feat(heads): production per-concept heads — train + score backend (#114 A)

The eval (#1130) proved the frozen-embedding + trained-head spine; this lands
its production form (the first of three slices that make heads the suggestion
source, replacing Camie + centroid).

- tag_head: one logistic-regression head per general/character concept with
  enough labelled positives. Weights (pgvector), honest CV-derived suggest
  threshold + earned-auto-apply point, and per-concept quality metrics.
- head_training_run: persisted batch lifecycle (mirrors tag_eval_run) so the
  admin card shows live + historical status across navigation.
- services/ml/heads.py: TRAIN (sync, ml worker, reuses tag_eval's proven data
  loaders + metric math so production heads match measured eval numbers) and
  SCORE (async, API worker — numpy via pgvector, no scikit-learn): score one
  image's embedding against all heads → the rail's suggestions, cached on
  (count, max trained_at) so a retrain invalidates without per-request loads.
- tasks.ml.train_heads (ml queue, commits per head so a kill leaves progress)
  + recover_stalled_head_training_runs sweep + retention(20) + 5-min beat
  (rule 89).
- api/heads.py: POST /api/heads/train (one run at a time, 409 guard) + GET
  /api/heads (count, graduated, last-trained, running, per-concept table,
  recent runs).
- ml_settings: head_min_positives + head_auto_apply_precision, tunable via
  /api/ml/settings.

Scoring isn't wired into the rail yet (slice C) and the admin UI is slice B —
this slice makes training + scoring exist and CI-verifiable. 'precision' column
stored as precision_cv (SQL reserved word). Migration 0058.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Ttrj5P7upUTueSfoJcxEqa

backend/app/models/head_training_run.py

@@ -0,0 +1,44 @@
+"""HeadTrainingRun — persisted lifecycle of a head-training batch (#114).
+
+Mirrors TagEvalRun so the run SURVIVES navigation and the admin card can show
+live + historical status instead of holding it in transient frontend state.
+Training is idempotent (it upserts tag_head rows), so a SIGKILL'd run is harmless
+— a maintenance recovery sweep flips a stalled `running` row to `error`, and the
+next run re-trains. State machine: running → ready / error.
+"""
+
+from datetime import datetime
+from typing import Any
+
+from sqlalchemy import DateTime, Integer, String, Text, func
+from sqlalchemy.dialects.postgresql import JSONB
+from sqlalchemy.orm import Mapped, mapped_column
+
+from .base import Base
+
+
+class HeadTrainingRun(Base):
+    __tablename__ = "head_training_run"
+
+    id: Mapped[int] = mapped_column(Integer, primary_key=True)
+    # Training parameters: {min_positives, neg_ratio, precision_target, ...}.
+    params: Mapped[dict[str, Any]] = mapped_column(JSONB, nullable=False)
+    status: Mapped[str] = mapped_column(
+        String(16), nullable=False, default="running", index=True
+    )
+    # running | ready | error
+    started_at: Mapped[datetime] = mapped_column(
+        DateTime(timezone=True), nullable=False, server_default=func.now()
+    )
+    finished_at: Mapped[datetime | None] = mapped_column(
+        DateTime(timezone=True), nullable=True
+    )
+    # How many concepts got a (re)trained head vs were skipped (too few labels).
+    n_trained: Mapped[int | None] = mapped_column(Integer, nullable=True)
+    n_skipped: Mapped[int | None] = mapped_column(Integer, nullable=True)
+    error: Mapped[str | None] = mapped_column(Text, nullable=True)
+    # Last time the task made progress — the recovery sweep tells a live run from
+    # a SIGKILL'd one by this (mirrors TagEvalRun).
+    last_progress_at: Mapped[datetime | None] = mapped_column(
+        DateTime(timezone=True), nullable=True
+    )