{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:A55BRRUU2BY6DFT3IDFZZ5JAFU","short_pith_number":"pith:A55BRRUU","canonical_record":{"source":{"id":"2605.21382","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-20T16:41:37Z","cross_cats_sorted":["math.QA","math.SG"],"title_canon_sha256":"55d3a7133abbcb5d766c30b9c64f4feac4a21fd12baf370cb49a2a958269c197","abstract_canon_sha256":"29e50fb53b85a1a65046d37768d3b74573f9b37663f79f8ea2db607f223d68ee"},"schema_version":"1.0"},"canonical_sha256":"077a18c694d071e1967b40cb9cf5202d1e6b7af357f36aee4780392ca2976c90","source":{"kind":"arxiv","id":"2605.21382","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21382","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21382v1","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21382","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"A55BRRUU2BY6","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"A55BRRUU2BY6DFT3","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"A55BRRUU","created_at":"2026-05-21T02:05:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:A55BRRUU2BY6DFT3IDFZZ5JAFU","target":"record","payload":{"canonical_record":{"source":{"id":"2605.21382","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-20T16:41:37Z","cross_cats_sorted":["math.QA","math.SG"],"title_canon_sha256":"55d3a7133abbcb5d766c30b9c64f4feac4a21fd12baf370cb49a2a958269c197","abstract_canon_sha256":"29e50fb53b85a1a65046d37768d3b74573f9b37663f79f8ea2db607f223d68ee"},"schema_version":"1.0"},"canonical_sha256":"077a18c694d071e1967b40cb9cf5202d1e6b7af357f36aee4780392ca2976c90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T02:05:31.995936Z","signature_b64":"xUevr4Fpen+PALI/9RT1pL7rOCXObzGAJ/iffDc21u0pQEj3p8woxiz9cdzhofU4JEzFHWC3WgFGejf11I38Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"077a18c694d071e1967b40cb9cf5202d1e6b7af357f36aee4780392ca2976c90","last_reissued_at":"2026-05-21T02:05:31.995038Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T02:05:31.995038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.21382","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T02:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nEj+5s5ROP/qBjxiooClS97FdXVLqnP31XIzL1opaQT/NwDXtQWTwhV1pQVJ6l3kVSds/oUHY21+f0+iVhhuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:17:38.400431Z"},"content_sha256":"741c4c2ec81e712d54f36252976a91d9398b673aa6b79191a83fd8081af4c260","schema_version":"1.0","event_id":"sha256:741c4c2ec81e712d54f36252976a91d9398b673aa6b79191a83fd8081af4c260"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:A55BRRUU2BY6DFT3IDFZZ5JAFU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flow loops and quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.SG"],"primary_cat":"math.GT","authors_text":"Sunghyuk Park","submitted_at":"2026-05-20T16:41:37Z","abstract_excerpt":"This paper connects two seemingly different ways of studying knots: quantum group invariants and the dynamics of Morse flows. For fibered knots, we define a two-variable series invariant by counting Morse flow loops in the complement. This dynamical series is conjectured to agree with the BPS $q$-series of the knot complement, which arises from Verma modules for quantum groups and encodes all colored Jones polynomials. We prove this correspondence for all braid-homogeneous knots."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21382","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/2605.21382/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":"2026-05-21T02:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x4Nki7JR4aypjO5DQaRVY2PKjBl+Rqgc8S665EDmuShZOA75cJzfjAHKmCX+5bh605obZTAsxNu1iGsnV/CzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:17:38.401156Z"},"content_sha256":"df0abed68114e2bb8bef36319168e5617d1e58f255ffe11bb36fef152126267b","schema_version":"1.0","event_id":"sha256:df0abed68114e2bb8bef36319168e5617d1e58f255ffe11bb36fef152126267b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A55BRRUU2BY6DFT3IDFZZ5JAFU/bundle.json","state_url":"https://pith.science/pith/A55BRRUU2BY6DFT