{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PPGEH3ZO4AWOHEBPZIV4UILWWF","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":"f8d7daab895b202f5bd85e422202bbfafc2f9f82efeb0bdc3304cf36a009d79a","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-12T17:32:37Z","title_canon_sha256":"5f685b7f45fc54937af0f644e21b603dafad875fa083f36b3a668f63f85d91db"},"schema_version":"1.0","source":{"id":"2209.05429","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.05429","created_at":"2026-07-05T10:01:59Z"},{"alias_kind":"arxiv_version","alias_value":"2209.05429v2","created_at":"2026-07-05T10:01:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.05429","created_at":"2026-07-05T10:01:59Z"},{"alias_kind":"pith_short_12","alias_value":"PPGEH3ZO4AWO","created_at":"2026-07-05T10:01:59Z"},{"alias_kind":"pith_short_16","alias_value":"PPGEH3ZO4AWOHEBP","created_at":"2026-07-05T10:01:59Z"},{"alias_kind":"pith_short_8","alias_value":"PPGEH3ZO","created_at":"2026-07-05T10:01:59Z"}],"graph_snapshots":[{"event_id":"sha256:7ad16b0c364498bbe80fbf6b4743949584dc1b2f1dfb24462063fae0ada1c014","target":"graph","created_at":"2026-07-05T10:01:59Z","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/2209.05429/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{H}_2$ be the Lie algebra of polynomial Hamiltonian vector fields on the symplectic plane. Let $X$ be the moduli space of stable Higgs bundles of fixed relatively prime rank and degree, or more generally the moduli space of stable parabolic Higgs bundles of arbitrary rank and degree for a generic stability condition. Let $H^*(X)$ be the cohomology with rational coefficients. Using the operations of cup-product by tautological classes and Hecke correspondences we construct an action of $\\mathcal{H}_2$ on $H^*(X)[x,y]$, where $x$ and $y$ are formal variables. We show that the perver","authors_text":"Alexandre Minets, Anton Mellit, Olivier Schiffmann, Tamas Hausel","cross_cats":["math.DG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-12T17:32:37Z","title":"$P=W$ via $\\mathcal{H}_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.05429","kind":"arxiv","version":2},"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":"sha256:743b865b113a8845beef9a985a501e333019469c6070abfc0563655e9b7eac6b","target":"record","created_at":"2026-07-05T10:01:59Z","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":"f8d7daab895b202f5bd85e422202bbfafc2f9f82efeb0bdc3304cf36a009d79a","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-12T17:32:37Z","title_canon_sha256":"5f685b7f45fc54937af0f644e21b603dafad875fa083f36b3a668f63f85d91db"},"schema_version":"1.0","source":{"id":"2209.05429","kind":"arxiv","version":2}},"canonical_sha256":"7bcc43ef2ee02ce3902fca2bca2176b16e6e8b678f6a68ed4db643a1f5f5f78e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bcc43ef2ee02ce3902fca2bca2176b16e6e8b678f6a68ed4db643a1f5f5f78e","first_computed_at":"2026-07-05T10:01:59.147100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:01:59.147100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"brUMfipOsoB5z18Jjpl5iHPJKGF7ZujlqzzKKSXjApXIKVdr60jR8hi9imJvt6YV6JrQ64xW+GFI8d2QBHHVDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:01:59.147532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.05429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:743b865b113a8845beef9a985a501e333019469c6070abfc0563655e9b7eac6b","sha256:7ad16b0c364498bbe80fbf6b4743949584dc1b2f1dfb24462063fae0ada1c014"],"state_sha256":"74a337585a6eb961f84ec8ef913c6f0be66999e5f3d169ec029187504dc2917c"}