{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OYUNOLPFWNJVU3DVE23S7CQKEC","short_pith_number":"pith:OYUNOLPF","canonical_record":{"source":{"id":"1303.1063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-05T15:22:03Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"47c36d0f02185ba99cdfd060def998404c9ca6f66a85fa16064aaccb7f9d9793","abstract_canon_sha256":"2f85ef8582c4c07069c350aadb554bf1dec5ff81b315cf3950b3a2a512d523ba"},"schema_version":"1.0"},"canonical_sha256":"7628d72de5b3535a6c7526b72f8a0a208d318b66e03268fcbea5f5def2bbd811","source":{"kind":"arxiv","id":"1303.1063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1063","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1063v1","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1063","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"OYUNOLPFWNJV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OYUNOLPFWNJVU3DV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OYUNOLPF","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OYUNOLPFWNJVU3DVE23S7CQKEC","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-05T15:22:03Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"47c36d0f02185ba99cdfd060def998404c9ca6f66a85fa16064aaccb7f9d9793","abstract_canon_sha256":"2f85ef8582c4c07069c350aadb554bf1dec5ff81b315cf3950b3a2a512d523ba"},"schema_version":"1.0"},"canonical_sha256":"7628d72de5b3535a6c7526b72f8a0a208d318b66e03268fcbea5f5def2bbd811","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:45.657071Z","signature_b64":"U/diENVxwzvPUo9UUjDw3TCpTktR28bCRrivk/dPsVNzQpRwCq0+tQeEdsk03U0FKm8Y71Lq0jAnHvFM6NufDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7628d72de5b3535a6c7526b72f8a0a208d318b66e03268fcbea5f5def2bbd811","last_reissued_at":"2026-05-18T03:31:45.656415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:45.656415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1063","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":"2026-05-18T03:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GO5Q+WEB6u3xOE6Kar5wz64wBSJK3REDyQqVpM653eRy9T1tP6EXuQYyzTWsknHhjkxkXAuEKYAZ/LU7p0QxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:02:05.269075Z"},"content_sha256":"c67a3decd6600b93c0e4238ddf8a87cffe08a6b2931ae2b2cfc8d2d26b69de63","schema_version":"1.0","event_id":"sha256:c67a3decd6600b93c0e4238ddf8a87cffe08a6b2931ae2b2cfc8d2d26b69de63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OYUNOLPFWNJVU3DVE23S7CQKEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological methods in 3-dimensional contact geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Patrick Massot","submitted_at":"2013-03-05T15:22:03Z","abstract_excerpt":"These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. They put a special emphasis on pictures and discussions of explicit examples. The first goal is to explain why all the information about a contact structure in a neighborhood of a generic surface is encoded by finitely many curves on the surface. Then we describe the bifurcations that happen in generic families of surfaces. As applications, we explain how Giroux used this technology to reprove Bennequin's theorem saying that the standard contact structure on S^3 is ti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1063","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":"2026-05-18T03:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AS/1KJV3rdOprbnOa4EkwfO9KDCUd9vjB4sRuQksK2WT18NxOEhQH11s223pb6Amukq5lVO1cdke/e9nqGMUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:02:05.269435Z"},"content_sha256":"968185b0cf4aded01b9925963ec17fc728c7bc9cc1186c7d0658625f6447597c","schema_version":"1.0","event_id":"sha256:968185b0cf4aded01b9925963ec17fc728c7bc9cc1186c7d0658625f6447597c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYUNOLPFWNJVU3DVE23S7CQKEC/bundle.json","state_url":"https://pith.science/pith/OYUNOLPFWNJVU3DVE23S7CQKEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYUNOLPFWNJVU3DVE23S7CQKEC/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":"2026-06-24T20:02:05Z","links":{"resolver":"https://pith.science/pith/OYUNOLPFWNJVU3DVE23S7CQKEC","bundle":"https://pith.science/pith/OYUNOLPFWNJVU3DVE23S7CQKEC/bundle.json","state":"https://pith.science/pith/OYUNOLPFWNJVU3DVE23S7CQKEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYUNOLPFWNJVU3DVE23S7CQKEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OYUNOLPFWNJVU3DVE23S7CQKEC","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":"2f85ef8582c4c07069c350aadb554bf1dec5ff81b315cf3950b3a2a512d523ba","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-05T15:22:03Z","title_canon_sha256":"47c36d0f02185ba99cdfd060def998404c9ca6f66a85fa16064aaccb7f9d9793"},"schema_version":"1.0","source":{"id":"1303.1063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1063","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1063v1","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1063","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"OYUNOLPFWNJV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OYUNOLPFWNJVU3DV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OYUNOLPF","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:968185b0cf4aded01b9925963ec17fc728c7bc9cc1186c7d0658625f6447597c","target":"graph","created_at":"2026-05-18T03:31:45Z","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":"These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. They put a special emphasis on pictures and discussions of explicit examples. The first goal is to explain why all the information about a contact structure in a neighborhood of a generic surface is encoded by finitely many curves on the surface. Then we describe the bifurcations that happen in generic families of surfaces. As applications, we explain how Giroux used this technology to reprove Bennequin's theorem saying that the standard contact structure on S^3 is ti","authors_text":"Patrick Massot","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-05T15:22:03Z","title":"Topological methods in 3-dimensional contact geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1063","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:c67a3decd6600b93c0e4238ddf8a87cffe08a6b2931ae2b2cfc8d2d26b69de63","target":"record","created_at":"2026-05-18T03:31:45Z","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":"2f85ef8582c4c07069c350aadb554bf1dec5ff81b315cf3950b3a2a512d523ba","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-05T15:22:03Z","title_canon_sha256":"47c36d0f02185ba99cdfd060def998404c9ca6f66a85fa16064aaccb7f9d9793"},"schema_version":"1.0","source":{"id":"1303.1063","kind":"arxiv","version":1}},"canonical_sha256":"7628d72de5b3535a6c7526b72f8a0a208d318b66e03268fcbea5f5def2bbd811","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7628d72de5b3535a6c7526b72f8a0a208d318b66e03268fcbea5f5def2bbd811","first_computed_at":"2026-05-18T03:31:45.656415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:45.656415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/diENVxwzvPUo9UUjDw3TCpTktR28bCRrivk/dPsVNzQpRwCq0+tQeEdsk03U0FKm8Y71Lq0jAnHvFM6NufDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:45.657071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c67a3decd6600b93c0e4238ddf8a87cffe08a6b2931ae2b2cfc8d2d26b69de63","sha256:968185b0cf4aded01b9925963ec17fc728c7bc9cc1186c7d0658625f6447597c"],"state_sha256":"bba29d528dd50328e7c3af4d83eb3609932e495a16688e9322d5fffa04c13a4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1xVkAUMVopYo7qUaUB3eIxPk88KFw1YVgKUrQgWtQ1VncDOlJ26uDc7hX8YV3RQPiLoSLhj4Gpg6gD1doDYBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:02:05.271344Z","bundle_sha256":"ab6473af899d5a16ecefa5335e70d532cf9ea5e6b4922469418e9d1f71004cb1"}}