{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:KG2LSKL5DWJVSLUJJFYTAWXFGO","short_pith_number":"pith:KG2LSKL5","canonical_record":{"source":{"id":"math/0605441","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-05-16T16:24:28Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"37e22fb8ab98e1e86c8008df3c7a14f167c9cb8cf9ba97f09e00b7d1133edaef","abstract_canon_sha256":"c14626c6d5cb45db962ace53c8b4bd8d3f6394c907b1227b01747271171f13fa"},"schema_version":"1.0"},"canonical_sha256":"51b4b9297d1d93592e894971305ae5338ed69e89018d35cb0faf35729ede6a22","source":{"kind":"arxiv","id":"math/0605441","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605441","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605441v1","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605441","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"KG2LSKL5DWJV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KG2LSKL5DWJVSLUJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KG2LSKL5","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:KG2LSKL5DWJVSLUJJFYTAWXFGO","target":"record","payload":{"canonical_record":{"source":{"id":"math/0605441","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-05-16T16:24:28Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"37e22fb8ab98e1e86c8008df3c7a14f167c9cb8cf9ba97f09e00b7d1133edaef","abstract_canon_sha256":"c14626c6d5cb45db962ace53c8b4bd8d3f6394c907b1227b01747271171f13fa"},"schema_version":"1.0"},"canonical_sha256":"51b4b9297d1d93592e894971305ae5338ed69e89018d35cb0faf35729ede6a22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:19.901048Z","signature_b64":"a8lmgIu+Xx2GWD/RjAmkz5ukAq5FsmCO2CrlZafWQiXWMoICNsSwZgfb1V6LsPSQ+9M4JbMj9nMw6I7Af5IuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51b4b9297d1d93592e894971305ae5338ed69e89018d35cb0faf35729ede6a22","last_reissued_at":"2026-05-18T00:12:19.900366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:19.900366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0605441","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":"2026-05-18T00:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dp2FCbzQG6m1eV8ubl/LskiUhp3ylGgyiDXCQhxyi5OzKrdnDvKUWT6cxMISWDeBpH27kD9wLlOXgsDBSzKaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:10:05.339989Z"},"content_sha256":"d43a8bd956cceec928282c185b58184d3bbf8f41e10fcd26fab3889c5a159508","schema_version":"1.0","event_id":"sha256:d43a8bd956cceec928282c185b58184d3bbf8f41e10fcd26fab3889c5a159508"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:KG2LSKL5DWJVSLUJJFYTAWXFGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants of contact structures from open books","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Burak Ozbagci, John B. Etnyre","submitted_at":"2006-05-16T16:24:28Z","abstract_excerpt":"In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components of a supporting open book for the contact structure with minimal genus pages) and the norm (which is minus the maximal Euler characteristic of a page of a supporting open book)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605441","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":"2026-05-18T00:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WJzmjAB7ZeqI7voSxm8HFZbLCbZvjzkQaj8WdqfiuEsuH07Ju0F/CuzB8xZKTUhcyYBAfQLZ1MBlrZn/NXpBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:10:05.340431Z"},"content_sha256":"aabb8e3c21ea2af176023b6b80d232865f9bd9188a18a9221d3e03fe01782bbd","schema_version":"1.0","event_id":"sha256:aabb8e3c21ea2af176023b6b80d232865f9bd9188a18a9221d3e03fe01782bbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KG2LSKL5DWJVSLUJJFYTAWXFGO/bundle.json","state_url":"https://pith.science/pith/KG2LSKL5DWJVSLUJJFYTAWXFGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KG2LSKL5DWJVSLUJJFYTAWXFGO/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":"2026-08-09T06:10:05Z","links":{"resolver":"https://pith.science/pith/KG2LSKL5DWJVSLUJJFYTAWXFGO","bundle":"https://pith.science/pith/KG2LSKL5DWJVSLUJJFYTAWXFGO/bundle.json","state":"https://pith.science/pith/KG2LSKL5DWJVSLUJJFYTAWXFGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KG2LSKL5DWJVSLUJJFYTAWXFGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:KG2LSKL5DWJVSLUJJFYTAWXFGO","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":"c14626c6d5cb45db962ace53c8b4bd8d3f6394c907b1227b01747271171f13fa","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2006-05-16T16:24:28Z","title_canon_sha256":"37e22fb8ab98e1e86c8008df3c7a14f167c9cb8cf9ba97f09e00b7d1133edaef"},"schema_version":"1.0","source":{"id":"math/0605441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605441","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605441v1","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605441","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"KG2LSKL5DWJV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KG2LSKL5DWJVSLUJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KG2LSKL5","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:aabb8e3c21ea2af176023b6b80d232865f9bd9188a18a9221d3e03fe01782bbd","target":"graph","created_at":"2026-05-18T00:12:19Z","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":"In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components of a supporting open book for the contact structure with minimal genus pages) and the norm (which is minus the maximal Euler characteristic of a page of a supporting open book).","authors_text":"Burak Ozbagci, John B. Etnyre","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2006-05-16T16:24:28Z","title":"Invariants of contact structures from open books"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605441","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:d43a8bd956cceec928282c185b58184d3bbf8f41e10fcd26fab3889c5a159508","target":"record","created_at":"2026-05-18T00:12:19Z","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":"c14626c6d5cb45db962ace53c8b4bd8d3f6394c907b1227b01747271171f13fa","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2006-05-16T16:24:28Z","title_canon_sha256":"37e22fb8ab98e1e86c8008df3c7a14f167c9cb8cf9ba97f09e00b7d1133edaef"},"schema_version":"1.0","source":{"id":"math/0605441","kind":"arxiv","version":1}},"canonical_sha256":"51b4b9297d1d93592e894971305ae5338ed69e89018d35cb0faf35729ede6a22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51b4b9297d1d93592e894971305ae5338ed69e89018d35cb0faf35729ede6a22","first_computed_at":"2026-05-18T00:12:19.900366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:19.900366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a8lmgIu+Xx2GWD/RjAmkz5ukAq5FsmCO2CrlZafWQiXWMoICNsSwZgfb1V6LsPSQ+9M4JbMj9nMw6I7Af5IuDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:19.901048Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d43a8bd956cceec928282c185b58184d3bbf8f41e10fcd26fab3889c5a159508","sha256:aabb8e3c21ea2af176023b6b80d232865f9bd9188a18a9221d3e03fe01782bbd"],"state_sha256":"5ef2278b798dd14f4432e94041d700d31755536d1361e53833d48d68af6a1619"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LYIZpRwOov3PlXNfdsWm6B6jPFeHHDC+zVarlMCa9+ZqN6FZzT6DT6TSrw2zK9x90enAriFebZFWWgz8CcACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:10:05.343714Z","bundle_sha256":"25766031be0dce38a8fd57ba22d9965131a48951122e2ac69a003fac0496d6a4"}}