feat(probe): P-COMMUNITY-BASIN-AGREE (S1) — empirical community≡basin agreement via jc

[AdaWorldAPI]

What

The S1 gate the #719 D-TRI-1 classid-half mint explicitly hands off ("the other session runs S1; the council mints"). An empirical probe that measures whether the operator's identity ruling holds — is_a category ≡ Leiden community ≡ episodic-witness basin (plan §3b.1).

The layer boundary (operator, this session)

"JC is a scientific crate. Yours are empirical."

jc is the certified scientific surface (reliability::{pearson, spearman, cronbach_alpha, icc}, weyl, jirak, …) — this probe consumes it, never extends it. The empirical construction (two partitions → pairwise co-membership vectors) is the probe's; the statistic is jc's. A partition metric jc lacks (Rand/ARI/NMI) is an observation reported to the scientific track, not a bolt-on from the empirical side. So the probe lives on the empirical side (lance-graph/examples/) and dev-depends jc (lib untouched).

The probe

crates/lance-graph/examples/p_community_basin_agree.rs:

• Community partition — TripletGraph::communities() (Louvain + Leiden refinement) over the whole relational field.
• Basin partition — connected components under only the is_a/part_of edges (the plan's basin rail), via a deterministic union-find.
• Agreement — φ = jc::reliability::pearson of the two partitions' pairwise co-membership vectors (φ=1 iff identical up to relabeling); names the bridges (a community that crosses a basin = revision candidate).

Result (synthetic mechanism)

Scenario	φ (jc::pearson)	reading
aligned	1.0000	IDENTITY — community ≡ basin, no bridges
one cross-basin entity (robot is_a pet, structurally in the tree cluster)	0.5500	DISTINCT — robot named as the single bridge

Mechanism proven; the S1 verdict needs a real is_a-annotated corpus (like G0's KILL/PASS). That verdict decides the mint: identity (φ→1) ⇒ community-id collapses into the is_a rail, no tenant minted; distinct (φ<1) ⇒ community-id earns the batched D-TRI-1 mint.

Verification

• cargo run -p lance-graph --example p_community_basin_agree runs clean (output above).
• cargo fmt clean; cargo clippy clean on the example.
• jc added as a dev-dependency only (light: lance-graph-contract + optional sigker); the lance-graph lib and its 945 tests are untouched. Cargo.lock updated for the dev-dep.

Board

EPIPHANIES E-EMPIRICAL-VS-SCIENTIFIC-JC-1 (the boundary + the S1 result); STATUS_BOARD graphrag §6 S1 row; stale (this PR) labels on the merged D-GR rows corrected to #716.

Not in this PR

• The S1 verdict (needs a real is_a corpus) — and therefore the community-id mint decision — stay open, as designed.

🤖 Generated with Claude Code

https://claude.ai/code/session_016b33swuXE23hKtqxsHu9p1

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