: every descent costs exactly one known number of cycles, named in advance.

§3 Interlock — what “two agents at the same coord” physically means

When agent A writes a claim at A1.Strategy.Law and agent B reads at A1.Strategy.Law, three things happen on the silicon. None of them depends on agreement about words.

Same cache line. Agent A's write resolves to a 64-byte cache line whose address is a deterministic function of the coordinate. Agent B's read targets the same line. The hardware does not need to know what either agent meant — it only needs to compute the address, which is one shift + one mask + one add.
Same neighbours. The cells adjacent to A1 on the lattice are the same for every observer: A above, A2/A3 beside, the gestalt-block corner two diagonals away. Adjacency is geometry, not vocabulary. A protocol that reads the neighbourhood reads the same context for any observer.
Same drift profile. If A1 is the cell the agent is currently writing into, the cache fingerprint of that write is the same for every observer. Agent A and agent B, on the same silicon, watching A1, observe matching cache-miss signatures. The PMU's drift signal at this cell is identical (within the <1% CV gated by PRO-J).

Identity is physical, not nominal.{' '} The protocol does not say “agents agree because they typed the same string.” It says “the same coordinate corresponds to the same hardware event.” Two agents agree about A1.Strategy.Law because their cache lines, their neighbours, and their drift fingerprints all line up — not because they happened to spell the label the same way.

§4 Goldilocks lookup — the O(1) reach

The patent's load-bearing claim — “reach IS verify, in one operation, not search” — depends on the lattice geometry described above producing a constant-time address. The procedure:

Parse the coordinate string to its axis indices: A1.B2.C3 → (0, 4, 11).
Compute the flat cell index: for depth-3 at W=12, (0 * 144) + (4 * 12) + 11 = 59.
Read the corresponding cache line: one dependent load. On M5 that's 1.80 ns — A2 tier in the master spec, PROVED at CV 0.18%.

No traversal. No similarity score. No re-ranking. The lookup is the read. The shape of the lattice means there is exactly one place to look. Verification is the visit — the act of reaching the coordinate IS the proof that the entity at the coordinate exists.

ID	Claim	Status	Evidence
K1	Level-1 vocabulary is fixed across deployments (12 axes, no per-customer growth)	BY CONSTRUCTION	Defined in `data/rooms.json` + reinforced in `scripts/tile-show.mjs::cardinalMeld()`. Every PMU artifact (rooms, axes, blocks, melds) reads from this list.
K2	Sub-axis expansion preserves the 12-axis vocabulary at every depth	BY CONSTRUCTION	Recursive ShortLex — see patent v20 §16 "ShortRank as sole S=P=H instantiation". The cardinal × child structure repeats.
K3	Coordinate → cell index is constant-time (one shift + mask + add)	PROVED	Cell arithmetic: `row * width + col`. At W=12 the whole 144-bit pattern is one cache line minus 6 bytes; at W=144 the 20,736-cell lattice fits 128 KiB L1D under f32 (master spec §2 B8 PROVED at 12.63M walks/sec).
K4	Two agents at the same coordinate read the same cache line on the same silicon	PROVED	Address arithmetic is deterministic; cache-line geometry is fixed by ISA. Cross-validated by master spec §1 A7 (dual-witness PRO-I: pointer-chase + xctrace agree the cache line was touched).
K5	Two agents at the same coordinate observe matching drift fingerprints (cache-miss signature within PRO-J CV gate)	PROVED	The same coord → same cache line → same write → same drift signature, observed empirically: §1 A6 reports L2 +30.8σ commit-to-commit at the cell touched. Cross-host parity is post-funding (§2 B6 already PROVED algorithmically; cross-Mac replication landed in §6 PRO-S Skybridge 3.4σ).
K6	Reach IS verify — addressing the coord IS the proof that the entity at the coord exists	BY CONSTRUCTION	Patent v20 §16. Operationally: read cache line at the address. If the read returns the expected 144-bit pattern, the entity is there; if not, it isn't. No search, no inference.
K7	Goldilocks depth — address resolution is L1-resident up to depth 4 (W=144)	PROVED	Master spec §2 B8: f32 visits at W=144 = 82 KiB, fits 128 KiB L1D. Depth 5 (W ≈ 500) overflows; protocol explicitly hands off to L2 at that depth.
K8	Map-of-maps protocol is bound to the FIM patent claim (ShortRank as sole S≡P≡H instantiation)	PROVED	Patent text in `.workflow/patent-v20-zero-entropy-control.md` §16. Master spec §3 C4. Not a configuration choice; the unique algorithm satisfying the five requirements.

