{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SZ5W4RBXWJCNQVPFCCPHTAAGGB","short_pith_number":"pith:SZ5W4RBX","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"},"canonical_sha256":"967b6e4437b244d855e5109e798006306cf1d1e9124e942563b1e9a96da29395","source":{"kind":"arxiv","id":"2507.12454","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12454","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12454v1","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12454","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"pith_short_12","alias_value":"SZ5W4RBXWJCN","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"pith_short_16","alias_value":"SZ5W4RBXWJCNQVPF","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"pith_short_8","alias_value":"SZ5W4RBX","created_at":"2026-07-05T11:38:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SZ5W4RBXWJCNQVPFCCPHTAAGGB","target":"record","payload":{"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"},"canonical_sha256":"967b6e4437b244d855e5109e798006306cf1d1e9124e942563b1e9a96da29395","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"},"source_kind":"arxiv","source_id":"2507.12454","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z3gFqKvmTp/SspmqZAZYwUTv3yYrjTHRTlVtYMHDfKWieUPK1DeG+ioIWbBocOnL4Dvd5emozH554gUQzwBfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:16:51.563014Z"},"content_sha256":"9ea946a1bf686b9c2f38f0c903af0e94b1c2baeda3d482a4aa44f86fc725e82b","schema_version":"1.0","event_id":"sha256:9ea946a1bf686b9c2f38f0c903af0e94b1c2baeda3d482a4aa44f86fc725e82b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SZ5W4RBXWJCNQVPFCCPHTAAGGB","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQ9SXAVlPdA54qznIg58Y+0kR0a5ZrK1H2iEbJcZKG1XliTvdGMXFI+WMDP7ez25KSjHHMsBAQQ+JmxlTIaeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:16:51.563665Z"},"content_sha256":"e7b52006e7cbb9e3bb45fc44a05524f166eb9f4cde5d4c1d804a3ddca93af5dc","schema_version":"1.0","event_id":"sha256:e7b52006e7cbb9e3bb45fc44a05524f166eb9f4cde5d4c1d804a3ddca93af5dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/bundle.json","state_url":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T20:16:51Z","links":{"resolver":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB","bundle":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/bundle.json","state":"https://pith.science/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZ5W4RBXWJCNQVPFCCPHTAAGGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SZ5W4RBXWJCNQVPFCCPHTAAGGB","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":"fe8e83eafa0710762cc29f0d337267d79cc8674fe1c2225ed2a75ab3fe00f251","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-16T17:54:45Z","title_canon_sha256":"d1c078520e379cd4ef61e0aa6e700e01f30ebe8a96737e1bd11c31a2e6fb6b47"},"schema_version":"1.0","source":{"id":"2507.12454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12454","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12454v1","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12454","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"pith_short_12","alias_value":"SZ5W4RBXWJCN","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"pith_short_16","alias_value":"SZ5W4RBXWJCNQVPF","created_at":"2026-07-05T11:38:20Z"},{"alias_kind":"pith_short_8","alias_value":"SZ5W4RBX","created_at":"2026-07-05T11:38:20Z"}],"graph_snapshots":[{"event_id":"sha256:e7b52006e7cbb9e3bb45fc44a05524f166eb9f4cde5d4c1d804a3ddca93af5dc","target":"graph","created_at":"2026-07-05T11:38:20Z","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/2507.12454/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Anton Mellit","cross_cats":["math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-16T17:54:45Z","title":"Cohomology rings of character varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12454","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":"sha256:9ea946a1bf686b9c2f38f0c903af0e94b1c2baeda3d482a4aa44f86fc725e82b","target":"record","created_at":"2026-07-05T11:38:20Z","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":"fe8e83eafa0710762cc29f0d337267d79cc8674fe1c2225ed2a75ab3fe00f251","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-16T17:54:45Z","title_canon_sha256":"d1c078520e379cd4ef61e0aa6e700e01f30ebe8a96737e1bd11c31a2e6fb6b47"},"schema_version":"1.0","source":{"id":"2507.12454","kind":"arxiv","version":1}},"canonical_sha256":"967b6e4437b244d855e5109e798006306cf1d1e9124e942563b1e9a96da29395","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"967b6e4437b244d855e5109e798006306cf1d1e9124e942563b1e9a96da29395","first_computed_at":"2026-07-05T11:38:20.506271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:20.506271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h7LYW/I9P1wGziVlH6G6b6IRKz1z0yeob08nQ1FEM97AOVgnkaLtaL6dO4FG2GbhWeCWZ4LSqDgDjjTELX/cCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:20.506842Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.12454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ea946a1bf686b9c2f38f0c903af0e94b1c2baeda3d482a4aa44f86fc725e82b","sha256:e7b52006e7cbb9e3bb45fc44a05524f166eb9f4cde5d4c1d804a3ddca93af5dc"],"state_sha256":"5e72dcc263b625ce520d97f9106ef2097502598001fe77eedd3e545489eb2ecd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A+TfdWM6ILiMl/qmpU/MOMgMhDsXkvRtu06sJYSIKUMCl2bcrmhwRg5lOVilcoDU3c4WAFUvvzKmE8dg/7FlAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:16:51.569477Z","bundle_sha256":"a8c7431adafabea367143ea4fc8eba2f3d38b9c5ebf66a37d1bec7a40a82dabb"}}