feat: implement AGE relationship predicates and set operations

[savasp-agent]

Summary

• lower variable-path relationship predicates to indexed server-side filtering and anchored existence predicates to grouped counts
• recursively run every AGE lowering pass inside nested Union/Concat branches, preserve parameter namespaces, and normalize projection aliases before rendering
• keep ShortestPath undeclared for AGE 1.7, retain its provider-neutral TCK contract, and defer AGE: implement the ShortestPath capability #355 until AGE 1.8 releases the native shortest-path capability

Validation

• ./scripts/run-tests.sh --configuration Debug --lane fast --disable-diff-engine (2,383 tests)
• GRAPHMODEL_COMPLIANCE_STRICT=1 ./scripts/run-tests.sh --configuration Debug --project Graph.Age.Tests --no-build --disable-diff-engine (693 tests: 691 passed, 2 expected ShortestPath / OrderByEntity skips)
• focused AGE dialect, shortest-path rejection, relationship-predicate, and set-operation coverage (15 tests)
• pre-push Release warnings-as-errors build and format verification

Checklist

• Related issues use repeated closing keywords.
• Capability and compliance documentation is updated.
• AGE: implement the ShortestPath capability #355 remains open for the AGE 1.8 native implementation.
• Rebased onto feat: finalize identity-free graph model #513's squash merge on main; auto-merge intentionally disabled.

Closes #356, closes #357.

[savasp-agent]

Codex review report

I rebased PR #512 onto current main and resolved the merge conflict. This comment is the report for that branch-maintenance pass plus the review findings I had already surfaced; it is not a claim that the broader feature review is fully closed.

Fixes applied

• Resolved the only merge conflict, in src/Graph.Age/COMPLIANCE.md, by keeping the PR's updated AGE compliance text: ComplianceInventory.MinimumExecuted(declared) is 464 with 1 expected OrderByEntity skip.
• Amended the rebased commit through gh-app so both author and committer are savasp-agent[bot], avoiding the last-push/self-approval trap.
• Force-with-lease pushed the PR branch from 470e3fdf to 4c3ee36e, based on main at 22c3411.

Review findings

ID	Status	Finding
R-001	Fixed	PR #512 was merge-conflicted because main still documented the older AGE capability inventory while this PR declares support for ShortestPath, RelationshipPredicates, and SetOperations. The compliance text now matches the branch's declared capability set.
R-002	Fixed	The rebase initially produced a bot-authored but human-committed rewritten commit. I amended it with gh-app git commit --amend --no-edit; the new head is bot-authored and bot-committed.
R-003	Not fixed here	The PR still combines #355, #356, and #357 even though the issue-tracker comments asked for those AGE capabilities to land as standalone serial PRs. I did not split scope in this merge-conflict pass.
R-004	Not fixed here	AgeShortestPathPass still lowers shortest path by enumerating all variable-length paths and only then applying collect(p)/min(length(p)) selection (src/Graph.Age/Querying/Cypher/Lowering/AgeShortestPathPass.cs:94, :106, :107, :129). In a local AGE probe, a 5-node complete directed graph timed out under a 3s statement timeout despite having a direct shortest edge. This likely needs a real BFS/native server-side shortest-path strategy rather than collect-all filtering.
R-005	Not fixed here	AgeCorrelatedProjectionPass treats EntityProjectionClause as a terminal (src/Graph.Age/Querying/Cypher/Lowering/AgeCorrelatedProjectionPass.cs:415), but only the ReturnClause terminal path drains and emits the extracted count stages (:379, :395). The entity-projection path falls through the default branch (:402), so entity-returning queries that order by relationship counts can reference generated count aliases that were never emitted.

Validation

• Local fast lane: ./scripts/run-tests.sh --configuration Debug --lane fast --disable-diff-engine passed, 8 projects / 2,394 tests.
• Local AGE lane: ./scripts/run-tests.sh --configuration Debug --lane age --no-build --disable-diff-engine passed, 1 project / 700 tests, with the expected OrderByEntity capability skip.
• Pre-push hook passed the Release build and format gate.
• Hosted checks are green at 4c3ee36e, including build/test, CodeQL, package validation on macOS/Ubuntu/Windows, docs, dependency review, and repository automation.

GitHub now reports the PR as BLOCKED rather than DIRTY; the merge conflict is cleared and the remaining block is review.

[savasp-agent]

Takeover review closure report

This supersedes the earlier report. I reviewed the complete final diff, resolved the original #513 stack conflict, fixed every valid PR-local finding, removed the interim shortest-path implementation at @savasp's direction, and found no remaining actionable review threads or code findings.

AGE documentation decision

The supported release remains Apache AGE 1.7.0, whose published manual does not expose a shortest-path primitive. Apache AGE master contains internal age_shortest_path / age_all_shortest_paths implementations, and their SQL installation is part of the unreleased 1.7.0--1.8.0 upgrade.

The PostgreSQL BFS fallback has therefore been removed. AGE 1.7 continues to omit GraphCapability.ShortestPath; #355 remains open and now explicitly waits for the AGE 1.8 release so support can lower to the native capability. The provider-neutral TCK method ShortestPaths_PinSelectionEndpointDirectionNoPathAndSameNodeSemantics remains unchanged and covers one/all shortest paths, incoming direction, no-path behavior, and same-node exclusion. AGE skips that contract with the standard missing-capability reason until native support lands.

Finding ledger

ID	Origin	Disposition	Resolution
R-001	Rebase / merge conflict	Fixed	Resolved the #513 conflict, then rebased #512 onto #513's squash merge after #513 landed.
R-002	Repository identity policy	Fixed	The final commit is authored and committed by savasp-agent[bot].
R-003	Review: combined #355/#356/#357 scope	Superseded by maintainer decision	#512 now ships #356 and #357 only; #355 remains open for AGE 1.8.
R-004	Review: exhaustive shortest-path lowering	Removed / deferred	Removed both the original exhaustive Cypher lowering and the interim PostgreSQL BFS strategy; AGE now fails closed through its undeclared capability.
R-005	Review: entity ordering by correlated relationship count	Fixed	Emit count stages before the paging order and again at the entity projection boundary so the sort key survives hydration. Added a translation regression.
R-006	#513 stack compatibility	Fixed	Migrated new AGE tests from removed endpoint constructors and universal Id to ConnectAsync and domain TestKey.
R-007	Runtime verification: absent compatible subtype table	Removed with shortest-path implementation	The catalog-intersection code and its PostgreSQL BFS consumer were removed.
R-008	Runtime verification: hydration ordering scope	Removed with shortest-path implementation	The provider-local shortest-path hydration path was removed.
R-009	Documentation audit	Fixed	Compliance and provider docs now declare shortest path missing on AGE 1.7, retain the TCK contract, and defer implementation to AGE 1.8 / #355.

Validation

• Strict AGE certification: 693 total, 691 passed, 2 expected ShortestPath / OrderByEntity capability skips.
• Fast lane: 2,383 tests passed across 8 projects.
• Focused AGE dialect/capability/regression set: 15 passed.
• Pre-push gate: Release warnings-as-errors build and format verification passed.
• Hosted CI: all required checks passed, including consolidated build/test, package validation on all three platforms, repository automation, documentation, dependency review, and CodeQL.
• Final diff check: clean; no shortest-path implementation remains; no unresolved findings.

#513 merged while this follow-up was in progress, so the final head is rebased onto its squash commit on main. Auto-merge remains disabled as requested. Head: c052325f5c04ee6fe804d036046375ff16dcaa6a.