{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:I2IDJNIWU44T6DUXNSFJNAWVCD","short_pith_number":"pith:I2IDJNIW","canonical_record":{"source":{"id":"2304.00699","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-04-03T03:35:27Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"3e1d5a7ba93cee8a1add36b69f09ba55421c147eebaca8c84b462e07f4d2882f","abstract_canon_sha256":"37c0bc6e1c3a2a89ae7041ba057d58ad86a7415085d060a53e62499b4aa041a9"},"schema_version":"1.0"},"canonical_sha256":"469034b516a7393f0e976c8a9682d510c2c06b7a656f95746b7dd08d67effd68","source":{"kind":"arxiv","id":"2304.00699","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00699","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00699v3","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00699","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"I2IDJNIWU44T","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_16","alias_value":"I2IDJNIWU44T6DUX","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_8","alias_value":"I2IDJNIW","created_at":"2026-07-05T11:59:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:I2IDJNIWU44T6DUXNSFJNAWVCD","target":"record","payload":{"canonical_record":{"source":{"id":"2304.00699","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-04-03T03:35:27Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"3e1d5a7ba93cee8a1add36b69f09ba55421c147eebaca8c84b462e07f4d2882f","abstract_canon_sha256":"37c0bc6e1c3a2a89ae7041ba057d58ad86a7415085d060a53e62499b4aa041a9"},"schema_version":"1.0"},"canonical_sha256":"469034b516a7393f0e976c8a9682d510c2c06b7a656f95746b7dd08d67effd68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:02.827222Z","signature_b64":"7/r/8y0t+eHkwP78hqZgD2dPdCoqftBlUDje99TPNal2C710F/MwLmAwMzynjijNSZhBPexMfVJHAp1t6idKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"469034b516a7393f0e976c8a9682d510c2c06b7a656f95746b7dd08d67effd68","last_reissued_at":"2026-07-05T11:59:02.826770Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:02.826770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.00699","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:59:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LRDPLRh8ZtvmPlQnPCUh9t+4oSNgketTKTCbIwwY6GL5tvNyNZ/MH42fajtgnbJzj8nDviKRieTQEdXAHOtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:36:16.101196Z"},"content_sha256":"315461e0d151423cfe2b478a92394332c985f9286be4528e558e58e624ba59a3","schema_version":"1.0","event_id":"sha256:315461e0d151423cfe2b478a92394332c985f9286be4528e558e58e624ba59a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:I2IDJNIWU44T6DUXNSFJNAWVCD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\widehat{Z}$ and Splice Diagrams","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.GT","authors_text":"Josef Svoboda, Ludmil Katzarkov, Sergei Gukov","submitted_at":"2023-04-03T03:35:27Z","abstract_excerpt":"We study quantum $q$-series invariants of 3-manifolds $\\widehat{Z}_\\sigma$ of Gukov-Pei-Putrov-Vafa, using techniques from the theory of normal surface singularities such as splice diagrams. We show that the (suitably normalized) sum of all $\\widehat{Z}_\\sigma$ depends only on the splice diagram, and in particular, it agrees for manifolds with the same universal abelian cover. We use these ideas to find simple formulas for $\\widehat{Z}_\\sigma$ invariants of Seifert manifolds. Applications include a better understanding of the vanishing of the $q$-series $\\widehat{Z}_\\sigma$. Additionally, we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00699","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/2304.00699/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:59:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yC97lI2XUnZ8ta4LOIGg+87UPzbMzysvjlqaaUWk9ISIlGAkJcsnIZVu6Q36/+qIwZM7E2FMXeGu5AX9cH9LAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:36:16.102086Z"},"content_sha256":"b207c69c28601a3a67448398adca81e6ca740aac0dbc4b1851f7ecf3754fd0b0","schema_version":"1.0","event_id":"sha256:b207c69c28601a3a67448398adca81e6ca740aac0dbc4b1851f7ecf3754fd0b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2IDJNIWU44T6DUXNSFJNAWVCD/bundle.json","state_url":"https://pith.science/pith/I2IDJNIWU44T6DUXNSFJNAWVCD