docs: name the statistical identity — Bayesian detective, frequentist court

The two halves of the system run on opposite statistical philosophies, on
purpose, and until now the docs never said so. The optimizer is a Bayesian
detective: playbook prior, ledger evidence, policy ranking, explain
feedback — belief-updating that decides what to try next. The trust layer
is a frequentist court: equivalence gates, per-machine calibrated error
rates (A/A false-positive bound, injected-regression power bound), and a
CI-lower-bound accept rule with no prior anywhere on the accept path —
because its audience is a hostile reviewer who shares none of your priors.

The load-bearing edge is the return path: evidence flows from court to
detective (ledger rows + explain); authority never flows the other way.
Invariant, now stated in four places: priors steer where we look; they
never touch what we conclude. A wrong prior costs compute — each wasted
attempt honestly ledgered. A prior in the verdict would cost a false
claim, the one unrecoverable failure for a project whose product is trust.

- thesis.md: full section with the two-box diagram incl. the return edge,
  in docket order (equivalence before measurement); notes that estimated
  payoff is a belief and dollar figures are minted only by the mechanical
  report from accepted rows, and that even the learning layer bets on
  Wilson LOWER bounds — the detective is a pessimist too.
- README: the one-breath version, linking the full argument.
- SPEC §1: dated note mapping each half to its sections.
- CLAUDE.md: the mental model, one paragraph under Mission.

Framing credit: emerged from a design conversation on whether peltier is
"Bayesian engineering" — it is exactly half of one.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

SPEC.md

@@ -9,6 +9,8 @@ Why this wins:
 - **The metric defends itself.** Same inputs, same outputs, fewer cycles, with confidence intervals. No correlation-causation problem is possible by construction.
 - **The ledger compounds.** Every accepted/rejected attempt with full evidence is future RL training data and, eventually, the substrate for learned optimization policies (see §13, research fork).
 
+> **Added 2026-07-20 — the statistical identity, named.** The optimizer is a **Bayesian detective**; the trust layer is a **frequentist court**. The detective (agent loop, playbook prior, §13 policy ranking, ledger evidence, §3.7 explain feedback) decides *what to try next* by belief-updating over accumulated evidence. The court (§3.1–§3.3: gates, calibrated bench, CI-lower-bound accept rule) decides *what is true* via procedures with empirically measured error rates — no prior appears anywhere on the accept path. Evidence flows from court to detective (ledger rows, explanations); authority never flows the other way. Invariant: **priors steer where we look; they never touch what we conclude.** A wrong prior costs compute; a prior in the verdict would cost trust.
+
 ## 2. System overview
 
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