Why

Follow-up to #1072. The two live-fact counts in resolution::merge_direction still omit kb_id. The existing subject/object indexes lead with kb_id, so choosing a merge direction can scan index entries from other knowledge bases.

What changes

• Scope each count using a scalar subquery that reads the entity's kb_id by primary key. Preserve the function signature and two-query execution flow.
• Preserve live-fact filtering, counting a self-reference only once, and retaining the smaller UUID when degrees tie. The existing same-KB foreign keys make the added predicate equivalent for valid data.
• Add a regression to the existing store integration binary covering unequal and equal degrees, both argument orders, incoming/outgoing facts, invalidation, self-references, and multiple knowledge bases.

Only the two queries and their regression coverage change. No new index, migration, or dependency.

How it was checked

PostgreSQL 16.15 in a dedicated test container, with session-local copies of the migrated tables and indexes: 4 knowledge bases, 20,000 entities, and 240,000 facts. EXPLAIN (ANALYZE, BUFFERS) used the exact old and final SQL.

The final plan has (kb_id = $0 AND subject_id = $1) and (kb_id = $0 AND object_id = $1) index conditions. A forced generic prepared plan also uses both composite keys and 23 buffer accesses. These synthetic-fixture measurements do not imply a stable elapsed-time speedup or production throughput result.

Passed locally:

• cargo fmt --all --check
• cargo clippy --workspace --all-targets -- -D warnings
• cargo test --workspace --no-fail-fast: 1,427 passed, 0 failed, 6 ignored; includes all 298 store integration tests.
• cargo test --locked -p utopia-store --test store merge_direction_counts_live_facts_in_each_base: passed separately.
• pnpm install --frozen-lockfile and pnpm build in web.
• git diff --check.

Database tests used UTOPIA_DATABASE_URL pointing to the dedicated container and UTOPIA_TEST_REQUIRE_DB=1. On Windows, the final full run used an explicit 127.0.0.1 database host and NO_PROXY=127.0.0.1,localhost,::1. No business database was used.

The six explicitly ignored live-service and isolated delivery/crash tests were not forced to run. Optional live MySQL/Trino/WebDAV services and opt-in benchmarks were not configured.

Before review

• Every commit is signed off (git commit -s)
• cargo fmt --all --check, cargo clippy --workspace --all-targets -- -D warnings and cargo test --workspace pass
• SQL under crates/utopia-store/ was tested with UTOPIA_DATABASE_URL set (those tests skip without it)