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2IDJNIWU44T6DUXNSFJNAWVCD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T22:36:16Z","links":{"resolver":"https://pith.science/pith/I2IDJNIWU44T6DUXNSFJNAWVCD","bundle":"https://pith.science/pith/I2IDJNIWU44T6DUXNSFJNAWVCD/bundle.json","state":"https://pith.science/pith/I2IDJNIWU44T6DUXNSFJNAWVCD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2IDJNIWU44T6DUXNSFJNAWVCD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:I2IDJNIWU44T6DUXNSFJNAWVCD","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":"37c0bc6e1c3a2a89ae7041ba057d58ad86a7415085d060a53e62499b4aa041a9","cross_cats_sorted":["math.AG","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-04-03T03:35:27Z","title_canon_sha256":"3e1d5a7ba93cee8a1add36b69f09ba55421c147eebaca8c84b462e07f4d2882f"},"schema_version":"1.0","source":{"id":"2304.00699","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00699","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00699v3","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00699","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"I2IDJNIWU44T","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_16","alias_value":"I2IDJNIWU44T6DUX","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_8","alias_value":"I2IDJNIW","created_at":"2026-07-05T11:59:02Z"}],"graph_snapshots":[{"event_id":"sha256:b207c69c28601a3a67448398adca81e6ca740aac0dbc4b1851f7ecf3754fd0b0","target":"graph","created_at":"2026-07-05T11:59:02Z","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/2304.00699/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study quantum $q$-series invariants of 3-manifolds $\\widehat{Z}_\\sigma$ of Gukov-Pei-Putrov-Vafa, using techniques from the theory of normal surface singularities such as splice diagrams. We show that the (suitably normalized) sum of all $\\widehat{Z}_\\sigma$ depends only on the splice diagram, and in particular, it agrees for manifolds with the same universal abelian cover. We use these ideas to find simple formulas for $\\widehat{Z}_\\sigma$ invariants of Seifert manifolds. Applications include a better understanding of the vanishing of the $q$-series $\\widehat{Z}_\\sigma$. Additionally, we s","authors_text":"Josef Svoboda, Ludmil Katzarkov, Sergei Gukov","cross_cats":["math.AG","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-04-03T03:35:27Z","title":"$\\widehat{Z}$ and Splice Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00699","kind":"arxiv","version":3},"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":"sha256:315461e0d151423cfe2b478a92394332c985f9286be4528e558e58e624ba59a3","target":"record","created_at":"2026-07-05T11:59:02Z","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":"37c0bc6e1c3a2a89ae7041ba057d58ad86a7415085d060a53e62499b4aa041a9","cross_cats_sorted":["math.AG","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-04-03T03:35:27Z","title_canon_sha256":"3e1d5a7ba93cee8a1add36b69f09ba55421c147eebaca8c84b462e07f4d2882f"},"schema_version":"1.0","source":{"id":"2304.00699","kind":"arxiv","version":3}},"canonical_sha256":"469034b516a7393f0e976c8a9682d510c2c06b7a656f95746b7dd08d67effd68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"469034b516a7393f0e976c8a9682d510c2c06b7a656f95746b7dd08d67effd68","first_computed_at":"2026-07-05T11:59:02.826770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:02.826770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/r/8y0t+eHkwP78hqZgD2dPdCoqftBlUDje99TPNal2C710F/MwLmAwMzynjijNSZhBPexMfVJHAp1t6idKBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:02.827222Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.00699","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:315461e0d151423cfe2b478a92394332c985f9286be4528e558e58e624ba59a3","sha256:b207c69c28601a3a67448398adca81e6ca740aac0dbc4b1851f7ecf3754fd0b0"],"state_sha256":"8e26e45e47a0b7889f92d2bb84a9ad92f9ba1cf1ff3498d1ab7db489bfdf07df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Y9eIqQ6tx87wip1MsfaigpSrse4OD55NoI3shJ3OorR69F/9ed7F7pAwHzW+1zgRvZTlrn80ewbWShEveeJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T22:36:16.107799Z","bundle_sha256":"b1533a5e7d9a2f0b9f8f20b52280a29b3e77f1dece256b79b0382da7c85eddf2"}}