diff --git a/CLAUDE.md b/CLAUDE.md
index 29241ea..e88354c 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -6,6 +6,8 @@
 
 An agent that profiles real binaries and services, isolates hot paths, proposes optimizations, and accepts a change **only** when (a) behavioral-equivalence gates pass and (b) the benchmark improvement is statistically significant on trusted infrastructure. Output: verified performance deltas translated into ROI reports nobody can dispute.
 
+Mental model: **the optimizer is a Bayesian detective; the trust layer is a frequentist court.** The detective (agent + playbook prior + policy ranking + ledger evidence + explain feedback) chooses what to try; the court (gates + calibrated bench + CI-lower-bound rule) decides what is true, with measured error rates and no priors on the accept path. Evidence flows back; authority never does. Priors steer where we look — they never touch what we conclude.
+
 Full engineering spec: `SPEC.md`. Read it before starting any phase.
 
 ## Non-negotiables (re-read every session)
diff --git a/README.md b/README.md
index 162e3b5..09b0ef6 100644
--- a/README.md
+++ b/README.md
@@ -15,6 +15,14 @@ deltas with the methodology attached** — a stopwatch on pinned hardware, a
 proof of equivalence, and an ROI figure whose confidence interval survives
 hostile review.
 
+The design in one breath: **the optimizer is a Bayesian detective; the
+trust layer is a frequentist court.** The detective holds priors, updates
+them from the ledger, and picks the next bet; the court runs calibrated
+procedures with measured error rates and no priors at all. Evidence flows
+back from court to detective — authority never does. Priors steer where we
+look; they never touch what we conclude.
+[The full argument](https://bdbrown4.github.io/peltier.io/thesis.html#the-detective-and-the-court).
+
 📖 **Full documentation: the [peltier.io book](https://bdbrown4.github.io/peltier.io/)**
 · Design spec: [SPEC.md](SPEC.md) · Charter: [CLAUDE.md](CLAUDE.md)
 
diff --git a/SPEC.md b/SPEC.md
index 4a03d7b..b7275bb 100644
--- a/SPEC.md
+++ b/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
 
 ```
diff --git a/docs/src/thesis.md b/docs/src/thesis.md
index 923d9b9..a323d32 100644
--- a/docs/src/thesis.md
+++ b/docs/src/thesis.md
@@ -46,3 +46,62 @@ cannot touch the thresholds. It can only propose a patch and ask the
 harness to judge it. The [architecture](./architecture.md) is designed so
 that even a compromised or adversarial proposer cannot manufacture a false
 win.
+
+## The detective and the court
+
+> The optimizer is a **Bayesian detective**. The trust layer is a
+> **frequentist court**.
+
+That sentence is the whole design. The two halves run on opposite
+statistical philosophies, deliberately:
+
+```
+     BAYESIAN DETECTIVE                        FREQUENTIST COURT
+     the optimizer: agent loop,                the trust layer: gates,
+     playbook prior, policy ranking            calibrated bench, verdict
+
+   ┌───────────────────────────┐            ┌────────────────────────────┐
+   │ generate hypotheses       │            │ prove equivalence first    │
+   │ prioritize the docket     │  proposes  │ calibrate the instrument   │
+   │ estimate likely payoff    │ ─────────▶ │ measure, interleaved A/B   │
+   └───────────────────────────┘            │ reject noise (CI lower     │
+               ▲                            │ bound vs. threshold)       │
+               │                            └─────────────┬──────────────┘
+               │                                          ▼
+               │        evidence flows back            verdict
+               └───── ledger row + explain ◀──────────────┘
+```
+
+The **detective** reasons like a Bayesian: it holds a prior over where wins
+live (the [playbook's](./playbook.md) cheapest-first ordering), updates it
+from accumulated evidence (the append-only ledger — failures included,
+because failures are the most informative updates), ranks its next bets
+(`crates/policy`, by the Wilson *lower* bound of each class's proven win
+rate — even the learning layer bets pessimistically), and reads the
+[post-verdict diagnosis](./explain.md) so the next hypothesis is sharper
+than the last. Its "estimate likely payoff" is a belief, and stays one:
+dollar figures are minted only by the court's
+[mechanical report](./roi.md), only from accepted rows.
+
+The **court** reasons like a frequentist, because its audience is a hostile
+reviewer who shares none of your priors. Its verdicts are decision
+procedures with *measured* long-run error rates: the A/A calibration bounds
+the false-positive rate and the injected-regression test bounds the power —
+per machine, empirically, before any real measurement is believed. The
+accept rule is a conservative bound, not a posterior; there is no prior
+anywhere on the accept path, so there is nothing to argue about except the
+evidence.
+
+The return edge is what makes the detective Bayesian at all — and note its
+direction. **Evidence flows back; authority never does.** The invariant
+underneath the whole system:
+
+> **Priors may steer where you look. They may never touch what you
+> conclude.**
+
+A wrong prior in the detective costs compute — a few wasted attempts, each
+honestly ledgered. A prior in the court could cost a false claim, the one
+unrecoverable failure for a project whose product is trust. The gates are
+what make speculative, prior-driven exploration *safe*: the detective can
+believe anything it likes, because nothing it believes survives into a
+number.