{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:YH3SFJEYZX6WMBECJ3HIRSPI7H","short_pith_number":"pith:YH3SFJEY","schema_version":"1.0","canonical_sha256":"c1f722a498cdfd6604824ece88c9e8f9f53a63c61f59384a4eefd35c043a4948","source":{"kind":"arxiv","id":"2106.03942","version":1},"attestation_state":"computed","paper":{"title":"Inverted state sums, inverted Habiro series, and indefinite theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"primary_cat":"math.GT","authors_text":"Sunghyuk Park","submitted_at":"2021-06-07T20:04:40Z","abstract_excerpt":"S. Gukov and C. Manolescu conjectured that the Melvin-Morton-Rozansky expansion of the colored Jones polynomials can be re-summed into a two-variable series $F_K(x,q)$, which is the knot complement version of the 3-manifold invariant $\\hat{Z}$ whose existence was predicted earlier by S. Gukov, P. Putrov and C. Vafa. In this paper we use an inverted version of the R-matrix state sum to prove this conjecture for a big class of links that includes all homogeneous braid links as well as all fibered knots up to 10 crossings. We also study an inverted version of Habiro's cyclotomic series that leads"},"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":"2106.03942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-06-07T20:04:40Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"title_canon_sha256":"3edf3a3e3b4defec8a9a7bfb325606fa21b6de384c5173c715bdac60b1dc19c3","abstract_canon_sha256":"15071f4943f73769dbb0a0cbee054dd23e8fe8938789a7afef2e433de6752423"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:47:10.558355Z","signature_b64":"R3C4O3kmR1k0OwGkMcApA+HKK31RxEoDBHYZV7E//Oh8aJf69WjuQbLTZ2nm3JB4Yhn7sT151riw3jb2Wv7hDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1f722a498cdfd6604824ece88c9e8f9f53a63c61f59384a4eefd35c043a4948","last_reissued_at":"2026-07-05T02:47:10.558001Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:47:10.558001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverted state sums, inverted Habiro series, and indefinite theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"primary_cat":"math.GT","authors_text":"Sunghyuk Park","submitted_at":"2021-06-07T20:04:40Z","abstract_excerpt":"S. Gukov and C. Manolescu conjectured that the Melvin-Morton-Rozansky expansion of the colored Jones polynomials can be re-summed into a two-variable series $F_K(x,q)$, which is the knot complement version of the 3-manifold invariant $\\hat{Z}$ whose existence was predicted earlier by S. Gukov, P. Putrov and C. Vafa. In this paper we use an inverted version of the R-matrix state sum to prove this conjecture for a big class of links that includes all homogeneous braid links as well as all fibered knots up to 10 crossings. We also study an inverted version of Habiro's cyclotomic series that leads"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03942","kind":"arxiv","version":1},"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/2106.03942/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":"2106.03942","created_at":"2026-07-05T02:47:10.558058+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.03942v1","created_at":"2026-07-05T02:47:10.558058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.03942","created_at":"2026-07-05T02:47:10.558058+00:00"},{"alias_kind":"pith_short_12","alias_value":"YH3SFJEYZX6W","created_at":"2026-07-05T02:47:10.558058+00:00"},{"alias_kind":"pith_short_16","alias_value":"YH3SFJEYZX6WMBEC","created_at":"2026-07-05T02:47:10.558058+00:00"},{"alias_kind":"pith_short_8","alias_value":"YH3SFJEY","created_at":"2026-07-05T02:47:10.558058+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2111.04763","citing_title":"Resurgence of Chern-Simons theory at the trivial flat connection","ref_index":47,"is_internal_anchor":false},{"citing_arxiv_id":"2508.10279","citing_title":"A supergroup series for knot complements","ref_index":51,"is_internal_anchor":false},{"citing_arxiv_id":"2508.10112","citing_title":"$c_{\\rm eff}$ from Resurgence at the Stokes Line","ref_index":35,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H","json":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H.json","graph_json":"https://pith.science/api/pith-number/YH3SFJEYZX6WMBECJ3HIRSPI7H/graph.json","events_json":"https://pith.science/api/pith-number/YH3SFJEYZX6WMBECJ3HIRSPI7H/events.json","paper":"https://pith.science/paper/YH3SFJEY"},"agent_actions":{"view_html":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H","download_json":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H.json","view_paper":"https://pith.science/paper/YH3SFJEY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.03942&json=true","fetch_graph":"https://pith.science/api/pith-number/YH3SFJEYZX6WMBECJ3HIRSPI7H/graph.json","fetch_events":"https://pith.science/api/pith-number/YH3SFJEYZX6WMBECJ3HIRSPI7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H/action/storage_attestation","attest_author":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H/action/author_attestation","sign_citation":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H/action/citation_signature","submit_replication":"https://pith.science/pith/YH3SFJEYZX6WMBECJ3HIRSPI7H/action/replication_record"}},"created_at":"2026-07-05T02:47:10.558058+00:00","updated_at":"2026-07-05T02:47:10.558058+00:00"}