[cnicholas]

Closes #129

Summary

• What: formulate(response=...) with no time, factors or plan is accepted and charted in the order received.
• Why: a column of values charted in order is the most common individuals chart there is, and the first thing a newcomer tries. The front door refused it, and the factors=[] side door classified the whole column as one replicated cell (ADS 1, one-point Xbar).
• Scope: formulate() numbers the rows 1..N in an Observation column (the same numbers as obs_id) on the raw frame, before detection, so the study is exactly the one time='Observation' gives. The design report says so.

Contract / Invariants (must remain true)

• Default behavior unchanged: every formulation with time, factors or plan is byte-identical
• Residuals unaffected: no detector, residual or series-length change
• Row/index alignment preserved: obs_id still stamped before the sort; Observation equals it row for row
• Lane boundaries preserved: single stream, no lanes
• Output schema compatible: only the factors=[], no-time spelling changes (chart tables gain Observation)

Behavior Changes (explicit)

• New API: pb.formulate(df, response='weight') -> ADS 2, recommended X, X/mR with sigma from N-1 moving ranges
• New semantics:
  • factors=[] with no time is the same study (was ADS 1 / Xbar, X plotted against the response values)
  • Design report: Time: received order (no time column given)
  • An existing Observation column with no time raises, asking for time='Observation' or a rename

Key Design Decisions

• Time source: a copy of obs_id under a display name, not obs_id itself as time_var (that would need deduping at 21 obs_id sites). The ordinary detector classifies the 1 x N grid; no special case like the one e429205 removed.
• NaN policy: numbered on the raw frame, so an NA response is an empty cell (ODS 5, ADS 2), as with an explicit time column
• Run rules policy: unchanged
• Edge cases: input frame never mutated (copy before stamping); N = 1 behaves as the explicit-time path

Risks & Mitigations

• P0 risks: a silent difference from the explicit-time study
• Mitigations: tests assert frame-equality of dataset, X and mR charts, statistics, ODS/ADS and series length against time='Observation' on the T100 reference data

Tests

Added / Updated

• TestReceivedOrderFormulation (test_process_behavior.py) — equality with explicit time on PM SDS 1 (factors omitted and []), NA path on PM SDS 2, report line, order sensitivity, Xbar/S refusal + why_not, name collision, no mutation, N = 1
• test_response_only_is_one_stream_in_received_order (test_sds_detector.py) — replaces the refusal test

Regression Focus (must fail if broken)

• bare response == time='Observation' study on reference data
• user DataFrame untouched

Manual Verification

• pytest tests/ — 2553 passed, 7 skipped
• python validation/e2e_bishop_report.py — 1547 passed, 0 failed, 4 pending (14 runs); docs/reference/validation.md unchanged
• App fast tests against the local library (PYTHONPATH): pass; its factors=["Sequence"] paste path is unchanged
• Visual check: both plot x-axes read "Observation"

Notes

• Docs: README quickstart leads with the two-call example; formulation, series-length and XmR pages; quickstart notebook gains a first section; formulate/read_clipboard docstrings; CHANGELOG Added + Changed
• Follow-ups (not in this PR): app paste path could move to the bare form; README chart image; "Available analyses" lists R2-R6 rows on time-only studies (pre-existing)