{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ODUQCPFL2EK5OKWK7CAXMBXNE6","short_pith_number":"pith:ODUQCPFL","schema_version":"1.0","canonical_sha256":"70e9013cabd115d72acaf8817606ed27be6afd40dc6b3c4b616d250d2c69e771","source":{"kind":"arxiv","id":"2307.16657","version":4},"attestation_state":"computed","paper":{"title":"Cell decomposition and dual boundary complexes of character varieties","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.AG","authors_text":"Tao Su","submitted_at":"2023-07-31T13:39:03Z","abstract_excerpt":"The weak geometric P=W conjecture of L. Katzarkov, A. Noll, P. Pandit, and C. Simpson asserts that for any smooth Betti moduli space $\\mathcal{M}_B$ of complex dimension $d$ over a punctured Riemann surface, the dual boundary complex $\\mathbb{D}\\partial\\mathcal{M}_B$ is homotopy equivalent to a $(d-1)$-dimensional sphere. Here, we consider $\\mathcal{M}_B$ as a generic $GL_n(\\mathbb{C})$-character variety defined on a Riemann surface of genus $g$, with local monodromies specified by generic semisimple conjugacy classes at $k$ punctures.\n  In this article, we establish the weak geometric P=W con"},"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":"2307.16657","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2023-07-31T13:39:03Z","cross_cats_sorted":["math.AT","math.RT"],"title_canon_sha256":"ac7efd6c749c0ce6206febcb11c4fd79a49c33d6f3b1de1b15f338518c80501d","abstract_canon_sha256":"e566755bea743dc65419faa4e02f3e151076033cb45a838d6a7fb5b41d97d33e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:08:24.394422Z","signature_b64":"VnNzgzKCDGcF9POluNHepPV/7j4DeYepn7VvJGC1miZO36tBUfCDOdSjl54s9N2G7Rr/q9oHJOIHMAcfJcnKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70e9013cabd115d72acaf8817606ed27be6afd40dc6b3c4b616d250d2c69e771","last_reissued_at":"2026-06-04T01:08:24.393657Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:08:24.393657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cell decomposition and dual boundary complexes of character varieties","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.AG","authors_text":"Tao Su","submitted_at":"2023-07-31T13:39:03Z","abstract_excerpt":"The weak geometric P=W conjecture of L. Katzarkov, A. Noll, P. Pandit, and C. Simpson asserts that for any smooth Betti moduli space $\\mathcal{M}_B$ of complex dimension $d$ over a punctured Riemann surface, the dual boundary complex $\\mathbb{D}\\partial\\mathcal{M}_B$ is homotopy equivalent to a $(d-1)$-dimensional sphere. Here, we consider $\\mathcal{M}_B$ as a generic $GL_n(\\mathbb{C})$-character variety defined on a Riemann surface of genus $g$, with local monodromies specified by generic semisimple conjugacy classes at $k$ punctures.\n  In this article, we establish the weak geometric P=W con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.16657","kind":"arxiv","version":4},"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/2307.16657/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":"2307.16657","created_at":"2026-06-04T01:08:24.393789+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.16657v4","created_at":"2026-06-04T01:08:24.393789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.16657","created_at":"2026-06-04T01:08:24.393789+00:00"},{"alias_kind":"pith_short_12","alias_value":"ODUQCPFL2EK5","created_at":"2026-06-04T01:08:24.393789+00:00"},{"alias_kind":"pith_short_16","alias_value":"ODUQCPFL2EK5OKWK","created_at":"2026-06-04T01:08:24.393789+00:00"},{"alias_kind":"pith_short_8","alias_value":"ODUQCPFL","created_at":"2026-06-04T01:08:24.393789+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/ODUQCPFL2EK5OKWK7CAXMBXNE6","json":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6.json","graph_json":"https://pith.science/api/pith-number/ODUQCPFL2EK5OKWK7CAXMBXNE6/graph.json","events_json":"https://pith.science/api/pith-number/ODUQCPFL2EK5OKWK7CAXMBXNE6/events.json","paper":"https://pith.science/paper/ODUQCPFL"},"agent_actions":{"view_html":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6","download_json":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6.json","view_paper":"https://pith.science/paper/ODUQCPFL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.16657&json=true","fetch_graph":"https://pith.science/api/pith-number/ODUQCPFL2EK5OKWK7CAXMBXNE6/graph.json","fetch_events":"https://pith.science/api/pith-number/ODUQCPFL2EK5OKWK7CAXMBXNE6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6/action/storage_attestation","attest_author":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6/action/author_attestation","sign_citation":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6/action/citation_signature","submit_replication":"https://pith.science/pith/ODUQCPFL2EK5OKWK7CAXMBXNE6/action/replication_record"}},"created_at":"2026-06-04T01:08:24.393789+00:00","updated_at":"2026-06-04T01:08:24.393789+00:00"}