{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:QC27US27PXDADAGRY72QJKMNHO","short_pith_number":"pith:QC27US27","schema_version":"1.0","canonical_sha256":"80b5fa4b5f7dc60180d1c7f504a98d3b80cd5ec7bea855611ff3f12c4abaf4b2","source":{"kind":"arxiv","id":"1912.07997","version":3},"attestation_state":"computed","paper":{"title":"Three-Manifold Quantum Invariants and Mock Theta Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.GT","math.MP"],"primary_cat":"math.NT","authors_text":"Francesca Ferrari, Gabriele Sgroi, Miranda C. N. Cheng","submitted_at":"2019-12-17T13:25:01Z","abstract_excerpt":"Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago. In this proceeding we highlight a new area where mock modular forms start to play an important role, namely the study of three-manifold invariants. For a certain class of Seifert three-manifolds, we describe a conjecture on the mock modular properties of a recently proposed quantum invariant. As an illustration, we include concrete computations for a specific three-manifold, the Brieskorn sphere $\\Sigma(2,3,7)$. This note is partially base"},"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":"1912.07997","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-12-17T13:25:01Z","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP"],"title_canon_sha256":"8476026106ca373649d73a27a8ee4025dd7563e41c977eaf2089e6f945669df0","abstract_canon_sha256":"7ecf175ef33acd3f971b39db5d7bbe3f2b4ccec65d8a1bce3ba41d82319d5b85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:01.737697Z","signature_b64":"B4ALuAuMOsOlNfAVLtide4VxknQVB44QonEQIkIfaeGFNHzk8//1Uh0l4Wy81Y3vfb3A+wOSMiJYBbR6XEkWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80b5fa4b5f7dc60180d1c7f504a98d3b80cd5ec7bea855611ff3f12c4abaf4b2","last_reissued_at":"2026-07-05T00:48:01.737251Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:01.737251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-Manifold Quantum Invariants and Mock Theta Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.GT","math.MP"],"primary_cat":"math.NT","authors_text":"Francesca Ferrari, Gabriele Sgroi, Miranda C. N. Cheng","submitted_at":"2019-12-17T13:25:01Z","abstract_excerpt":"Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago. In this proceeding we highlight a new area where mock modular forms start to play an important role, namely the study of three-manifold invariants. For a certain class of Seifert three-manifolds, we describe a conjecture on the mock modular properties of a recently proposed quantum invariant. As an illustration, we include concrete computations for a specific three-manifold, the Brieskorn sphere $\\Sigma(2,3,7)$. This note is partially base"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.07997","kind":"arxiv","version":3},"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/1912.07997/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":"1912.07997","created_at":"2026-07-05T00:48:01.737323+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.07997v3","created_at":"2026-07-05T00:48:01.737323+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.07997","created_at":"2026-07-05T00:48:01.737323+00:00"},{"alias_kind":"pith_short_12","alias_value":"QC27US27PXDA","created_at":"2026-07-05T00:48:01.737323+00:00"},{"alias_kind":"pith_short_16","alias_value":"QC27US27PXDADAGR","created_at":"2026-07-05T00:48:01.737323+00:00"},{"alias_kind":"pith_short_8","alias_value":"QC27US27","created_at":"2026-07-05T00:48:01.737323+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.02939","citing_title":"Quantum invariants of 3-manifolds and links: a review","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO","json":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO.json","graph_json":"https://pith.science/api/pith-number/QC27US27PXDADAGRY72QJKMNHO/graph.json","events_json":"https://pith.science/api/pith-number/QC27US27PXDADAGRY72QJKMNHO/events.json","paper":"https://pith.science/paper/QC27US27"},"agent_actions":{"view_html":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO","download_json":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO.json","view_paper":"https://pith.science/paper/QC27US27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.07997&json=true","fetch_graph":"https://pith.science/api/pith-number/QC27US27PXDADAGRY72QJKMNHO/graph.json","fetch_events":"https://pith.science/api/pith-number/QC27US27PXDADAGRY72QJKMNHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO/action/storage_attestation","attest_author":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO/action/author_attestation","sign_citation":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO/action/citation_signature","submit_replication":"https://pith.science/pith/QC27US27PXDADAGRY72QJKMNHO/action/replication_record"}},"created_at":"2026-07-05T00:48:01.737323+00:00","updated_at":"2026-07-05T00:48:01.737323+00:00"}