3IDFZZ5JAFU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A55BRRUU2BY6DFT3IDFZZ5JAFU/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":"2026-05-26T20:17:38Z","links":{"resolver":"https://pith.science/pith/A55BRRUU2BY6DFT3IDFZZ5JAFU","bundle":"https://pith.science/pith/A55BRRUU2BY6DFT3IDFZZ5JAFU/bundle.json","state":"https://pith.science/pith/A55BRRUU2BY6DFT3IDFZZ5JAFU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A55BRRUU2BY6DFT3IDFZZ5JAFU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:A55BRRUU2BY6DFT3IDFZZ5JAFU","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":"29e50fb53b85a1a65046d37768d3b74573f9b37663f79f8ea2db607f223d68ee","cross_cats_sorted":["math.QA","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-20T16:41:37Z","title_canon_sha256":"55d3a7133abbcb5d766c30b9c64f4feac4a21fd12baf370cb49a2a958269c197"},"schema_version":"1.0","source":{"id":"2605.21382","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21382","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21382v1","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21382","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"A55BRRUU2BY6","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"A55BRRUU2BY6DFT3","created_at":"2026-05-21T02:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"A55BRRUU","created_at":"2026-05-21T02:05:31Z"}],"graph_snapshots":[{"event_id":"sha256:df0abed68114e2bb8bef36319168e5617d1e58f255ffe11bb36fef152126267b","target":"graph","created_at":"2026-05-21T02:05:31Z","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/2605.21382/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper connects two seemingly different ways of studying knots: quantum group invariants and the dynamics of Morse flows. For fibered knots, we define a two-variable series invariant by counting Morse flow loops in the complement. This dynamical series is conjectured to agree with the BPS $q$-series of the knot complement, which arises from Verma modules for quantum groups and encodes all colored Jones polynomials. We prove this correspondence for all braid-homogeneous knots.","authors_text":"Sunghyuk Park","cross_cats":["math.QA","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-20T16:41:37Z","title":"Flow loops and quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21382","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":"sha256:741c4c2ec81e712d54f36252976a91d9398b673aa6b79191a83fd8081af4c260","target":"record","created_at":"2026-05-21T02:05:31Z","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":"29e50fb53b85a1a65046d37768d3b74573f9b37663f79f8ea2db607f223d68ee","cross_cats_sorted":["math.QA","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-20T16:41:37Z","title_canon_sha256":"55d3a7133abbcb5d766c30b9c64f4feac4a21fd12baf370cb49a2a958269c197"},"schema_version":"1.0","source":{"id":"2605.21382","kind":"arxiv","version":1}},"canonical_sha256":"077a18c694d071e1967b40cb9cf5202d1e6b7af357f36aee4780392ca2976c90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"077a18c694d071e1967b40cb9cf5202d1e6b7af357f36aee4780392ca2976c90","first_computed_at":"2026-05-21T02:05:31.995038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T02:05:31.995038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xUevr4Fpen+PALI/9RT1pL7rOCXObzGAJ/iffDc21u0pQEj3p8woxiz9cdzhofU4JEzFHWC3WgFGejf11I38Dg==","signature_status":"signed_v1","signed_at":"2026-05-21T02:05:31.995936Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21382","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:741c4c2ec81e712d54f36252976a91d9398b673aa6b79191a83fd8081af4c260","sha256:df0abed68114e2bb8bef36319168e5617d1e58f255ffe11bb36fef152126267b"],"state_sha256":"8eb8ad54cdcbba88fb4411726e8535c2e28e1f255d168eeb1f0690df3a5a6023"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPiwqTeWOx3lq8et8SUSgYe1HV/Jr8/ADtjr5t+bP2qmUwsZUaw1o3dBX4mJ/BwujyeSOu/5BLtGaJhHF7NmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:17:38.404808Z","bundle_sha256":"8414ed32b371c5d448364c1fe9bf09bd4de8374284d7669c550bf011ce174ac9"}}