{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TZUR73XBXVM6KNNDT4GDPDT6EG","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":"317913202011b4e833257562f69777250ceed4282bbdcaf4902c720c479e9958","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-18T00:37:53Z","title_canon_sha256":"b1d6176e461230d1efbd5e1b5ad98c2ee95f08cceda20bb78a54a6554216603c"},"schema_version":"1.0","source":{"id":"1511.05628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05628","created_at":"2026-05-18T01:26:33Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05628v1","created_at":"2026-05-18T01:26:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05628","created_at":"2026-05-18T01:26:33Z"},{"alias_kind":"pith_short_12","alias_value":"TZUR73XBXVM6","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"TZUR73XBXVM6KNND","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"TZUR73XB","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:ef9a51bc01ba33453bbb90e82dbdf54691c3a26592c95fcecf4a79cf7f263252","target":"graph","created_at":"2026-05-18T01:26:33Z","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"},"paper":{"abstract_excerpt":"The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of the knot complement and a geometric solution to the gluing equations) and a complex root of unity $\\zeta$. We prove that the coefficients of our series lie in the trace field of the knot, adjoined a complex root of unity. We conjecture that our series are those that appear in the Q","authors_text":"Stavros Garoufalidis, Tudor Dimofte","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-18T00:37:53Z","title":"Quantum modularity and complex Chern-Simons theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05628","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":"sha256:4465ee923ea2a1c49cd37e04a502b70619cfe3935d6844f08dacc0b3afd9468c","target":"record","created_at":"2026-05-18T01:26:33Z","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":"317913202011b4e833257562f69777250ceed4282bbdcaf4902c720c479e9958","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-18T00:37:53Z","title_canon_sha256":"b1d6176e461230d1efbd5e1b5ad98c2ee95f08cceda20bb78a54a6554216603c"},"schema_version":"1.0","source":{"id":"1511.05628","kind":"arxiv","version":1}},"canonical_sha256":"9e691feee1bd59e535a39f0c378e7e21bc931748a542349742785d17203e10c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e691feee1bd59e535a39f0c378e7e21bc931748a542349742785d17203e10c5","first_computed_at":"2026-05-18T01:26:33.209429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:33.209429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ctKLFyAs7BV/pRHxRPJNg1fG5KCJVSywiw2EgRrUBs3e1yO6T3ckAKlfOhmiMdctXgbqpCGHtq5jeN+LQhL5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:33.210102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4465ee923ea2a1c49cd37e04a502b70619cfe3935d6844f08dacc0b3afd9468c","sha256:ef9a51bc01ba33453bbb90e82dbdf54691c3a26592c95fcecf4a79cf7f263252"],"state_sha256":"70391005d3998bb1455d4f65d632b43fcd865feb3cfb6b1815ef5075feb568a7"}