{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:4MMKTEDF6Z73OYF4MQRC6N7T36","short_pith_number":"pith:4MMKTEDF","schema_version":"1.0","canonical_sha256":"e318a99065f67fb760bc64222f37f3df9f2b3fcec56608ccb582eaedc434458c","source":{"kind":"arxiv","id":"2104.05697","version":2},"attestation_state":"computed","paper":{"title":"A new spin on Hurwitz theory and ELSV via theta characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Alessandro Giacchetto, Danilo Lewa\\'nski, Reinier Kramer","submitted_at":"2021-04-12T17:57:05Z","abstract_excerpt":"We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of K\\\"ahler surfaces and to representation theory of the Sergeev group, and are generated by BKP tau-functions. We use the latter interpretation to give polynomiality properties of these numbers and we derive a spectral curve which we conjecture computes spin Hurwitz numbers via a new type of topological recursion. We prove that this conjectural topological recursion is equivalent to an ELSV-type formula, "},"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":"2104.05697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-04-12T17:57:05Z","cross_cats_sorted":["math.AG","math.DG","math.MP","math.RT"],"title_canon_sha256":"4d0b5330713d2982bfa775c4bcea79479bcd6a0bafddee90a9813fce77d150be","abstract_canon_sha256":"cd91e09d644411598de754d5a9a14b95c0b925dbe5432d869d662ef236fd748d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:33:19.732636Z","signature_b64":"ZLe76GyBV7KHerZBGl7lDlunsH7Iy8NT2d/r5N90/wG+e+x1m6NKoxxTMO/aqxgnvfnzj0vOp5BEXWsm+l8tCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e318a99065f67fb760bc64222f37f3df9f2b3fcec56608ccb582eaedc434458c","last_reissued_at":"2026-07-05T08:33:19.732193Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:33:19.732193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new spin on Hurwitz theory and ELSV via theta characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Alessandro Giacchetto, Danilo Lewa\\'nski, Reinier Kramer","submitted_at":"2021-04-12T17:57:05Z","abstract_excerpt":"We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of K\\\"ahler surfaces and to representation theory of the Sergeev group, and are generated by BKP tau-functions. We use the latter interpretation to give polynomiality properties of these numbers and we derive a spectral curve which we conjecture computes spin Hurwitz numbers via a new type of topological recursion. We prove that this conjectural topological recursion is equivalent to an ELSV-type formula, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.05697","kind":"arxiv","version":2},"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/2104.05697/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":"2104.05697","created_at":"2026-07-05T08:33:19.732257+00:00"},{"alias_kind":"arxiv_version","alias_value":"2104.05697v2","created_at":"2026-07-05T08:33:19.732257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.05697","created_at":"2026-07-05T08:33:19.732257+00:00"},{"alias_kind":"pith_short_12","alias_value":"4MMKTEDF6Z73","created_at":"2026-07-05T08:33:19.732257+00:00"},{"alias_kind":"pith_short_16","alias_value":"4MMKTEDF6Z73OYF4","created_at":"2026-07-05T08:33:19.732257+00:00"},{"alias_kind":"pith_short_8","alias_value":"4MMKTEDF","created_at":"2026-07-05T08:33:19.732257+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.26038","citing_title":"The Super Virasoro Minimal String from 3d Supergravity","ref_index":75,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36","json":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36.json","graph_json":"https://pith.science/api/pith-number/4MMKTEDF6Z73OYF4MQRC6N7T36/graph.json","events_json":"https://pith.science/api/pith-number/4MMKTEDF6Z73OYF4MQRC6N7T36/events.json","paper":"https://pith.science/paper/4MMKTEDF"},"agent_actions":{"view_html":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36","download_json":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36.json","view_paper":"https://pith.science/paper/4MMKTEDF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2104.05697&json=true","fetch_graph":"https://pith.science/api/pith-number/4MMKTEDF6Z73OYF4MQRC6N7T36/graph.json","fetch_events":"https://pith.science/api/pith-number/4MMKTEDF6Z73OYF4MQRC6N7T36/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36/action/storage_attestation","attest_author":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36/action/author_attestation","sign_citation":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36/action/citation_signature","submit_replication":"https://pith.science/pith/4MMKTEDF6Z73OYF4MQRC6N7T36/action/replication_record"}},"created_at":"2026-07-05T08:33:19.732257+00:00","updated_at":"2026-07-05T08:33:19.732257+00:00"}