{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HZRJXXXTUR2J64JGR36MZZUH25","short_pith_number":"pith:HZRJXXXT","canonical_record":{"source":{"id":"2505.03720","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-06T17:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"e38436983e6838f0e207edc78632e95c790585b58ed44843a2ce6b98614dadb4","abstract_canon_sha256":"1f1078a5ab82dd3e6299bc3bbe898e684fff620c06702145440a6d94d313c33a"},"schema_version":"1.0"},"canonical_sha256":"3e629bdef3a4749f71268efccce687d7726450765dd6bec69116b59908d7995b","source":{"kind":"arxiv","id":"2505.03720","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.03720","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"arxiv_version","alias_value":"2505.03720v1","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.03720","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"pith_short_12","alias_value":"HZRJXXXTUR2J","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"pith_short_16","alias_value":"HZRJXXXTUR2J64JG","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"pith_short_8","alias_value":"HZRJXXXT","created_at":"2026-07-05T10:59:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HZRJXXXTUR2J64JGR36MZZUH25","target":"record","payload":{"canonical_record":{"source":{"id":"2505.03720","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-06T17:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"e38436983e6838f0e207edc78632e95c790585b58ed44843a2ce6b98614dadb4","abstract_canon_sha256":"1f1078a5ab82dd3e6299bc3bbe898e684fff620c06702145440a6d94d313c33a"},"schema_version":"1.0"},"canonical_sha256":"3e629bdef3a4749f71268efccce687d7726450765dd6bec69116b59908d7995b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:21.021107Z","signature_b64":"8T/NQUfChwmMOrqsM8hUAfvugJSFu+6nb3jkw1nCgNJ/gcBDgCITF87dy+xG6dcvg9UId/ApOeV+/GTGulfHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e629bdef3a4749f71268efccce687d7726450765dd6bec69116b59908d7995b","last_reissued_at":"2026-07-05T10:59:21.020625Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:21.020625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.03720","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":"2026-07-05T10:59:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHjQ5tBH1e9QxyFO/JYoveCmdGyTFPUBd07xSX8BbVSrNfw0b4fi0qenrXOR5xyVTkYolxpXBQoYxnCSZyeKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T21:36:52.287730Z"},"content_sha256":"5e1679d3757ae058953d9ca202e0afbc8a43c28214ad0c02ccc9bcb02902e514","schema_version":"1.0","event_id":"sha256:5e1679d3757ae058953d9ca202e0afbc8a43c28214ad0c02ccc9bcb02902e514"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HZRJXXXTUR2J64JGR36MZZUH25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smooth concordance of cables of the figure-eight knot","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Junghwan Park, Masaki Taniguchi, Sungkyung Kang","submitted_at":"2025-05-06T17:47:16Z","abstract_excerpt":"We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all $(2n,1)$-cables of the figure-eight knot. To this end, we introduce a family of concordance invariants $\\kappa_R^{(k)}$, defined via $2^k$-fold branched covers and real Seiberg--Witten Floer $K$-theory. These invariants generalize the real $K$-theoretic Fr\\o yshov invariant developed by Konno, Miyazawa, and Taniguchi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03720","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/2505.03720/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":"2026-07-05T10:59:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPzeqdQdNVdp5fcpQBU/MCN5fDq3QxArgs3sjT4/LciJEytV4Lu7gZdXGJppBz9wuJtE7FZM4Hvoehdr1QywDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T21:36:52.288066Z"},"content_sha256":"0afa5a862b5b16524e02713f09a605b9dce3f4b669c77461e302529c84eccc01","schema_version":"1.0","event_id":"sha256:0afa5a862b5b16524e02713f09a605b9dce3f4b669c77461e302529c84eccc01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HZRJXXXTUR2J64JGR36MZZUH25/bundle.json","state_url":"https://pith.science/pith/HZRJXXXTUR2J64JGR36MZZUH25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HZRJXXXTUR2J64JGR36MZZUH25/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":"2026-08-18T21:36:52Z","links":{"resolver":"https://pith.science/pith/HZRJXXXTUR2J64JGR36MZZUH25","bundle":"https://pith.science/pith/HZRJXXXTUR2J64JGR36MZZUH25/bundle.json","state":"https://pith.science/pith/HZRJXXXTUR2J64JGR36MZZUH25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HZRJXXXTUR2J64JGR36MZZUH25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HZRJXXXTUR2J64JGR36MZZUH25","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":"1f1078a5ab82dd3e6299bc3bbe898e684fff620c06702145440a6d94d313c33a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-06T17:47:16Z","title_canon_sha256":"e38436983e6838f0e207edc78632e95c790585b58ed44843a2ce6b98614dadb4"},"schema_version":"1.0","source":{"id":"2505.03720","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.03720","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"arxiv_version","alias_value":"2505.03720v1","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.03720","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"pith_short_12","alias_value":"HZRJXXXTUR2J","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"pith_short_16","alias_value":"HZRJXXXTUR2J64JG","created_at":"2026-07-05T10:59:21Z"},{"alias_kind":"pith_short_8","alias_value":"HZRJXXXT","created_at":"2026-07-05T10:59:21Z"}],"graph_snapshots":[{"event_id":"sha256:0afa5a862b5b16524e02713f09a605b9dce3f4b669c77461e302529c84eccc01","target":"graph","created_at":"2026-07-05T10:59:21Z","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/2505.03720/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all $(2n,1)$-cables of the figure-eight knot. To this end, we introduce a family of concordance invariants $\\kappa_R^{(k)}$, defined via $2^k$-fold branched covers and real Seiberg--Witten Floer $K$-theory. These invariants generalize the real $K$-theoretic Fr\\o yshov invariant developed by Konno, Miyazawa, and Taniguchi.","authors_text":"Junghwan Park, Masaki Taniguchi, Sungkyung Kang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-06T17:47:16Z","title":"Smooth concordance of cables of the figure-eight knot"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03720","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":"sha256:5e1679d3757ae058953d9ca202e0afbc8a43c28214ad0c02ccc9bcb02902e514","target":"record","created_at":"2026-07-05T10:59:21Z","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":"1f1078a5ab82dd3e6299bc3bbe898e684fff620c06702145440a6d94d313c33a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-06T17:47:16Z","title_canon_sha256":"e38436983e6838f0e207edc78632e95c790585b58ed44843a2ce6b98614dadb4"},"schema_version":"1.0","source":{"id":"2505.03720","kind":"arxiv","version":1}},"canonical_sha256":"3e629bdef3a4749f71268efccce687d7726450765dd6bec69116b59908d7995b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e629bdef3a4749f71268efccce687d7726450765dd6bec69116b59908d7995b","first_computed_at":"2026-07-05T10:59:21.020625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:21.020625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8T/NQUfChwmMOrqsM8hUAfvugJSFu+6nb3jkw1nCgNJ/gcBDgCITF87dy+xG6dcvg9UId/ApOeV+/GTGulfHCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:21.021107Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.03720","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e1679d3757ae058953d9ca202e0afbc8a43c28214ad0c02ccc9bcb02902e514","sha256:0afa5a862b5b16524e02713f09a605b9dce3f4b669c77461e302529c84eccc01"],"state_sha256":"e5a44facc9c19a7733e76b03265a9922dd55be43926462c43eadcca854ad6478"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Pe4LPZguN8glntS68stvnT/Nbbmd7fIEeNgBgVjMstaanGhQnuqiAYyYSKjFDZK2nzvZnU/k1aaPJmPq1KTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T21:36:52.291409Z","bundle_sha256":"5fa3b2830b42c3ff5c130e678e80678f3b5231cb3d2d91ce574e10c660df6dbb"}}