feat(math): group-k-smoother in clojure-legacy engine mode (PR-D smoother)

[jucor]

Ports Clojure's :group-k-smoother (conversation.clj:454-478), which damps K
(the number of opinion groups) so it only switches to a new best value after
:group-k-buffer (= 4, conversation.clj:154) consecutive ticks agree. Default
'improved' mode keeps the existing best_k logic bit-for-bit.

• New polismath/pca_kmeans_rep/group_k_smoother.py: pure
  group_k_smoother_update(prev_state, silhouettes_by_k, buffer=4) ->
  (new_state, smoothed_k). Implements the exact Clojure rule, INCLUDING:
  • HIGHER-k-wins tie-break (Clojure apply max-key ... (keys ...) returns
    the LAST maximal arg; array-map keys iterate ascending — so ties go to
    the higher k). conversation.py's improved best_k uses strict '>' (LOWER
    k wins) and is left untouched.
  • the Fix stale group-k-smoother crash on large conversations #2536 clamp (conversation.clj:469-478): a carried smoothed_k absent
    from the current clusterings falls back to this_k — smoothed_k is always
    a valid key, so downstream never KeyErrors.
  • first-tick acceptance of this_k (smoothed_k None), the cold-start
    invariant that keeps the two modes identical on tick 1.
    Only the top-level smoother is ported; Python has no subgroups
    (subgroup_clusters is hardcoded {}), so the parallel subgroup smoother
    (conversation.clj:520-560) is intentionally omitted.
• Conversation._compute_clusters: in legacy mode computes silhouettes_by_k from
  group_clusterings, runs the smoother against prev_group_k_smoother (threaded
  via recompute(), PR-A), picks group_clusters = group_clusterings[smoothed_k],
  and stores the new smoother state + per-k clusterings on the conv (NOT
  persisted — conv_man.clj:52-74). Improved mode: selected_k = best_k, and the
  new fields stay {} (inert).

Semantic judgment call (integrator, please verify): the degenerate early-return
paths in _compute_clusters (<2 in-conv ptpts / <2 base clusters) do NOT touch
the smoother state, so a degenerate tick preserves the prior in-memory smoother
memory rather than resetting it; the clamp protects the next real tick.

TDD RED evidence (before implementing group_k_smoother.py):
tests/test_group_k_smoother.py collection error:
"ModuleNotFoundError: No module named
'polismath.pca_kmeans_rep.group_k_smoother'"

Tests: 12 new — 10 pure-function (buffer counting, reset-on-change, brief
alternation, clamp present/absent, first-tick, higher-k tie-break) + 2 pipeline
integration (legacy no-flicker-then-switch-after-4 via silhouette stub over 9
chained update_votes ticks: smoothed_k == [2,2,2,2,2,2,2,3,3]; improved mode
leaves the smoother inert). Full suite 434 passed, 17 skipped, 47 xfailed.

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

commit-id:d4dbbfa9

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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

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