feat(aura-registry): optimize — argmax over a SweepFamily by a named metric

Ships C12 orchestration axis 2 (optimize): pick the single best point of
a sweep family by a named RunMetrics field. The GREEN half of the
RED-first iteration whose executable-spec landed in the previous commit.

  optimize(&SweepFamily, metric) -> Result<SweepPoint, RegistryError>

returns the whole winning SweepPoint — its params coordinate AND its
RunReport — because the caller needs the params that won, not just the
metric. "Best" is fixed per metric (total_pips higher-is-better;
max_drawdown / exposure_sign_flips lower-is-better); ties resolve to the
earliest enumeration-order point (the family is in odometer order, and
only a strictly-better later point displaces the incumbent).

Single source of truth for "best", as #67 required ("reuse rank_by; do
not fork"): rank_by's per-metric direction is extracted into a private
`metric_cmp` helper that resolves the boundary metric *name* to a closed
`enum Metric` once and returns one comparator closure. Both rank_by
(sort by it) and optimize (argmax via `reduce`, strictly-better-displaces)
now call it, so the per-metric direction lives in exactly one match.
rank_by is behaviour-preserving — its existing tests pass unchanged.
The sweep executor is untouched.

No caller-supplied `direction`: one definition of best per metric,
consistent with the shipped rank_by invariant (a caller direction would
admit incoherent asks like the worst max_drawdown). An unknown metric is
UnknownMetric. A SweepFamily is non-empty by construction (EmptyAxis is
rejected upstream), so the argmax always yields a winner.

CLI surface: the "pick the best" view is already served by
`aura runs rank <metric>`, whose first line is the optimum over the
persisted registry; optimize() is the new *programmatic* axis-2 entry,
for World programs that hold a live SweepFamily and need the winning
params back in-process — which the registry/RunReport path cannot give.
No redundant CLI command added.

closes #67

crates/aura-registry/src/lib.rs

@@ -5,12 +5,13 @@
 //! serde_json; display is the caller's concern (the CLI prints via
 //! `RunReport::to_json`).
 
+use std::cmp::Ordering;
 use std::fmt;
 use std::fs;
 use std::io::Write;
 use std::path::{Path, PathBuf};
 
-use aura_engine::RunReport;
+use aura_engine::{RunReport, SweepFamily, SweepPoint};
 
 /// An append-only run registry over a JSONL file: one serde_json line per
 /// `RunReport`.
@@ -59,28 +60,75 @@ impl Registry {
     }
 }
 
+/// Which metric a best-first comparison keys on. Resolves a metric *name* (a
+/// string at the API boundary) to a closed kind once, so the per-comparison hot
+/// path branches on this rather than re-parsing the name.
+#[derive(Clone, Copy)]
+enum Metric {
+    TotalPips,
+    MaxDrawdown,
+    ExposureSignFlips,
+}
+
+/// The per-metric **best-first ordering** of two reports: `Less` means `a` is
+/// better than `b`. "Best" is fixed by each metric's meaning: `total_pips`
+/// higher-is-better; `max_drawdown` and `exposure_sign_flips` lower-is-better.
+/// `f64` keys use `partial_cmp` (total, since metrics are finite by
+/// construction). An unknown metric name is a `RegistryError::UnknownMetric`.
+///
+/// The single source of truth for "best" — both [`rank_by`] (sort by it) and
+/// [`optimize`] (argmax by it) call this, so the per-metric direction lives in
+/// exactly one place. The metric name is matched once here; the returned closure
+/// carries the resolved `Metric`, so per-comparison work is just the key compare.
+fn metric_cmp(
+    metric: &str,
+) -> Result<impl Fn(&RunReport, &RunReport) -> Ordering, RegistryError> {
+    let metric = match metric {
+        "total_pips" => Metric::TotalPips,
+        "max_drawdown" => Metric::MaxDrawdown,
+        "exposure_sign_flips" => Metric::ExposureSignFlips,
+        other => return Err(RegistryError::UnknownMetric(other.to_string())),
+    };
+    Ok(move |a: &RunReport, b: &RunReport| match metric {
+        // higher-is-better -> better when greater
+        Metric::TotalPips => b.metrics.total_pips.partial_cmp(&a.metrics.total_pips).unwrap(),
+        // lower-is-better -> better when smaller
+        Metric::MaxDrawdown => a.metrics.max_drawdown.partial_cmp(&b.metrics.max_drawdown).unwrap(),
+        Metric::ExposureSignFlips => {
+            a.metrics.exposure_sign_flips.cmp(&b.metrics.exposure_sign_flips)
+        }
+    })
+}
+
 /// Sort `reports` **best-first** by a named metric. "Best" is per-metric, fixed
-/// by each metric's meaning: `total_pips` higher-is-better (descending);
-/// `max_drawdown` and `exposure_sign_flips` lower-is-better (ascending). A stable
-/// sort keeps file (insertion) order among ties; `f64` keys use `partial_cmp`
-/// (total, since metrics are finite by construction). An unknown metric name is a
+/// by each metric's meaning (see [`metric_cmp`]). A stable sort keeps file
+/// (insertion) order among ties. An unknown metric name is a
 /// `RegistryError::UnknownMetric`.
 pub fn rank_by(mut reports: Vec<RunReport>, metric: &str) -> Result<Vec<RunReport>, RegistryError> {
-    match metric {
-        "total_pips" => {
-            reports.sort_by(|a, b| b.metrics.total_pips.partial_cmp(&a.metrics.total_pips).unwrap())
-        }
-        "max_drawdown" => {
-            reports.sort_by(|a, b| a.metrics.max_drawdown.partial_cmp(&b.metrics.max_drawdown).unwrap())
-        }
-        "exposure_sign_flips" => {
-            reports.sort_by(|a, b| a.metrics.exposure_sign_flips.cmp(&b.metrics.exposure_sign_flips))
-        }
-        other => return Err(RegistryError::UnknownMetric(other.to_string())),
-    }
+    let cmp = metric_cmp(metric)?;
+    reports.sort_by(|a, b| cmp(a, b));
     Ok(reports)
 }
 
+/// `rank_by`'s argmax: return the single best `SweepPoint` of a `SweepFamily`
+/// under a named metric, by the same fixed per-metric sense of best (see
+/// [`metric_cmp`]). The whole point is carried — its `params` coordinate AND its
+/// `RunReport` — because the caller needs the params that won. Ties on the metric
+/// resolve to the **earliest** enumeration-order point (the family is already in
+/// odometer order; only a strictly-better later point displaces the incumbent).
+/// An unknown metric is a `RegistryError::UnknownMetric`. A `SweepFamily` is
+/// non-empty by construction (a sweep over a zero-point grid is rejected upstream
+/// by `EmptyAxis`), so `reduce` always yields a winner.
+pub fn optimize(family: &SweepFamily, metric: &str) -> Result<SweepPoint, RegistryError> {
+    let cmp = metric_cmp(metric)?;
+    let winner = family
+        .points
+        .iter()
+        .reduce(|best, p| if cmp(&p.report, &best.report) == Ordering::Less { p } else { best })
+        .expect("a SweepFamily is non-empty by construction (EmptyAxis is rejected upstream)");
+    Ok(winner.clone())
+}
+
 /// What can go wrong reading or ranking the registry.
 #[derive(Debug)]
 pub enum RegistryError {