{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PE254L6IKQ7DADR5WGHBZTFME2","short_pith_number":"pith:PE254L6I","canonical_record":{"source":{"id":"1109.1319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-06T22:49:00Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"39bec99e04450456ad13b9af3c6605aefabc227383cf7fe1d7f6257660ee86a4","abstract_canon_sha256":"617199754e69dab404a0dab48c61cde060f7a6172d0a993dbf08667fd8577f16"},"schema_version":"1.0"},"canonical_sha256":"7935de2fc8543e300e3db18e1cccac26a13c3456a60c199ebac215376b6af063","source":{"kind":"arxiv","id":"1109.1319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1319","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1319v1","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1319","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"PE254L6IKQ7D","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PE254L6IKQ7DADR5","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PE254L6I","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PE254L6IKQ7DADR5WGHBZTFME2","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-06T22:49:00Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"39bec99e04450456ad13b9af3c6605aefabc227383cf7fe1d7f6257660ee86a4","abstract_canon_sha256":"617199754e69dab404a0dab48c61cde060f7a6172d0a993dbf08667fd8577f16"},"schema_version":"1.0"},"canonical_sha256":"7935de2fc8543e300e3db18e1cccac26a13c3456a60c199ebac215376b6af063","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:55.980571Z","signature_b64":"azgoD309eawDN69Yk6r1QwMKQjlqRuqAiw0GLT/nFXPNWRivG3NImxaBS8UX2VzrrDDyKNOn2Hr0kH++1WdcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7935de2fc8543e300e3db18e1cccac26a13c3456a60c199ebac215376b6af063","last_reissued_at":"2026-05-18T04:13:55.980069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:55.980069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1319","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":"2026-05-18T04:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Co+0EfUtUkyixreA9FFWl3A1CiUp3Ffg/4QIouhJuj5BZ6kA2JyysiKbUmR5r8zkCwbrPTRnlE/k56VfURpvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:00:16.371988Z"},"content_sha256":"5056ea870d39dafbb4fa4f4d9b69b76c98a20da8710a8ee650dd3a9dd66e293a","schema_version":"1.0","event_id":"sha256:5056ea870d39dafbb4fa4f4d9b69b76c98a20da8710a8ee650dd3a9dd66e293a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PE254L6IKQ7DADR5WGHBZTFME2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized normal rulings and invariants of Legendrian solid torus links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Dan Rutherford, Mikhail Lavrov","submitted_at":"2011-09-06T22:49:00Z","abstract_excerpt":"For Legendrian links in the 1-jet space of $S^1$ we show that the 1-graded ruling polynomial may be recovered from the Kauffman skein module. For such links a generalization of the notion of normal ruling is introduced. We show that the existence of such a generalized normal ruling is equivalent to sharpness of the Kauffman polynomial estimate for the Thurston-Bennequin number as well as to the existence of an ungraded augmentation of the Chekanov-Eliashberg DGA. Parallel results involving the HOMFLY-PT polynomial and 2-graded generalized normal rulings are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1319","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":""},"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":"2026-05-18T04:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVQGN6XBz+F0fWMOSI9BReJKXKSL3m6EoVil1KJm+tKaYOXgeTar7Dr/arVcoDBg8hX/LOR6w1uEZmec5c+LDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:00:16.372809Z"},"content_sha256":"00c2fbb86423b2833a7c69bc240b42615c2bca9af167c902c7a81453f7d057bc","schema_version":"1.0","event_id":"sha256:00c2fbb86423b2833a7c69bc240b42615c2bca9af167c902c7a81453f7d057bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PE254L6IKQ7DADR5WGHBZTFME2/bundle.json","state_url":"https://pith.science/pith/PE254L6IKQ7DADR5WGHBZTFME2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PE254L6IKQ7DADR5WGHBZTFME2/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":"2026-05-30T09:00:16Z","links":{"resolver":"https://pith.science/pith/PE254L6IKQ7DADR5WGHBZTFME2","bundle":"https://pith.science/pith/PE254L6IKQ7DADR5WGHBZTFME2/bundle.json","state":"https://pith.science/pith/PE254L6IKQ7DADR5WGHBZTFME2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PE254L6IKQ7DADR5WGHBZTFME2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PE254L6IKQ7DADR5WGHBZTFME2","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":"617199754e69dab404a0dab48c61cde060f7a6172d0a993dbf08667fd8577f16","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-06T22:49:00Z","title_canon_sha256":"39bec99e04450456ad13b9af3c6605aefabc227383cf7fe1d7f6257660ee86a4"},"schema_version":"1.0","source":{"id":"1109.1319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1319","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1319v1","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1319","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"PE254L6IKQ7D","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PE254L6IKQ7DADR5","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PE254L6I","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:00c2fbb86423b2833a7c69bc240b42615c2bca9af167c902c7a81453f7d057bc","target":"graph","created_at":"2026-05-18T04:13:55Z","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"},"paper":{"abstract_excerpt":"For Legendrian links in the 1-jet space of $S^1$ we show that the 1-graded ruling polynomial may be recovered from the Kauffman skein module. For such links a generalization of the notion of normal ruling is introduced. We show that the existence of such a generalized normal ruling is equivalent to sharpness of the Kauffman polynomial estimate for the Thurston-Bennequin number as well as to the existence of an ungraded augmentation of the Chekanov-Eliashberg DGA. Parallel results involving the HOMFLY-PT polynomial and 2-graded generalized normal rulings are established.","authors_text":"Dan Rutherford, Mikhail Lavrov","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-06T22:49:00Z","title":"Generalized normal rulings and invariants of Legendrian solid torus links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1319","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":"sha256:5056ea870d39dafbb4fa4f4d9b69b76c98a20da8710a8ee650dd3a9dd66e293a","target":"record","created_at":"2026-05-18T04:13:55Z","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":"617199754e69dab404a0dab48c61cde060f7a6172d0a993dbf08667fd8577f16","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-06T22:49:00Z","title_canon_sha256":"39bec99e04450456ad13b9af3c6605aefabc227383cf7fe1d7f6257660ee86a4"},"schema_version":"1.0","source":{"id":"1109.1319","kind":"arxiv","version":1}},"canonical_sha256":"7935de2fc8543e300e3db18e1cccac26a13c3456a60c199ebac215376b6af063","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7935de2fc8543e300e3db18e1cccac26a13c3456a60c199ebac215376b6af063","first_computed_at":"2026-05-18T04:13:55.980069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:55.980069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"azgoD309eawDN69Yk6r1QwMKQjlqRuqAiw0GLT/nFXPNWRivG3NImxaBS8UX2VzrrDDyKNOn2Hr0kH++1WdcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:55.980571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5056ea870d39dafbb4fa4f4d9b69b76c98a20da8710a8ee650dd3a9dd66e293a","sha256:00c2fbb86423b2833a7c69bc240b42615c2bca9af167c902c7a81453f7d057bc"],"state_sha256":"13f78fe843a415981dafc94afff03453cefcf059365aafc8ace4b6308f9f8be0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPJh2nU5GTbGIiJsPEHRK1NkTozlA3L3btxfi7mht+RN/tLZuCoxK9wIkdY0T1mc00xD9cYx9gdiaDjX/OzLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:00:16.377247Z","bundle_sha256":"06d88395838df59115623aa35671a88bd03f5650cb960ae513aec2f3ab947c46"}}