[cnicholas]

Part of #144 (PR 1 of 4). Stacked on #148: the base is fix/xbar-s-table-subgroup-n, so the diff shows only this change; it retargets to main when #148 merges.

Summary

• What: the code the global and stratified Xbar/S builders had in duplicate now lives in five helpers (_aggregate_subgroups, _fit_xbar_group, _apply_xbar_limits, _apply_s_limits, _subgroup_label_column); the lane-divider label rule is its own function (_lane_labels); calculate_limits_vectorized takes a sigma-hat per row.
• Why: phased Xbar/S (Phased (staged) limits for Xbar and S charts #144) is N per-stage charts on one axis, and each stage needs exactly the per-stratum estimator. Extracting it first means the feature PR adds a loop over phases, not new arithmetic, and the per-row sigma is the hook for a vectorised path if the app ever needs one.
• Scope: refactor only. No chart, statistic, metadata or error message changes.

Contract / invariants

• Defaults unchanged — validation/xbar_s_sweep.py (new) fingerprints 504 Xbar/S requests on T100 PM SDS 1 and 3 (chart x companion x seven by= shapes x value x n_mode: 420 charts and 84 refusals). Identical output on 7f32215 and this branch: 0 differing lines.
• Residuals unaffected
• Row/index alignment preserved — the fingerprints cover row order; the gate's drawn-limit comparisons pass
• Output schema compatible — golden masters untouched and passing, not regenerated
• Pinned error strings unchanged

Behaviour changes

None.

Methodology

• No methodology change — implementation only

Tests

• tests/test_xbar_s_helpers.py (14 tests): _lane_labels keeps the astype date rendering and the _ join; a per-row sigma matches the formula row by row, a scalar equals a constant Series exactly, and a Series sigma supplies the result index; _fit_xbar_group returns None without replication, charts n = 1 and drops n = 0, decides constant-n separately for Xbar and S, and under n_mode='average' overwrites N while n keeps the actual sizes; _apply_s_limits is B3/B4 per row around S-bar; _aggregate_subgroups with and without the cached cell mean and with an R2 limits column; the four subgroup-label rules
• pytest tests/ — 2567 passed, 7 skipped
• ruff check .
• mypy processbehavior — 14 errors, all pre-existing and outside the touched code (X/mR and Histogram sites)
• Golden masters: untouched, 22 pass
• python validation/e2e_bishop_report.py — 1547 passed, 0 failed, 4 pending; docs/reference/validation.md unchanged

Notes

• Committed with the ruff-format hook skipped: analysis.py and spc_constants.py have never been ruff-formatted, and the hook would have rewritten about twenty unrelated blocks. A formatting-only commit can follow separately if wanted.
• Next: PR 2 adds phased=True for Xbar and S on top of these helpers.