How We Use It — the actuary's rating variables
The answer to "so how do we use this?" is a table an actuary can price from: every variable the machine produces, what it means in underwriting terms, the command that computes it, and its evidentiary status. This is the three-layer split cashed out — layer 3 gave the formulas credibility, layers 1 and 2 produce the variables, and each variable below is one line of a rate filing waiting to happen.
MEASUREDThe trigger variable — off-lane percentage vs the sealed kill threshold. The parametric event itself: reality mass outside the declared lane, per commit, against a pre-registered threshold. Underwriting meaning: the claim trigger — pays or doesn't, no adjuster. npx thetacog-mcp attest-demo shows the machinery end to end.
MEASUREDFrequency — the crossing count per window. Boundary crossings are the countable loss-frequency events (layer 2, the thing banks' math has no analogue of). Decidable by integer comparison against the ShortLex boxes. Underwriting meaning: claim-frequency basis. node scripts/pmu/rc-compute.mjs prints crossings, hits, and windows.
MEASUREDThe solvency ratio — Rc in a window (claim 2's own metric). Hits over total accesses: structural floor 3/11 exactly, walk-measured 0.48. Underwriting meaning: the insured system's running health gauge — a covenant variable a policy can reference. Same command as above, 70 milliseconds.
MEASUREDThe margin variable — distance to criticality, cλ. The knee sits at c = 1/λ ≈ 0.085; the receipt runs at cλ ≈ 0.59 with the pole measured (35× blow-up on approach). Underwriting meaning: how far the book stands from the cliff — a portfolio-level stability margin, per commit. node scripts/pmu/spectral-radius.mjs --sweep.
CALIBRATEDSeverity-over-time — the depreciation schedule, k_E and the 231-crossing half-life. The count is physics; the price per crossing is a calibrated exchange rate (patent's own "determined during calibration"), now sitting inside a disinterested published band (0.002–0.04 per crossing, ACL 2025). Underwriting meaning: the amortization table for unattested output — how stale work loses insurable value. Status honestly CALIBRATED until the pre-registered half-life protocol runs.
MEASUREDThe concentration haircut — N_eff versus raw path count. Participation ratio 3162 of 3168 on the bare lattice: mass is near-equidistributed, so the certainty denominator survives the mass axis. Underwriting meaning: the anti-double-counting adjustment — confirmations priced by effective, not raw, multiplicity. node scripts/pmu/effective-paths.mjs.
CONJECTUREThe independence spectrum — the block-τ top eigenvalue. First reading: a global factor on the bare lattice (13.14 of 16), so certainty-from-multiplicity is a conjecture pending the word-salad run — and the instrument printing that null is the exhibit that the MEASURED rows above mean something. Underwriting meaning: the correlation load an actuary would charge for until independence is shown. node scripts/pmu/block-tau.mjs.
CONJECTUREThe loss-correlation link — drift-to-loss. The one variable no theorem or guard can supply: whether high drift predicts real-world loss. Produced only by a pilot book of business — named by the underwriter ghost-read as the meeting condition, and named here as the last mile between a structurally sound trigger and a priceable one.
The use, in one paragraph
So this is how we use it: the trigger variable writes the policy's operative clause; frequency and the solvency ratio set the rating basis; the margin and concentration variables price portfolio stability; the depreciation schedule prices time; the independence spectrum states today's honest correlation load; and the drift-to-loss study — the pilot — is the ask we make of the first carrier in the room. Every row is a command a stranger can run, which means the rate filing references measurements, not opinions. That is the entire commercial meaning of the week: the variables an actuary needs now exist as running code, and the two that don't yet are named experiments instead of hidden gaps.