{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:5DCRB4S54DGETWBERAB4FWBQ2D","short_pith_number":"pith:5DCRB4S5","canonical_record":{"source":{"id":"0911.0452","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-02T22:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"04fbb6218a40181fd7aefb4ccd8a398daeefc1a5934823b0ea61a57205a31528","abstract_canon_sha256":"bc0efe5821318cd71beddbb4d70440e654fb07287013436d8f0890b9d384ed5b"},"schema_version":"1.0"},"canonical_sha256":"e8c510f25de0cc49d8248803c2d830d0fc589dda41b1942341b146c926a0d80d","source":{"kind":"arxiv","id":"0911.0452","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0452","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0452v2","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0452","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"5DCRB4S54DGE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5DCRB4S54DGETWBE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5DCRB4S5","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:5DCRB4S54DGETWBERAB4FWBQ2D","target":"record","payload":{"canonical_record":{"source":{"id":"0911.0452","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-02T22:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"04fbb6218a40181fd7aefb4ccd8a398daeefc1a5934823b0ea61a57205a31528","abstract_canon_sha256":"bc0efe5821318cd71beddbb4d70440e654fb07287013436d8f0890b9d384ed5b"},"schema_version":"1.0"},"canonical_sha256":"e8c510f25de0cc49d8248803c2d830d0fc589dda41b1942341b146c926a0d80d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:26.214216Z","signature_b64":"C6AFzLA+vGw9rolmyo1dl1geTEyivWdrFHOV/16+mGpgsqXSRutEQF6h0aMADxkgx+8sl0Q1aEeB69DpCr3LBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8c510f25de0cc49d8248803c2d830d0fc589dda41b1942341b146c926a0d80d","last_reissued_at":"2026-05-18T04:41:26.213490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:26.213490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.0452","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":"2026-05-18T04:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s1Xci7VpZykj6ukK6Z9lEBuXBUpjhnnqUC7r8ZCfFZxUrFIQGp7leQ4yKOsobUdgaEZ1vLrEcTudd5cSNUdfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:26:49.094045Z"},"content_sha256":"35d0e510b579e2c1fabca9e4a12d0787d191540e778617626d98c7caa3d4eed7","schema_version":"1.0","event_id":"sha256:35d0e510b579e2c1fabca9e4a12d0787d191540e778617626d98c7caa3d4eed7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:5DCRB4S54DGETWBERAB4FWBQ2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unexpected behaviour of crossing sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bojan Mohar, Matt DeVos, Robert Samal","submitted_at":"2009-11-02T22:42:57Z","abstract_excerpt":"The n-th crossing number of a graph G, denoted cr_n(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a>b>0, there exists a graph G for which cr_0(G) = a, cr_1(G) = b, and cr_2(G) = 0. This provides support for a conjecture of Archdeacon et al. and resolves a problem of Salazar."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0452","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":"2026-05-18T04:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JP70ReiUkqJmYV5B7IlBPCSqzqDdRX3oti+gOT2Lg1Y7sGuBRqg5waB7RZfT5hbYrXrZKmmBc1FiHrCra0oCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:26:49.094400Z"},"content_sha256":"73900db513834398f5c1077054b52d4022664d702b442e6493b5c0689f2fac22","schema_version":"1.0","event_id":"sha256:73900db513834398f5c1077054b52d4022664d702b442e6493b5c0689f2fac22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DCRB4S54DGETWBERAB4FWBQ2D/bundle.json","state_url":"https://pith.science/pith/5DCRB4S54DGETWBERAB4FWBQ2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DCRB4S54DGETWBERAB4FWBQ2D/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":"2026-06-20T22:26:49Z","links":{"resolver":"https://pith.science/pith/5DCRB4S54DGETWBERAB4FWBQ2D","bundle":"https://pith.science/pith/5DCRB4S54DGETWBERAB4FWBQ2D/bundle.json","state":"https://pith.science/pith/5DCRB4S54DGETWBERAB4FWBQ2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DCRB4S54DGETWBERAB4FWBQ2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5DCRB4S54DGETWBERAB4FWBQ2D","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":"bc0efe5821318cd71beddbb4d70440e654fb07287013436d8f0890b9d384ed5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-02T22:42:57Z","title_canon_sha256":"04fbb6218a40181fd7aefb4ccd8a398daeefc1a5934823b0ea61a57205a31528"},"schema_version":"1.0","source":{"id":"0911.0452","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0452","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0452v2","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0452","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"5DCRB4S54DGE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5DCRB4S54DGETWBE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5DCRB4S5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:73900db513834398f5c1077054b52d4022664d702b442e6493b5c0689f2fac22","target":"graph","created_at":"2026-05-18T04:41:26Z","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":"The n-th crossing number of a graph G, denoted cr_n(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a>b>0, there exists a graph G for which cr_0(G) = a, cr_1(G) = b, and cr_2(G) = 0. This provides support for a conjecture of Archdeacon et al. and resolves a problem of Salazar.","authors_text":"Bojan Mohar, Matt DeVos, Robert Samal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-02T22:42:57Z","title":"Unexpected behaviour of crossing sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0452","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":"sha256:35d0e510b579e2c1fabca9e4a12d0787d191540e778617626d98c7caa3d4eed7","target":"record","created_at":"2026-05-18T04:41:26Z","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":"bc0efe5821318cd71beddbb4d70440e654fb07287013436d8f0890b9d384ed5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-02T22:42:57Z","title_canon_sha256":"04fbb6218a40181fd7aefb4ccd8a398daeefc1a5934823b0ea61a57205a31528"},"schema_version":"1.0","source":{"id":"0911.0452","kind":"arxiv","version":2}},"canonical_sha256":"e8c510f25de0cc49d8248803c2d830d0fc589dda41b1942341b146c926a0d80d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c510f25de0cc49d8248803c2d830d0fc589dda41b1942341b146c926a0d80d","first_computed_at":"2026-05-18T04:41:26.213490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:26.213490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C6AFzLA+vGw9rolmyo1dl1geTEyivWdrFHOV/16+mGpgsqXSRutEQF6h0aMADxkgx+8sl0Q1aEeB69DpCr3LBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:26.214216Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0452","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35d0e510b579e2c1fabca9e4a12d0787d191540e778617626d98c7caa3d4eed7","sha256:73900db513834398f5c1077054b52d4022664d702b442e6493b5c0689f2fac22"],"state_sha256":"ddaaadc22c8baa6082f15cb242e2f7531aef7f07090a15aa703e4a5383794e12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaJ42aSiV4HhbkQrf3JwjQ75dJdKX+Pulp1Ab8sayNlrZ5fJ/ix/K5lVQ2u2mz+/qxqVoplPf7zE78Bkyim5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:26:49.096237Z","bundle_sha256":"ff3d923765e04008d7baf365f06edd783756221c1d241026b16cb26a115877b8"}}