{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:I4JHVKM33T2ALSLRCS4ZOSNWSI","short_pith_number":"pith:I4JHVKM3","canonical_record":{"source":{"id":"2012.12148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-12-22T16:38:18Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"6a0097c2fb9c5a4cd626d8e724ebb5d53cc37e381065a4f0e43740895dc6aa95","abstract_canon_sha256":"448f51a26a54fe2fe8a4650cfec494b6e6a7b53c7c75f639f23ffcb4d96c38e2"},"schema_version":"1.0"},"canonical_sha256":"47127aa99bdcf405c97114b99749b6922dbf05c4268f3ebcafbb8cfdfefff4ef","source":{"kind":"arxiv","id":"2012.12148","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.12148","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"2012.12148v2","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.12148","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"I4JHVKM33T2A","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"pith_short_16","alias_value":"I4JHVKM33T2ALSLR","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"pith_short_8","alias_value":"I4JHVKM3","created_at":"2026-07-05T03:24:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:I4JHVKM33T2ALSLRCS4ZOSNWSI","target":"record","payload":{"canonical_record":{"source":{"id":"2012.12148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-12-22T16:38:18Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"6a0097c2fb9c5a4cd626d8e724ebb5d53cc37e381065a4f0e43740895dc6aa95","abstract_canon_sha256":"448f51a26a54fe2fe8a4650cfec494b6e6a7b53c7c75f639f23ffcb4d96c38e2"},"schema_version":"1.0"},"canonical_sha256":"47127aa99bdcf405c97114b99749b6922dbf05c4268f3ebcafbb8cfdfefff4ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:24:40.803376Z","signature_b64":"MfQ+BHRbw/7wcAvOltLtA87NLQbpItB7Vq05hce1qCVFcmB+/vyUx+nIhdc1BO7lLX3BYlZAgsAUF71lolXjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47127aa99bdcf405c97114b99749b6922dbf05c4268f3ebcafbb8cfdfefff4ef","last_reissued_at":"2026-07-05T03:24:40.802927Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:24:40.802927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.12148","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzUr6tOnfEu9a+oPCNvlAUYuhS7h26ryVfXhdBB7Z26UunksmeoG1DD2A1v7As/hdUj4sj1MdC/49Hh8LUbWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:18:56.237370Z"},"content_sha256":"ecf38f2229ca341fc477669cbf8e5437f2cae0a33774b7e823b11d848c1c0a0a","schema_version":"1.0","event_id":"sha256:ecf38f2229ca341fc477669cbf8e5437f2cae0a33774b7e823b11d848c1c0a0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:I4JHVKM33T2ALSLRCS4ZOSNWSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cabling Legendrian and transverse knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Apratim Chakraborty, Hyunki Min, John B. Etnyre","submitted_at":"2020-12-22T16:38:18Z","abstract_excerpt":"In this paper we will show how to classify Legendrian and transverse knots in the knot type of \"sufficiently positive\" cables of a knot in terms of the classification of the underlying knot. We will also completely explain the phenomena of \"Legendrian large\" cables. These are Legendrian representatives of cables that have Thurston-Bennequin invariant larger that the framing coming from the cabling torus. Such examples have only recently, and unexpectedly, been found. We will also give criteria that determines the classification of Legendrian and transverse knots the the knot type of negative c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.12148","kind":"arxiv","version":2},"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/2012.12148/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":"2026-07-05T03:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1wRzC+AehXEgOug9rCzXEkjKDpujwPW52r3LQQuNcT65SXAHFKi3+T7CNaVT9pvxO96OcmsRZa5XmoiGQ9oDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:18:56.237912Z"},"content_sha256":"e110f981587d0e076eed46625c92c044447f0cba84716fa0775624f3beab15b1","schema_version":"1.0","event_id":"sha256:e110f981587d0e076eed46625c92c044447f0cba84716fa0775624f3beab15b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4JHVKM33T2ALSLRCS4ZOSNWSI/bundle.json","state_url":"https://pith.science/pith