caugi

• Add first-class "CPDAG" graph class support across the constructor (caugi()), coercion (as_caugi()), and class mutation (mutate_caugi()). Construction validates the full CPDAG invariant (chordal chain components, an acyclic component DAG, Meek closure, and strong arrow protection). generate_graph(class = "CPDAG") now returns a graph with @graph_class = "CPDAG" instead of "MPDAG", the precise label for the essential graph of a Markov equivalence class. Predicates defined on PDAGs and MPDAGs (is_pdag(), is_mpdag(), etc.) continue to accept CPDAGs unchanged.
• Meek-closed PDAGs are now reported with @graph_class = "MPDAG" instead of "PDAG". This affects the result of meek_closure() and generate_graph(class = "CPDAG"). Predicates and verbs defined on PDAGs (is_pdag(), mutate_caugi(), etc.) continue to accept MPDAGs unchanged.

Improvements

• aid() is now implemented natively in caugi's Rust backend, removing the external gadjid dependency (and its pinned git revision and vendored sources). Results are unchanged. The AID implementation (src/rust/src/graph/aid.rs) is a derivative of gadjid and is licensed MPL-2.0; the rest of the crate remains MIT. aid() now takes inputs of class "DAG" or "CPDAG" (previously "DAG" or "PDAG").
• Licensing of bundled code is now declared for CRAN: a top-level LICENSE.note documents the MPL-2.0 component (the AID files derived from gadjid) and the licenses of the vendored Rust crates, and their copyright holders are recorded via cph/ctb roles in Authors@R.
• adjustment_set(type = "backdoor") now returns an inclusion-minimal backdoor adjustment set, computed in linear time as a minimal d-separator in the proper backdoor graph, rather than the full set of parents of the exposure.
• The performance vignette is now a true vignette (rather than a pkgdown-only article) and is rebuilt manually from a cross-language harness under tools/benchmark/. The harness compares caugi to igraph, bnlearn, dagitty, ggm, pcalg, pgmpy, and Tetrad on a n ∈ {100, 1000, 10000} grid. The d-separation benchmark now uses a minimal d-separator computed via minimal_separator() (previously used a backdoor adjustment set, which is not in general a d-separating set).

Bug Fixes

• Fix hd() returning results that depended on the order in which nodes were declared. The Hamming distance now aligns nodes by name before comparing, so logically identical graphs always give the same distance (#323).
• Fix dag_from_pdag() failing with ` from, edge, to must be equal length. ` when a sink had multiple undirected neighbors (#298).
• Fixed a bug causing a partially undirected (--o) edges to be plotted as undirected edges.
• Fix adjustment_set(type = "backdoor") returning an invalid (often empty) set when a parent of the exposure lies on a backdoor path but is not an ancestor of the outcome (#308). The result is now always a valid backdoor adjustment set.
• Fixed is_mag() returning incorrect results for some ancestral graphs (#309). Adjacency was tested by binary-searching the concatenation of separately sorted neighbor buckets, which is not globally sorted, so some adjacent pairs were missed.
• Stripped non-build files (tests/, examples/, trybuild fixtures) from the vendored Rust dependencies so no vendored path exceeds 100 characters. This silences pak's "very long paths" warning and avoids installation failures on Windows without long-path support (#319).
• Fixed to_dot() and to_mermaid() (and write_dot()/write_mermaid()) silently converting partial --o and o-o edges into plain directed edges, dropping the circle endpoints (#307).

Deprecations

• The first argument of dag_from_pdag() is now named cg, matching the convention used by the rest of the package. The previous name PDAG continues to work as an alias but emits a deprecation warning.