[tpc] Add sepnodes_on_path flag to tskeleton to enforce path-constrained edge rejection

[felixleopoldo]

Summary

Add a sepnodes_on_path parameter to tskeleton (default FALSE) that, when set to TRUE, only rejects an edge x–y if all elements of the separating set lie on some indirect simple path between x and y in the current skeleton.

Motivation

Issue #161 added a diagnostic log that records whether each separating set is structurally plausible. The natural next step is to make this actionable: if sepnodes_on_path = TRUE, a candidate separating set that contains a node not on any indirect path between x and y is considered structurally implausible and the edge is not removed on its basis.

As a side effect, when sepnodes_on_path = TRUE all rows in the diagnostic log will have sepset_on_path = TRUE by construction — the log remains useful for recording pval and n_complete.

Proposed Behaviour

sepnodes_on_path	Behaviour
FALSE (default)	Standard PC skeleton: edge removed whenever pval >= alpha. No change to existing behaviour.
TRUE	Edge x–y is only removed if pval >= alpha and is_sepset_on_path(x, y, nbrs[S], G) returns TRUE.

Implementation

The change in tskeleton.R is localised to the pval >= alpha block:

if (pval >= alpha) {
    if (verbose) { ...log row... }  # always log when pval >= alpha
    if (!sepnodes_on_path || is_sepset_on_path(x, y, nbrs[S], G)) {
        G[x, y] <- G[y, x] <- FALSE
        sepset[[x]][[y]] <- nbrs[S]
        break
    }
}

The diagnostic log is written whenever pval >= alpha, independent of sepnodes_on_path, so it always reflects the raw CI test results.

Acceptance Criteria

• sepnodes_on_path = FALSE is the default — existing behaviour fully preserved
• When TRUE, edge removal additionally requires is_sepset_on_path to return TRUE
• Diagnostic log still records all pval >= alpha events regardless of the flag
• Flag threaded from tpc() → tskeleton()
• Flag exposed as a wildcard in script.R and rule.smk
• schema.json updated with sepnodes_on_path boolean field

Related

• [tpc] Save edge-rejection diagnostics to file in tskeleton (sepset path sanity check + test stats) #161 — introduced is_sepset_on_path, bfs_reachable, and the diagnostic edge log
• workflow/rules/structure_learning_algorithms/tpc/R/tskeleton.R — pval >= alpha block (~line 565)
• workflow/rules/structure_learning_algorithms/tpc/R/tpc.R — tskeleton(...) call (~line 371)
• workflow/rules/structure_learning_algorithms/tpc/script.R
• workflow/rules/structure_learning_algorithms/tpc/rule.smk
• workflow/rules/structure_learning_algorithms/tpc/schema.json