{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AOI6XRG7JTSBOIGGEZJ73NHGT5","short_pith_number":"pith:AOI6XRG7","canonical_record":{"source":{"id":"1301.3767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-01-16T17:57:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"7353a8d02c4473b80572f88aa661b651e9191ea0bcc3b138d0cdc22059dc5357","abstract_canon_sha256":"f4b9a567fedbee88ac164d7fca40c20353c7acce274a39e03360820117cf81dc"},"schema_version":"1.0"},"canonical_sha256":"0391ebc4df4ce41720c62653fdb4e69f4f147db868f7427afeaeaeb2ecc34c5f","source":{"kind":"arxiv","id":"1301.3767","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3767","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3767v2","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3767","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"AOI6XRG7JTSB","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AOI6XRG7JTSBOIGG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AOI6XRG7","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AOI6XRG7JTSBOIGGEZJ73NHGT5","target":"record","payload":{"canonical_record":{"source":{"id":"1301.3767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-01-16T17:57:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"7353a8d02c4473b80572f88aa661b651e9191ea0bcc3b138d0cdc22059dc5357","abstract_canon_sha256":"f4b9a567fedbee88ac164d7fca40c20353c7acce274a39e03360820117cf81dc"},"schema_version":"1.0"},"canonical_sha256":"0391ebc4df4ce41720c62653fdb4e69f4f147db868f7427afeaeaeb2ecc34c5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:45.228181Z","signature_b64":"zJfgtm2xxd1SIgodP6S9nyPJFlM6QIdI4FLHGlCpxh630LGcUkeqyN0ypL3Q/GXjBrYtFBDZoz9o3Q1BfPseAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0391ebc4df4ce41720c62653fdb4e69f4f147db868f7427afeaeaeb2ecc34c5f","last_reissued_at":"2026-05-18T03:15:45.227425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:45.227425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.3767","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":"2026-05-18T03:15:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7s7nXV/IAu5H6uRAPEJjrNRJdKcBI7gJueEL6F+52n7Ah1cWzNKfMC63vUBUmBUfTInu4i61geVNQ28zrZ6MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:41:57.586783Z"},"content_sha256":"cd6c874df088384dff00beef61390e49571c91337b066079d1722b66acde1095","schema_version":"1.0","event_id":"sha256:cd6c874df088384dff00beef61390e49571c91337b066079d1722b66acde1095"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AOI6XRG7JTSBOIGGEZJ73NHGT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lagrangian concordance is not a symmetric relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Baptiste Chantraine","submitted_at":"2013-01-16T17:57:17Z","abstract_excerpt":"We provide an explicit example of a non trivial Legendrian knot $\\Lambda$ such that there exists a Lagrangian concordance from $\\Lambda_0$ to $\\Lambda$ where $\\Lambda_0$ is the trivial Legendrian knot. We then use the map induced in Legendrian contact homology by a concordance and the augmentation category of $\\Lambda$ to show that no Lagrangian concordance exists in the other direction. This proves that the relation of Lagrangian concordance is not symmetric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3767","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":""},"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":"2026-05-18T03:15:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYbBTjoE5gXqe5S1IkRBsAJ7EsCD/1UqM6Lguov9ufn1xFa1i0yCdXPtQX7VUKk27vOJY8rwkKvLeiHlXOy3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:41:57.587466Z"},"content_sha256":"1948e2bcbbd356b37f35807782af26bdc3539e0fa2da0165d20690b658e11c80","schema_version":"1.0","event_id":"sha256:1948e2bcbbd356b37f35807782af26bdc3539e0fa2da0165d20690b658e11c80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOI6XRG7JTSBOIGGEZJ73NHGT5/bundle.json","state_url":"https://pith.science/pith/AOI6XRG7JTSBOIGGEZJ73NHGT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOI6XRG7JTSBOIGGEZJ73NHGT5/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":"2026-05-31T14:41:57Z","links":{"resolver":"https://pith.science/pith/AOI6XRG7JTSBOIGGEZJ73NHGT5","bundle":"https://pith.science/pith/AOI6XRG7JTSBOIGGEZJ73NHGT5/bundle.json","state":"https://pith.science/pith/AOI6XRG7JTSBOIGGEZJ73NHGT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOI6XRG7JTSBOIGGEZJ73NHGT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AOI6XRG7JTSBOIGGEZJ73NHGT5","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":"f4b9a567fedbee88ac164d7fca40c20353c7acce274a39e03360820117cf81dc","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-01-16T17:57:17Z","title_canon_sha256":"7353a8d02c4473b80572f88aa661b651e9191ea0bcc3b138d0cdc22059dc5357"},"schema_version":"1.0","source":{"id":"1301.3767","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3767","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3767v2","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3767","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"AOI6XRG7JTSB","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AOI6XRG7JTSBOIGG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AOI6XRG7","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:1948e2bcbbd356b37f35807782af26bdc3539e0fa2da0165d20690b658e11c80","target":"graph","created_at":"2026-05-18T03:15:45Z","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":"We provide an explicit example of a non trivial Legendrian knot $\\Lambda$ such that there exists a Lagrangian concordance from $\\Lambda_0$ to $\\Lambda$ where $\\Lambda_0$ is the trivial Legendrian knot. We then use the map induced in Legendrian contact homology by a concordance and the augmentation category of $\\Lambda$ to show that no Lagrangian concordance exists in the other direction. This proves that the relation of Lagrangian concordance is not symmetric.","authors_text":"Baptiste Chantraine","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-01-16T17:57:17Z","title":"Lagrangian concordance is not a symmetric relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3767","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:cd6c874df088384dff00beef61390e49571c91337b066079d1722b66acde1095","target":"record","created_at":"2026-05-18T03:15:45Z","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":"f4b9a567fedbee88ac164d7fca40c20353c7acce274a39e03360820117cf81dc","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-01-16T17:57:17Z","title_canon_sha256":"7353a8d02c4473b80572f88aa661b651e9191ea0bcc3b138d0cdc22059dc5357"},"schema_version":"1.0","source":{"id":"1301.3767","kind":"arxiv","version":2}},"canonical_sha256":"0391ebc4df4ce41720c62653fdb4e69f4f147db868f7427afeaeaeb2ecc34c5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0391ebc4df4ce41720c62653fdb4e69f4f147db868f7427afeaeaeb2ecc34c5f","first_computed_at":"2026-05-18T03:15:45.227425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:45.227425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zJfgtm2xxd1SIgodP6S9nyPJFlM6QIdI4FLHGlCpxh630LGcUkeqyN0ypL3Q/GXjBrYtFBDZoz9o3Q1BfPseAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:45.228181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3767","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd6c874df088384dff00beef61390e49571c91337b066079d1722b66acde1095","sha256:1948e2bcbbd356b37f35807782af26bdc3539e0fa2da0165d20690b658e11c80"],"state_sha256":"fcd482cc6174d9cddf7a320eff508ded98880ceb0343528f36454994c3fd58f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LkmUx2gVByNpnRaNv5cghoQdCZMuNLDbxyN6Z2gjreyatGVPdtCdS90y0DHar2sJx3Y2NHq4Ac9opYBHYUh5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:41:57.591119Z","bundle_sha256":"63a9db66826f6716d6c35fcab7b37430411561044c4008992f17c8306b7c0e33"}}