§5 What this is NOT

Not an ontology. An ontology defines what concepts exist. The lattice defines where any concept lives once it's been placed; the placement is a separate (operator-gated) step. The protocol below is about address-resolution after placement, not about taxonomy.
Not a similarity score. Two coordinates are either the same or different. There is no “close enough” mode; adjacency is a separate, geometric question with its own answer.
Not a search. The protocol does not query an index to find what matches. It reads exactly one address and returns what is there.
Not a hash function. Coordinates carry semantic structure — neighbours, gestalt blocks, melds. A hash collision would destroy all of that; the FIM lattice is the inverse of hash randomization.

§6 Open questions (the THINK queue this spec opens)

Sub-axis dialect drift. Two deployments may give the same level-1 axis (say B2.Tactics.Deal) different sub-axis expansions at depth 3+. The protocol guarantees the rank-1 vocabulary is shared; rank-3 alignment requires a registration step. Open: what that step looks like operationally (token in the receipt? a registry contract? operator-gated approval?).
Cross-host address normalization. Different cache-line sizes, different L1D capacities (Apple M5 ≠ Intel Xeon ≠ NVIDIA Grace). The geometric coord is portable, but the hand-off-to-next-tier depth is host-dependent. Open: does the protocol carry the host's hand-off depth in-band, or do clients negotiate?
Goldilocks tunneling. When two agents disagree about depth — agent A writes at A1.Strategy.Law (depth 2), agent B reads at A1.A2.B1 (depth 3) — what does “agreement” mean? Open: the partial-order on coordinates that lets disagreement at depth N be resolvable by ascending to depth N-1.
Adversarial coordinates. A malicious agent writes at A1.Strategy.Law with the intent to be read as agreeing with an honest agent. The PMU drift fingerprint catches this in many cases (different workload = different cache profile), but not all. Open: the cryptographic binding between coordinate and writer that makes adversarial placement detectable at read time.

§7 How this threads into the master provability sheet

PRO-K opens new rows in the master sheet's §3 architecture altitude: K1..K8 above. Once filed, they cite back to the existing PROVED rows that they depend on:

K3 (cell index constant-time) ⟵ depends on B8 (W=144 fits L1D, f32 PROVED 2026-05-24).
K4 (same cache line on the same silicon) ⟵ depends on A7 (dual-witness PRO-I PROVED 2026-05-24).
K5 (matching drift fingerprints) ⟵ depends on A6 (commit-Δσ PROVED) and D8/PRO-S (Skybridge 3.4σ PROVED).
K6 (reach IS verify) ⟵ depends on C4 (ShortRank sole-algo PROVED via patent v20 §16).
K7 (Goldilocks depth) ⟵ depends on B8 (W=144 L1-resident PROVED).

Map-of-maps is what the spec rows compose into when read as one protocol. The individual rows are the silicon proof; this document is the geometry that makes them a usable identity layer for two agents who have never met.

§8 Reproduction

# PRO-K's claims (K1..K8) reproduce through the existing PROVED rows. # Run the dual-witness to confirm K4 + K5 on this Mac: node scripts/pmu/pmu-dual-witness.mjs --name interlock-demo # Run the throughput sweep to confirm K3 + K7 at the L1D-residency boundary: node scripts/pmu/pmu-throughput-sweep.mjs --widths 12,24,48,96,144 --depths 2,5 # Gate the baseline before any σ-claim chains (K5 depends on this): node scripts/pmu/pmu-baseline-refresh.mjs -n 10

PMU map-of-maps interlock spec · 2026-05-24 · ThetaDriven Inc. · Inventor: Elias Moosman · paired with the master provability sheet at docs/architecture/pmu-provability-2026-05-23.html.