A covariate check that cannot report is worse than no covariate check

[logannye]

The defect

check_covariates decided path-opening as

separated_alone = d_separated(back_door, target, outcome)      # computed ONCE
opens = separated_alone and not d_separated(back_door, target, outcome, (name,))

So whenever the target and outcome were already d-connected in the back-door graph — what an unmeasured common cause produces, and therefore the normal case in any real system — opens was False for every covariate and the report read:

Admissible: ['A', 'B', 'C', 'W']

with both finding sections empty. Three defects at once, and the second is what makes this more than cosmetic:

1. Nothing distinguished "tested and clean" from "the test could not fire".
2. A collider the module flags correctly on a clean graph goes unflagged the moment a confounder exists anywhere else. The finding is not merely unstated — it is lost.
3. W is unobserved. Covariates were validated against variable_set, never observed_set, so the report advised conditioning on a latent variable.

The module's own docstring warns about exactly this shape for the name-clash case — "a check that runs, passes, and cannot report — every covariate would come back admissible for the wrong reason" — and the guard was installed there and not here.

The repair is not a warning label

Path opening asks whether conditioning breaks a separation. When nothing was separated there is nothing to break — and the question that does have an answer is whether the covariate closes the open path. That is the entire purpose of an adjustment set, and a check that only ever asks "does this open a path?" cannot express it. So the previously-vacuous branch now answers rather than merely refusing.

field	meaning
back_door_open	graph-level finding, reported once, leading the summary
blocks_path	names the covariates that close the open path
undecided	no path-level verdict was reachable; never admissible
observed	unobserved is a structural refusal, not an undecided one, so a hard fact is not filed under an "unanswerable" heading

  'knockdown' and 'IFNG' are d-connected in the back-door graph given nothing:
  there is an open back-door path, so the effect is confounded before any covariate is chosen.
    Closes it: ['donor']
  For the rest, no path-level verdict is reachable -- reported as undecided, not as clean.

⚠️ Found while mutation-testing, unrelated to the above

The O(n²) gate on mechanism_dependencies had stopped gating anything. It timed construction, on the stated grounds that "every MechanismGraph validates acyclicity at construction" — true when written, and PR #9 made it false by lifting C1 to a query-time condition. Restoring the pairwise implementation left construction at 0.0038s/0.0154s, unchanged, while mechanism_dependencies itself went 0.0006s → 0.2764s at n=1500.

Now timed on the routine (mutation-tested: fires, 28s vs 0.08s), with a companion test that counts the calls to pin the premise — a timing proxy there would be the same mistake one layer down. It also takes min-of-5 after a warm-up: a single 4 ms sample was dominated by whatever ran before it, and it fired when this branch merely added a test file.

Verification

Five mutations on the covariate repair, all dead, restored and verified by content:

mutation	result
path_test_applicable := True (the bug reinstated)	red
admissible := True in the open-back-door branch	red
drop the observed-variable check	red
back_door_open := False	4 red
closes := False	red

README gains the third finding with its real output, gated by a new test_readme_smoke case including Closes it: ['donor']. The 2,596-verdict conformance sweep is unchanged and still green.

340 passed, 1 xfailed. ruff check . clean.

🤖 Generated with Claude Code