{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZDNMDNJO4TP6HDBVS5C4XSHE7E","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":"110b9c0d62a5d6d4061dd108fb78f5486655df2cc8efef881011b47e7aaebe07","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-12T06:26:36Z","title_canon_sha256":"143732b61021869f1f53e4b6105a920d41faff0978e6bc96d0d577ffcb8f183c"},"schema_version":"1.0","source":{"id":"1904.06057","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06057","created_at":"2026-07-05T01:14:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06057v2","created_at":"2026-07-05T01:14:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06057","created_at":"2026-07-05T01:14:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZDNMDNJO4TP6","created_at":"2026-07-05T01:14:24Z"},{"alias_kind":"pith_short_16","alias_value":"ZDNMDNJO4TP6HDBV","created_at":"2026-07-05T01:14:24Z"},{"alias_kind":"pith_short_8","alias_value":"ZDNMDNJO","created_at":"2026-07-05T01:14:24Z"}],"graph_snapshots":[{"event_id":"sha256:f21ad1656f3a8a5de427867e9b65c36be4dc19cee4493a85bdd31571c07d8b9e","target":"graph","created_at":"2026-07-05T01:14:24Z","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/1904.06057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The physical 3d $\\mathcal{N}=2$ theory T[Y] was previously used to predict the existence of some 3-manifold invariants $\\hat{Z}_{a}(q)$ that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten-Reshetikhin-Turaev invariants. In this paper we discuss how, for complements of knots in $S^3$, the analogue of the invariants $\\hat{Z}_{a}(q)$ should be a two-variable series $F_K(x,q)$ obtained by parametric resurgence from the asymptotic expansion of the colored Jones polynomial. The terms in this ser","authors_text":"Ciprian Manolescu, Sergei Gukov","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-12T06:26:36Z","title":"A two-variable series for knot complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06057","kind":"arxiv","version":2},"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:fbab896d15cea881c9aa9d26e4a12e7bd72e6604ebeb4805ab708476b181fd20","target":"record","created_at":"2026-07-05T01:14:24Z","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":"110b9c0d62a5d6d4061dd108fb78f5486655df2cc8efef881011b47e7aaebe07","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-12T06:26:36Z","title_canon_sha256":"143732b61021869f1f53e4b6105a920d41faff0978e6bc96d0d577ffcb8f183c"},"schema_version":"1.0","source":{"id":"1904.06057","kind":"arxiv","version":2}},"canonical_sha256":"c8dac1b52ee4dfe38c359745cbc8e4f90adf06a9825b26febd45149b32951468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8dac1b52ee4dfe38c359745cbc8e4f90adf06a9825b26febd45149b32951468","first_computed_at":"2026-07-05T01:14:24.473265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:14:24.473265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mWQqJp4NJHNZsRzRd05WmRQs+q7DRB3t5tNX+W40NNygTkzNzjcBhbXJlcPm1dale4DJb3TOJjIrZ7b7D2HlDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:14:24.473764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06057","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbab896d15cea881c9aa9d26e4a12e7bd72e6604ebeb4805ab708476b181fd20","sha256:f21ad1656f3a8a5de427867e9b65c36be4dc19cee4493a85bdd31571c07d8b9e"],"state_sha256":"4126bc6606835770b2318bac1e1a478b80ca02b9fe07f38ede0e1ab454740620"}