{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TUV62RFK7SYS6ALO2QHQ33DT5Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"992c198759d2cdb82dee5d24dc87ba0e832370294df93decf36efee6f50ee5fd","cross_cats_sorted":["math.AG","math.CO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-22T15:19:03Z","title_canon_sha256":"fff10d2e56338800b240ec282cf08bb2b3d1affb50420afeeccc93e300437a93"},"schema_version":"1.0","source":{"id":"2606.23474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23474","created_at":"2026-06-23T03:14:20Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23474v1","created_at":"2026-06-23T03:14:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23474","created_at":"2026-06-23T03:14:20Z"},{"alias_kind":"pith_short_12","alias_value":"TUV62RFK7SYS","created_at":"2026-06-23T03:14:20Z"},{"alias_kind":"pith_short_16","alias_value":"TUV62RFK7SYS6ALO","created_at":"2026-06-23T03:14:20Z"},{"alias_kind":"pith_short_8","alias_value":"TUV62RFK","created_at":"2026-06-23T03:14:20Z"}],"graph_snapshots":[{"event_id":"sha256:e605677cdb33e9a8c1b472d79847f8783cb3c3c47a81bf1315cbc3b75e62a5a1","target":"graph","created_at":"2026-06-23T03:14:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.23474/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Continuing our previous work, this paper closely studies the relationship between the cluster algebra structures on the coordinate ring of Schubert cells and those on the coordinate ring of partial flag varieties. We give a finite-type classification for these cluster structures and point out several results that were left open in our previous work.","authors_text":"Fayadh Kadhem","cross_cats":["math.AG","math.CO","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-22T15:19:03Z","title":"On Two Approaches to Cluster Structures on Partial Flag Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23474","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c41b6d34d7899679ae2d6779ed7d133e265256b17ebdd877850948e54fa9899e","target":"record","created_at":"2026-06-23T03:14:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"992c198759d2cdb82dee5d24dc87ba0e832370294df93decf36efee6f50ee5fd","cross_cats_sorted":["math.AG","math.CO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-22T15:19:03Z","title_canon_sha256":"fff10d2e56338800b240ec282cf08bb2b3d1affb50420afeeccc93e300437a93"},"schema_version":"1.0","source":{"id":"2606.23474","kind":"arxiv","version":1}},"canonical_sha256":"9d2bed44aafcb12f016ed40f0dec73ec0a4ffbb7416e02702809c4f399d3f08e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d2bed44aafcb12f016ed40f0dec73ec0a4ffbb7416e02702809c4f399d3f08e","first_computed_at":"2026-06-23T03:14:20.884527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:20.884527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZI8UAT6/uT9jwDIp++8dc9V6jYleOhFfjKCflmzEa/PIfmOt55udnRKSGGIqBu56sSgPPyv9WGXexbz/vprUBA==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:20.884895Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c41b6d34d7899679ae2d6779ed7d133e265256b17ebdd877850948e54fa9899e","sha256:e605677cdb33e9a8c1b472d79847f8783cb3c3c47a81bf1315cbc3b75e62a5a1"],"state_sha256":"5ef273cf044f078920f2934384b080030190d6c186b628279ba25f3e37334a1b"}