{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SZ5W4RBXWJCNQVPFCCPHTAAGGB","short_pith_number":"pith:SZ5W4RBX","schema_version":"1.0","canonical_sha256":"967b6e4437b244d855e5109e798006306cf1d1e9124e942563b1e9a96da29395","source":{"kind":"arxiv","id":"2507.12454","version":1},"attestation_state":"computed","paper":{"title":"Cohomology rings of character varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Anton Mellit","submitted_at":"2025-07-16T17:54:45Z","abstract_excerpt":"In this talk I give an introduction and present some recent progress towards understanding the cohomology rings of character varieties of Riemann surfaces, such as the proof of the $P=W$ conjecture and the computation of the zero-dimensional COHA. In the case of punctured sphere I present an explicit description relating the cohomology rings to the Hilbert scheme of $\\mathbb{C}^2$, refining conjectures of Hausel-Letellier-Rodriguez-Villegas and Chuang-Diaconescu-Donagi-Pantev. I explain how the general case should be related to the symplectic geometry of the Hilbert scheme."},"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":"2507.12454","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-16T17:54:45Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d1c078520e379cd4ef61e0aa6e700e01f30ebe8a96737e1bd11c31a2e6fb6b47","abstract_canon_sha256":"fe8e83eafa0710762cc29f0d337267d79cc8674fe1c2225ed2a75ab3fe00f251"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:20.506842Z","signature_b64":"h7LYW/I9P1wGziVlH6G6b6IRKz1z0yeob08nQ1FEM97AOVgnkaLtaL6dO4FG2GbhWeCWZ4LSqDgDjjTELX/cCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"967b6e4437b244d855e5109e798006306cf1d1e9124e942563b1e9a96da29395","last_reissued_at":"2026-07-05T11:38:20.506271Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:20.506271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology rings of character varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Anton Mellit","submitted_at":"2025-07-16T17:54:45Z","abstract_excerpt":"In this talk I give an introduction and present some recent progress towards understanding the cohomology rings of character varieties of Riemann surfaces, such as the proof of the $P=W$ conjecture and the computation of the zero-dimensional COHA. In the case of punctured sphere I present an explicit description relating the cohomology rings to the Hilbert scheme of $\\mathbb{C}^2$, refining conjectures of Hausel-Letellier-Rodriguez-Villegas and Chuang-Diaconescu-Donagi-Pantev. I explain how the general case should be related to the symplectic geometry of the Hilbert scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12454","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/2507.12454/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":"2507.12454","created_at":"2026-07-05T11:38:20.506337+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12454v1","created_at":"2026-07-05T11:38:20.506337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12454","created_at":"2026-07-05T11:38:20.506337+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZ5W4RBXWJCN","created_at":"2026-07-05T11:38:20.506337+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZ5W4RBXWJCNQVPF","created_at":"2026-07-05T11:38:20.506337+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZ5W4RBX","created_at":"2026-07-05T11:38:20.506337+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/SZ5W4RBXWJCNQVPFCCPHTAAGGB","json":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB.json","graph_json":"https://pith.science/api/pith-number/SZ5W4RBXWJCNQVPFCCPHTAAGGB/graph.json","events_json":"https://pith.science/api/pith-number/SZ5W4RBXWJCNQVPFCCPHTAAGGB/events.json","paper":"https://pith.science/paper/SZ5W4RBX"},"agent_actions":{"view_html":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB","download_json":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB.json","view_paper":"https://pith.science/paper/SZ5W4RBX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12454&json=true","fetch_graph":"https://pith.science/api/pith-number/SZ5W4RBXWJCNQVPFCCPHTAAGGB/graph.json","fetch_events":"https://pith.science/api/pith-number/SZ5W4RBXWJCNQVPFCCPHTAAGGB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/action/storage_attestation","attest_author":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/action/author_attestation","sign_citation":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/action/citation_signature","submit_replication":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/action/replication_record"}},"created_at":"2026-07-05T11:38:20.506337+00:00","updated_at":"2026-07-05T11:38:20.506337+00:00"}