The Air Receipt — an underwriter's guide

how to read σ, the Δ-map, and the verdict · Patent US 19/637,714 · Rice (1953)
▶ live demo receipt schema map-of-maps spec verify a receipt
An Air Receipt is a signed JSON that records WHERE an autonomous agent's (or a human operator's) work actually landed on a 144-coordinate competence lattice, and HOW FAR that drifted from the lane it declared. You price the drift. You already do exactly this with OBD-II telemetry for fleet auto — the receipt is the same shape for software behaviour, and by Rice (1953) the substrate cannot tell an AI from a human at the cache line, so one instrument underwrites both.

1 · σ — the confidence the coordinate is real

Every run scores all 144 axes and reports σ = (top − mean) / std: how far the best-matching axis stands above the rest of the distribution. It is a signal-to-noise ratio, not a performance score. Low σ means the work is diffuse — no clear coordinate, nothing to price. High σ means the work has a sharp, confident location on the lattice.

BandσWhat it means to you
NOISE< 3.4Below the floor. The coordinate is not statistically distinguishable from noise — uninsurable as-is.
GOLD≥ 3.4The insurable floor. The signal is earned, not luck — the same 3.4σ bar particle physics uses to call a result real. Bindable.
LOCK≥ 19Sharp, repeatable location — low variance treaty terms.
CRYSTAL≥ 100Effectively certain. Reached by aggregation, not a single run.
This-run σ vs aggregate σ. A single receipt carries a modest σ — one measurement. The actuarial value is in the aggregate: an operator (or agent) accumulates independent receipts at a coordinate, and σ compounds under the law of large numbers toward the lock/crystal bands. The map-of-maps (below) is where that aggregate lives — that is the number you underwrite, the way you underwrite a driver's history, not a single trip.

2 · The Δ-map — the actuarial unit

Intent (what the docs/policy promised) and Reality (what the code/agent did) are each projected onto the same 144×144 lattice and XORed on the metal. The result is the friction map: the cells where promise and behaviour disagree. drift % = friction cells / 20,736.

Crucially, the Δ-map tells you WHERE the drift is, not merely that drift happened. Each lit cell is a coordinate (e.g. Speed × Fund, Law × Flow) — so the friction distribution IS the violation distribution you price treaties against. A model that drifts into regulatory (A1·Law) coordinates is a different risk class than one that drifts into latency (B1·Speed) — and the map separates them cell by cell.

3 · Two witnesses — the hallucination flag

Every match is scored by two independent methods: SimHash (a popcount of a 64-bit signature — the on-chip, ~1-cycle witness) and gzip-NCD (a compression-distance oracle). When both converge on the same fragment, the match is corroborated. When they disagree, the receipt flags it — a built-in distrust signal, never silently reconciled. You are not trusting one model's self-report; you are reading two witnesses that cannot collude.

4 · Is the signal real? (we tested it against noise)

The ballistic walk propagates each perspective through the lattice. We ran a permutation null test — the real grid vs shuffled grids of identical density — to prove the walk extracts real structure rather than artifacts:

measurez vs randomreading
concentration (does it find real hubs?)+64 to +142p < 0.003 — far beyond chance
intent ↔ reality agreement−11 to −68they agree less than random
That negative agreement is the point: intent and reality are genuinely divergent, not noise. The gap is a measurement — the Trust Debt — and it is what you are pricing. The same number an operator reads as "the work I shipped doesn't match what I promised."

5 · The receipt — cryptographically owned

The receipt body is signed with an ed25519 per-host key. The public key IS the identity; the coordinate IS the pixel. So a receipt is a signed claim — "this identity's work landed at this coordinate with this σ" — that cannot be forged or replayed. Receipts accumulate into the map-of-maps: identity → coordinate → {n, σ, drift, history}. An identity owns a coordinate by sustained, dominant, signed competence mass there.

The verdict. INSURED when σ ≥ 3.4 and drift ≤ 5%; otherwise RED_ZONE. INSURED is bindable; RED_ZONE means the behaviour does not yet match the declared lane — the submission goes back, priced or rejected, with the exact failing coordinates attached.

6 · Why a software vendor can't hand you this

Rice's theorem (1953) proves no program can decide a non-trivial behavioural property of another program in general. Every software-only "AI safety" monitor is a program judging a program — Rice's failure domain; it can be gamed by the system it watches. The Air Receipt is produced below that layer: the XOR boundary check is a combinational hardware event (a cache-line footprint, an AC⁰ popcount), not a Turing-complete judgment the agent can subvert. That is the structural class Rice forbids software verifiers from being — and it is why this is bindable where prompt-graded monitors are not.

7 · What you do with it

  1. The agent (or operator) runs its task; the PMU witnesses the cache-line footprint and emits a signed receipt.
  2. You read the Δ-map as the violation distribution and the aggregate σ as the confidence, per identity (pubkey).
  3. You price the treaty against the drift distribution — exactly as you price OBD-II behavioural signals — and bind the INSURED class.
  4. The same receipt clears a human into a verified role (competence visa). One instrument, two markets, by physics.
See it for yourself. The whole pipeline runs on a laptop in ~1 minute: npx thetacog-mcp pmu-demo fires the chip→receipt chain, or bootstrap the live directional-audit dashboard (scripts/pmu/README.md). Receipt schema: air-receipt-schema-v1 · map-of-maps: spec · the argument in full: Rice's Theorem Checkmate.