feat(math): add POLISMATH_ENGINE_MODE flag + prev-tick warm-start scaffolding (PR-A)

[jucor]

Introduces the engine-mode switch that will select between Clojure-parity
warm-start (clojure-legacy) and the current cold-recompute behavior
(improved, default). This commit only adds the flag and the plumbing to
capture the previous tick's state; no behavior changes yet (commits B and D
consume the captured state).

• New polismath/utils/engine_mode.py: ENGINE_MODE_* constants +
  resolve_engine_mode(), reusing pca._resolve_impl_flag (pca.py:37-57) so
  resolution rules match the PCA-solver switch. Default 'improved'.
• Conversation.init gains cold-default fields group_clusterings={} and
  group_k_smoother={} (Clojure threads these on the conv,
  conversation.clj:433-484; NOT persisted, per conv_man.clj:52-74).
• recompute() captures prev_pca / prev_group_clusterings /
  prev_group_k_smoother from the deepcopied result BEFORE the compute steps
  overwrite them (mirrors Clojure fnks reading the incoming conv:
  conversation.clj:385, 457) and threads them into _compute_pca /
  _compute_clusters as optional params (unused in this commit).

TDD RED evidence (before implementing engine_mode.py):
tests/test_engine_mode.py collection error:
"ModuleNotFoundError: No module named 'polismath.utils.engine_mode'"

Cold-start invariance guard: a single-shot vw pipeline run is byte-identical
under both modes (first-tick warm-start state is empty, so the modes must
coincide). This guards commits B and D from drifting on the cold path.

Tests: 8 new (7 flag-resolution + 1 cold invariance). Full suite 414 passed,
17 skipped, 47 xfailed (was 406/17/47).

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

commit-id:d61d82ad

---

Stack:

• docs(delphi): overnight pre-cutover audit (s6) — CUTOVER_RUNBOOK + journal #2659
• feat(delphi): zid-sharding for the math poller — one shard = one process #2658
• ci: run postgres integration tests #2637
• feat(delphi): poller-equivalence harness (goal condition 2) — PASSES live on vw + pc-meta-02 #2657
• feat(math): moderation + restart replay parity — mod_update, restart-seam restore, Q13-Q18 #2656
• docs(delphi): R1-parity goal docs, journal (2026-07-18 → 07-24 s5), quirks + divergence ledger #2626
• feat(delphi): Q12 carve-out — pin the cold-tick PCA start to ones in both replay drivers #2655
• feat(math): Q11 — replicate vectorz distance cancellation in legacy kmeans #2654
• feat(math): small-N degenerate parity — run the real math on tiny matrices in clojure-legacy mode #2653
• feat(delphi): Q10 carve-out — pin large-conv cutoffs to certify the deterministic full-PCA path #2652
• feat(delphi): replay loader resolves private datasets under real_data/.local #2651
• feat(math): Clojure hash-map iteration order for the in-conv greedy tie-break (legacy) #2650
• feat(math): clojure-legacy blob emission + selection parity — Clojure-exact math_main at step 0 #2649
• feat(delphi): acceptance canonicalization — suppress cross-engine ordering artifacts in certify comparer #2648
• feat(delphi): certify.py battery runner + focuser + fingerprint ledger (Spec A, Phase 0) #2647
• feat(delphi): prodclone extractor — feature-filtered dataset export (Spec B) #2646
• feat(math): un-mirror priority_metric (#2571 resolved) + Q2 prev-tick group-votes #2645
• feat(math): participant-ban leak replication in clojure-legacy mode (Q1) #2644
• feat(delphi): Clojure timing probe (Spec C) #2643
• feat(math): degenerate-tick group-clusterings overwrite + <2-participants edge (legacy mode) #2642
• refactor(math): move impl-flag resolver to polismath/utils/env_flags.py #2641
• feat(delphi): Python math poller service (phase 1) — Clojure math-container replacement #2625
• fix(delphi): Clojure-parity math writers + committing write path in PostgresClient #2624
• feat(math): in-conv greedy floor + persistent carry (PR-E) #2623
• feat(math): Clojure-exact base-cluster lineage + warm start (PR-C) #2622
• feat(math): replay harness H-B — Clojure Mode A driver (dev/replay.clj) + cross-language comparer shim #2621
• feat(math): group-k-smoother in clojure-legacy engine mode (PR-D smoother) #2620
• feat(math): PCA warm start in clojure-legacy engine mode (PR-B) #2640
• feat(math): add POLISMATH_ENGINE_MODE flag + prev-tick warm-start scaffolding (PR-A) #2618 ⬅
• feat(delphi): replay harness H-A — schedule spec+slicer, Python driver, store, step comparer, CLI #2639
• fix(delphi): cold-start generator copies FULL revote history (no DISTINCT ON dedup) #2638
• fix(math): correct comment-extremity sign in pca_project_cmnts (D1b) #2615
• docs(delphi): add math-algorithm history & routing-regression reference #2613

---

⚠️ Part of a stack created by spr. Do not merge manually using the UI - doing so may have unexpected results.