fix: the ML dial offered slots the machine had no cores to feed (4295)

Operator's 2026-09-23 log: embed_image taking 107-246s each, ~49 slots in
flight by Little's law, and the daily CCIP sweep dying on its 1800s soft
limit in a numpy matmul. The billiard/pool.py frame in that traceback is
the soft-timeout signal handler, not a pool fault.

Two causes, both mine.

1. `derived_ceiling` computed the ML lane from MEMORY ALONE. Meanwhile
   `embedder.py` carried `_INTRA_OP_THREADS = 4` beside a comment reading
   "keep N_replicas x this within the cores allotted to ML" — a constraint
   stated where nothing could act on it. A large-memory host offered ~49
   slots, the operator took what the dial offered, and the lane asked the
   box for ~200 torch threads.

   The number moves onto the lane as `threads_per_slot`, the embedder
   reads it rather than restating it, and the ceiling is now the smaller
   of the two bounds. They fail differently on purpose: too little memory
   is honestly zero, because the first task would OOM the container; too
   few cores is merely slow, so it floors at one rather than making the
   lane unreachable on a small box.

2. `scheduled_ccip_auto_apply` scored one image per matmul, over every
   image in the library, on every daily run — ~119k products each too
   small to pay for its own BLAS setup. `char_maxima` does the same
   arithmetic in blocks bounded by elements, so its memory stays flat as
   either axis grows.

   Batching changes no arithmetic: a character's score for an image is a
   max over that image's figures AND that character's prototypes, and max
   does not care how it is grouped. Pinned against the old loop written
   out longhand, and against itself with the blocking forced to split
   every row.

The UI copy said the ML ceiling came from memory; it says cores or
memory, whichever runs out first.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LVjrnpQjRgHdvq95rASoiR

backend/app/tasks/ml.py

@@ -488,7 +488,7 @@ def scheduled_ccip_auto_apply() -> str:
 
     from ..models import ImageRegion, MLSettings, Tag, TagKind
     from ..models.tag import image_tag
-    from ..services.ml.ccip import _FIGURE_KINDS
+    from ..services.ml.ccip import _FIGURE_KINDS, char_maxima
     from ..services.ml.training_data import _applied_or_rejected, _l2norm
 
     SessionLocal = _sync_session_factory()
@@ -553,11 +553,22 @@ def scheduled_ccip_auto_apply() -> str:
             by_img: dict[int, list] = {}
             for iid, vec in rows:
                 by_img.setdefault(iid, []).append(vec)
-            for iid, vecs in by_img.items():
-                q = _l2norm(np.asarray(vecs, dtype=np.float32), np)  # (nq, 768)
-                colmax = (q @ allref.T).max(axis=0)              # (total,)
-                charmax = np.maximum.reduceat(colmax, seg)       # (n_chars,)
-                for ci in np.where(charmax >= thr)[0]:
+            if not by_img:
+                continue
+
+            # One matmul per BLOCK of figures, not one per image. This loop ran
+            # over every image in the library on every daily run and did a
+            # matmul too small to pay for itself each time; it hit the 1800s
+            # soft limit on the operator's instance on 2026-09-23. Same
+            # arithmetic — see `char_maxima`.
+            iids = list(by_img)
+            charmax = char_maxima(
+                [_l2norm(np.asarray(by_img[i], dtype=np.float32), np) for i in iids],
+                allref, seg, np,
+            )                                                    # (n_img, n_chars)
+
+            for row, iid in enumerate(iids):
+                for ci in np.where(charmax[row] >= thr)[0]:
                     t = ref_tags[int(ci)]
                     if iid in skip[t]:
                         continue