{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:35Y4Y5R5ASANHKMMDFKS4D532A","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":"bc6227dfe71bca8598fda5736344fe862a625374e34ecf78f3cbbfbeadb23f09","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-08T16:20:46Z","title_canon_sha256":"c5f9410a47b5bce3858f9b41c536d6175b8607567863a1b6b99ab7e4856b6a91"},"schema_version":"1.0","source":{"id":"2306.05326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.05326","created_at":"2026-07-05T06:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"2306.05326v1","created_at":"2026-07-05T06:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.05326","created_at":"2026-07-05T06:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"35Y4Y5R5ASAN","created_at":"2026-07-05T06:18:55Z"},{"alias_kind":"pith_short_16","alias_value":"35Y4Y5R5ASANHKMM","created_at":"2026-07-05T06:18:55Z"},{"alias_kind":"pith_short_8","alias_value":"35Y4Y5R5","created_at":"2026-07-05T06:18:55Z"}],"graph_snapshots":[{"event_id":"sha256:68ea7855dfb3f70e1cba2f1f6552ff1667233b021849f4de0112d0bf60eb8a32","target":"graph","created_at":"2026-07-05T06:18:55Z","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/2306.05326/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Starting from a torus knot $\\mathcal{K}$ in the lens space $L(p,-1)$, we construct a Lagrangian sub-manifold $L_{\\mathcal{K}}$ in $\\mathcal{X}=\\big(\\mathcal{O}_{\\mathbb{P}^1}(-1)\\oplus \\mathcal{O}_{\\mathbb{P}^1}(-1)\\big)/\\mathbb{Z}_p$ under the conifold transition. We prove a mirror theorem which relates the all genus open-closed Gromov-Witten invariants of $(\\mathcal{X},L_{\\mathcal{K}})$ to the topological recursion on the B-model spectral curve. This verifies a conjecture in \\cite{Bor-Bri} in the case of lens space.","authors_text":"Jinghao Yu, Zhengyu Zong","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-08T16:20:46Z","title":"Torus knots in Lens spaces, open Gromov-Witten invariants, and topological recursion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05326","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":"sha256:65d6941574db7fcc710898c1389072b5bf8288c968da49e2d2de3bd3fbfef575","target":"record","created_at":"2026-07-05T06:18:55Z","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":"bc6227dfe71bca8598fda5736344fe862a625374e34ecf78f3cbbfbeadb23f09","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-08T16:20:46Z","title_canon_sha256":"c5f9410a47b5bce3858f9b41c536d6175b8607567863a1b6b99ab7e4856b6a91"},"schema_version":"1.0","source":{"id":"2306.05326","kind":"arxiv","version":1}},"canonical_sha256":"df71cc763d0480d3a98c19552e0fbbd015dbc7b8450a310a094273601517bae5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df71cc763d0480d3a98c19552e0fbbd015dbc7b8450a310a094273601517bae5","first_computed_at":"2026-07-05T06:18:55.528237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:18:55.528237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yPmwK1EIkgx4ciNuoWYAwP20xFG0in94yFI59MOhLsyZBmDxQC38fo7H7r9+UctOO1EWo+jysKdtUjN/eAWbBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:18:55.528637Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.05326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65d6941574db7fcc710898c1389072b5bf8288c968da49e2d2de3bd3fbfef575","sha256:68ea7855dfb3f70e1cba2f1f6552ff1667233b021849f4de0112d0bf60eb8a32"],"state_sha256":"6d9c16b0cff14a075699987983bb1ad79d4a91e9a823a1039a09aeca2c58cc45"}