{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XDHE5TW55TUIVBH63OBYMBVIJ2","short_pith_number":"pith:XDHE5TW5","schema_version":"1.0","canonical_sha256":"b8ce4eceddece88a84fedb838606a84ebff52dccc4edbe0b165dbdd3b79bc3d6","source":{"kind":"arxiv","id":"2503.08020","version":3},"attestation_state":"computed","paper":{"title":"Weighted Cycles on Weaves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Daping Weng","submitted_at":"2025-03-11T04:01:21Z","abstract_excerpt":"We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a quantization for this algebra using the skew-symmetric intersection pairing in the simply-laced case. We define merodromies along weighted cycles as functions on the decorated flag moduli space of the weave. We relate weighted cycles with cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster varia"},"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":"2503.08020","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-03-11T04:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"5ed13eb849c25911c711445a5803e2cee507cfe119fb3098448ebfb36ea8031f","abstract_canon_sha256":"ac1a02b36240e7e32724fe6e9538ba6f357344befcd3f2bcfcd77a0d931da9c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:02.807722Z","signature_b64":"keijLj/31+GBHJs2vyFZKbm6CJDVllkf+/l7IdWa3v3JYwsxvMKEpkvqw5MF7VwRZGJP3OsytGSZEZmR3zrHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8ce4eceddece88a84fedb838606a84ebff52dccc4edbe0b165dbdd3b79bc3d6","last_reissued_at":"2026-05-25T02:01:02.806898Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:02.806898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted Cycles on Weaves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Daping Weng","submitted_at":"2025-03-11T04:01:21Z","abstract_excerpt":"We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a quantization for this algebra using the skew-symmetric intersection pairing in the simply-laced case. We define merodromies along weighted cycles as functions on the decorated flag moduli space of the weave. We relate weighted cycles with cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08020","kind":"arxiv","version":3},"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/2503.08020/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":"2503.08020","created_at":"2026-05-25T02:01:02.807014+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.08020v3","created_at":"2026-05-25T02:01:02.807014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.08020","created_at":"2026-05-25T02:01:02.807014+00:00"},{"alias_kind":"pith_short_12","alias_value":"XDHE5TW55TUI","created_at":"2026-05-25T02:01:02.807014+00:00"},{"alias_kind":"pith_short_16","alias_value":"XDHE5TW55TUIVBH6","created_at":"2026-05-25T02:01:02.807014+00:00"},{"alias_kind":"pith_short_8","alias_value":"XDHE5TW5","created_at":"2026-05-25T02:01:02.807014+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/XDHE5TW55TUIVBH63OBYMBVIJ2","json":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2.json","graph_json":"https://pith.science/api/pith-number/XDHE5TW55TUIVBH63OBYMBVIJ2/graph.json","events_json":"https://pith.science/api/pith-number/XDHE5TW55TUIVBH63OBYMBVIJ2/events.json","paper":"https://pith.science/paper/XDHE5TW5"},"agent_actions":{"view_html":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2","download_json":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2.json","view_paper":"https://pith.science/paper/XDHE5TW5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.08020&json=true","fetch_graph":"https://pith.science/api/pith-number/XDHE5TW55TUIVBH63OBYMBVIJ2/graph.json","fetch_events":"https://pith.science/api/pith-number/XDHE5TW55TUIVBH63OBYMBVIJ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2/action/storage_attestation","attest_author":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2/action/author_attestation","sign_citation":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2/action/citation_signature","submit_replication":"https://pith.science/pith/XDHE5TW55TUIVBH63OBYMBVIJ2/action/replication_record"}},"created_at":"2026-05-25T02:01:02.807014+00:00","updated_at":"2026-05-25T02:01:02.807014+00:00"}