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Our $r$-ELSV formula is an equality between a Hurwitz number and an integral over the space of $r$-spin structures, that is, the space of stable curves with an $r$th root of the canonical bundle. Our $r$-BM conjecture is the statement that $n$-point functions for Hurwitz numbers satisfy the topological recursion asso"},"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":"1306.6226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-26T12:49:28Z","cross_cats_sorted":[],"title_canon_sha256":"69bcda960abdaa33e6d7ef84ba9af1183f109da859b89ccf9472c29b4a2e965e","abstract_canon_sha256":"87bc0de6a8eb991242752a3daaa68ffb11d2594bbeaa46b8ad5d74d9b2f95246"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:49.133159Z","signature_b64":"cndLjBf2LpU8PxheBiYr4Eo/XDijSWepOWP7B7vDOAM5zhInvTPgRaEcphWDx2sDEkpGUSTPlBQc7FkUC5BPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cde0506f08f78f7c0bc018143f27e55844d0a6a68b596a5893ec924bd82a975e","last_reissued_at":"2026-05-18T00:37:49.132605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:49.132605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalence of ELSV and Bouchard-Mari\\~no conjectures for $r$-spin Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. Zvonkine, L. Spitz, S. Shadrin","submitted_at":"2013-06-26T12:49:28Z","abstract_excerpt":"We propose two conjectures on Huwritz numbers with completed $(r+1)$-cycles, or, equivalently, on certain relative Gromov-Witten invariants of the projective line. The conjectures are analogs of the ELSV formula and of the Bouchard-Mari\\~no conjecture for ordinary Hurwitz numbers. Our $r$-ELSV formula is an equality between a Hurwitz number and an integral over the space of $r$-spin structures, that is, the space of stable curves with an $r$th root of the canonical bundle. 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