{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2SM4WJQHIV54RZMHPSUZEQDYBN","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":"60b9dbd39f7b2b60d1e93af8551747d0a9d196a2da080962f186c425a8f481f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-08T11:34:52Z","title_canon_sha256":"d0c66aa66e984d5c96a94744a4a663410068e7b2a23445c6ff894e74a65a1082"},"schema_version":"1.0","source":{"id":"2112.04238","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04238","created_at":"2026-07-05T09:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04238v2","created_at":"2026-07-05T09:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04238","created_at":"2026-07-05T09:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"2SM4WJQHIV54","created_at":"2026-07-05T09:55:50Z"},{"alias_kind":"pith_short_16","alias_value":"2SM4WJQHIV54RZMH","created_at":"2026-07-05T09:55:50Z"},{"alias_kind":"pith_short_8","alias_value":"2SM4WJQH","created_at":"2026-07-05T09:55:50Z"}],"graph_snapshots":[{"event_id":"sha256:7aa935b0216b4ef7b6b56cb20b285702e795d418a5ae97cd8754764cac094f64","target":"graph","created_at":"2026-07-05T09:55:50Z","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/2112.04238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a closed formula for the integral of a power of a single $\\psi$-class on strata of $k$-differentials. In many cases, these integrals correspond to intersection numbers on twisted double ramification cycles. Then we conjecture an expression of a refinement of double ramification cycles according to the parity of spin structures. Assuming that this conjecture is valid, we also compute the integral of a single $\\psi$-class on the even and odd components of strata of $k$-differentials. As an application of these results we give a closed formula for the Euler characteristic of components o","authors_text":"Adrien Sauvaget, Johannes Schmitt, Matteo Costantini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-08T11:34:52Z","title":"Integrals of $\\psi$-classes on twisted double ramification cycles and spaces of differentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04238","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":"sha256:78b0f0a61360dead11574288c56b5c29a4f1baa2377f342893dd0cb5f36b0ff7","target":"record","created_at":"2026-07-05T09:55:50Z","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":"60b9dbd39f7b2b60d1e93af8551747d0a9d196a2da080962f186c425a8f481f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-08T11:34:52Z","title_canon_sha256":"d0c66aa66e984d5c96a94744a4a663410068e7b2a23445c6ff894e74a65a1082"},"schema_version":"1.0","source":{"id":"2112.04238","kind":"arxiv","version":2}},"canonical_sha256":"d499cb2607457bc8e5877ca99240780b6ef583664c4e67f7fa7e9a558c522beb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d499cb2607457bc8e5877ca99240780b6ef583664c4e67f7fa7e9a558c522beb","first_computed_at":"2026-07-05T09:55:50.397124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:55:50.397124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKE2OZziTFbRqeoewViQsTNQHHZ4eromKHu0o2pDxt9JPvHMVOCecCGPytjVvdCag4sGoseTUwma3FcCmFL6AA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:55:50.397599Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.04238","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78b0f0a61360dead11574288c56b5c29a4f1baa2377f342893dd0cb5f36b0ff7","sha256:7aa935b0216b4ef7b6b56cb20b285702e795d418a5ae97cd8754764cac094f64"],"state_sha256":"2207e349c7f11e1744abdf86be33e3d75a3c38c2d0170b0ef0714657c6408dc1"}