/I4JHVKM33T2ALSLRCS4ZOSNWSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4JHVKM33T2ALSLRCS4ZOSNWSI/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":"2026-08-19T13:18:56Z","links":{"resolver":"https://pith.science/pith/I4JHVKM33T2ALSLRCS4ZOSNWSI","bundle":"https://pith.science/pith/I4JHVKM33T2ALSLRCS4ZOSNWSI/bundle.json","state":"https://pith.science/pith/I4JHVKM33T2ALSLRCS4ZOSNWSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4JHVKM33T2ALSLRCS4ZOSNWSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I4JHVKM33T2ALSLRCS4ZOSNWSI","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":"448f51a26a54fe2fe8a4650cfec494b6e6a7b53c7c75f639f23ffcb4d96c38e2","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-12-22T16:38:18Z","title_canon_sha256":"6a0097c2fb9c5a4cd626d8e724ebb5d53cc37e381065a4f0e43740895dc6aa95"},"schema_version":"1.0","source":{"id":"2012.12148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.12148","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"2012.12148v2","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.12148","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"I4JHVKM33T2A","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"pith_short_16","alias_value":"I4JHVKM33T2ALSLR","created_at":"2026-07-05T03:24:40Z"},{"alias_kind":"pith_short_8","alias_value":"I4JHVKM3","created_at":"2026-07-05T03:24:40Z"}],"graph_snapshots":[{"event_id":"sha256:e110f981587d0e076eed46625c92c044447f0cba84716fa0775624f3beab15b1","target":"graph","created_at":"2026-07-05T03:24:40Z","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/2012.12148/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we will show how to classify Legendrian and transverse knots in the knot type of \"sufficiently positive\" cables of a knot in terms of the classification of the underlying knot. We will also completely explain the phenomena of \"Legendrian large\" cables. These are Legendrian representatives of cables that have Thurston-Bennequin invariant larger that the framing coming from the cabling torus. Such examples have only recently, and unexpectedly, been found. We will also give criteria that determines the classification of Legendrian and transverse knots the the knot type of negative c","authors_text":"Apratim Chakraborty, Hyunki Min, John B. Etnyre","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-12-22T16:38:18Z","title":"Cabling Legendrian and transverse knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.12148","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:ecf38f2229ca341fc477669cbf8e5437f2cae0a33774b7e823b11d848c1c0a0a","target":"record","created_at":"2026-07-05T03:24:40Z","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":"448f51a26a54fe2fe8a4650cfec494b6e6a7b53c7c75f639f23ffcb4d96c38e2","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-12-22T16:38:18Z","title_canon_sha256":"6a0097c2fb9c5a4cd626d8e724ebb5d53cc37e381065a4f0e43740895dc6aa95"},"schema_version":"1.0","source":{"id":"2012.12148","kind":"arxiv","version":2}},"canonical_sha256":"47127aa99bdcf405c97114b99749b6922dbf05c4268f3ebcafbb8cfdfefff4ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47127aa99bdcf405c97114b99749b6922dbf05c4268f3ebcafbb8cfdfefff4ef","first_computed_at":"2026-07-05T03:24:40.802927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:24:40.802927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MfQ+BHRbw/7wcAvOltLtA87NLQbpItB7Vq05hce1qCVFcmB+/vyUx+nIhdc1BO7lLX3BYlZAgsAUF71lolXjCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:24:40.803376Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.12148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecf38f2229ca341fc477669cbf8e5437f2cae0a33774b7e823b11d848c1c0a0a","sha256:e110f981587d0e076eed46625c92c044447f0cba84716fa0775624f3beab15b1"],"state_sha256":"10c6bf72439007be6da43ce1d665f69a44a0a0c4a7692d4208a75d1dfd3990a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QB6XW3/J/oYrZfjnv5S18Qvm7lxaxIC8QNbsxSLbrwFXcJYzrY2KApaiMhDgG76LYC1ltdW03CGxE5PUzF02AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T13:18:56.243273Z","bundle_sha256":"367f36bebc2a078d7c232d24c43455255c83fa54808beac752839184ba0317e0"}}