{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ASBK5RYQW5ARTMYROZNNFXCALR","short_pith_number":"pith:ASBK5RYQ","schema_version":"1.0","canonical_sha256":"0482aec710b74119b311765ad2dc405c7068b82db95c1255ddc57e43c0841f0d","source":{"kind":"arxiv","id":"2508.18618","version":1},"attestation_state":"computed","paper":{"title":"Combinatorial Approaches to Exceptional Sequences for Weighted Projective Lines of Type $(p,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Jianmin Chen, Yiting Zheng","submitted_at":"2025-08-26T02:45:40Z","abstract_excerpt":"We provide a combinatorial description of morphisms in the coherent sheaf category ${\\rm coh}\\mbox{-}\\mathbb{X}(p,q)$ over weighted projective line of type $(p,q)$ via a marked annulus. This leads to a geometric realization of exceptional sequences in ${\\rm coh}\\mbox{-}\\mathbb{X}(p,q)$. As applications, we present a classification of complete exceptional sequences, an effective method for enlarging exceptional sequences, and a new proof of the transitivity of the braid group action on complete exceptional sequences. Besides, we offer a combinatorial description of tilting bundles via lattice p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.18618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-26T02:45:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7f66739e7454c11679caf7bfcd68dd6d6f3cb8b3a595f6559f809ec1434c31f1","abstract_canon_sha256":"d70c292ec88831d6d8c67f57d67a4db06e3bdda80242a736df0f0c242ba4dbbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:27.855847Z","signature_b64":"q8hcPm6xNOwaKvEkX6fmwygbf/IkeMGlrfO3ZxBuHXmC+ac420CC2+NscDX0RBcUl8acOf87kZgT8Hn77yh8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0482aec710b74119b311765ad2dc405c7068b82db95c1255ddc57e43c0841f0d","last_reissued_at":"2026-07-05T11:59:27.855313Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:27.855313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial Approaches to Exceptional Sequences for Weighted Projective Lines of Type $(p,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Jianmin Chen, Yiting Zheng","submitted_at":"2025-08-26T02:45:40Z","abstract_excerpt":"We provide a combinatorial description of morphisms in the coherent sheaf category ${\\rm coh}\\mbox{-}\\mathbb{X}(p,q)$ over weighted projective line of type $(p,q)$ via a marked annulus. This leads to a geometric realization of exceptional sequences in ${\\rm coh}\\mbox{-}\\mathbb{X}(p,q)$. As applications, we present a classification of complete exceptional sequences, an effective method for enlarging exceptional sequences, and a new proof of the transitivity of the braid group action on complete exceptional sequences. Besides, we offer a combinatorial description of tilting bundles via lattice p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18618","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.18618/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.18618","created_at":"2026-07-05T11:59:27.855388+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.18618v1","created_at":"2026-07-05T11:59:27.855388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18618","created_at":"2026-07-05T11:59:27.855388+00:00"},{"alias_kind":"pith_short_12","alias_value":"ASBK5RYQW5AR","created_at":"2026-07-05T11:59:27.855388+00:00"},{"alias_kind":"pith_short_16","alias_value":"ASBK5RYQW5ARTMYR","created_at":"2026-07-05T11:59:27.855388+00:00"},{"alias_kind":"pith_short_8","alias_value":"ASBK5RYQ","created_at":"2026-07-05T11:59:27.855388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR","json":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR.json","graph_json":"https://pith.science/api/pith-number/ASBK5RYQW5ARTMYROZNNFXCALR/graph.json","events_json":"https://pith.science/api/pith-number/ASBK5RYQW5ARTMYROZNNFXCALR/events.json","paper":"https://pith.science/paper/ASBK5RYQ"},"agent_actions":{"view_html":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR","download_json":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR.json","view_paper":"https://pith.science/paper/ASBK5RYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.18618&json=true","fetch_graph":"https://pith.science/api/pith-number/ASBK5RYQW5ARTMYROZNNFXCALR/graph.json","fetch_events":"https://pith.science/api/pith-number/ASBK5RYQW5ARTMYROZNNFXCALR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR/action/storage_attestation","attest_author":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR/action/author_attestation","sign_citation":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR/action/citation_signature","submit_replication":"https://pith.science/pith/ASBK5RYQW5ARTMYROZNNFXCALR/action/replication_record"}},"created_at":"2026-07-05T11:59:27.855388+00:00","updated_at":"2026-07-05T11:59:27.855388+00:00"}