{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZBTB6BCQYVOYMRT4RPWXH3GVPZ","short_pith_number":"pith:ZBTB6BCQ","canonical_record":{"source":{"id":"1309.3870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-16T09:18:53Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"0e194e749a67605a5269cd6ae9fa0aa476c2a0b2b8b77028b15bef2ec2d106f2","abstract_canon_sha256":"6ff90cde3389c49c7fe94811d745808537008240f8c98f8f1c413b8c2da4e5ac"},"schema_version":"1.0"},"canonical_sha256":"c8661f0450c55d86467c8bed73ecd57e6f2c4d0915b9fe5256d82c03c3acdd0d","source":{"kind":"arxiv","id":"1309.3870","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3870","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3870v2","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3870","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZBTB6BCQYVOY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBTB6BCQYVOYMRT4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBTB6BCQ","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZBTB6BCQYVOYMRT4RPWXH3GVPZ","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-16T09:18:53Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"0e194e749a67605a5269cd6ae9fa0aa476c2a0b2b8b77028b15bef2ec2d106f2","abstract_canon_sha256":"6ff90cde3389c49c7fe94811d745808537008240f8c98f8f1c413b8c2da4e5ac"},"schema_version":"1.0"},"canonical_sha256":"c8661f0450c55d86467c8bed73ecd57e6f2c4d0915b9fe5256d82c03c3acdd0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:09.708860Z","signature_b64":"xA69hPg6LnK2drKPhET1VwGjI9V6FdSKj/5DNaUguBvVdSChMnSt9XGZXTd73ZByR8bIv06WvOnXdjnVcC6pBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8661f0450c55d86467c8bed73ecd57e6f2c4d0915b9fe5256d82c03c3acdd0d","last_reissued_at":"2026-05-18T03:03:09.708157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:09.708157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3870","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":"2026-05-18T03:03:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDZ9UXGMbo+zpOjbORGHleWaxxbSbMxYsiH0+SChiIvQlJx0bV0meLvBkYSBf0aR2Km+iTDF5EdCf9Y18cLRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:09:52.616334Z"},"content_sha256":"4ee56102e0c6b3eef5c5917c5cfe3f4ffab0bcf102ccbc7691aad55604bc29e0","schema_version":"1.0","event_id":"sha256:4ee56102e0c6b3eef5c5917c5cfe3f4ffab0bcf102ccbc7691aad55604bc29e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZBTB6BCQYVOYMRT4RPWXH3GVPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved bounds for the shortness coefficient of cyclically 4-edge connected cubic graphs and snarks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Klas Markstr\\\"om","submitted_at":"2013-09-16T09:18:53Z","abstract_excerpt":"We present a construction which shows that there is an infinite set of cyclically 4-edge connected cubic graphs on $n$ vertices with no cycle longer than $c_4 n$ for $c_4=\\frac{12}{13}$, and at the same time prove that a certain natural family of cubic graphs cannot be used to lower the shortness coefficient $c_4$ to 0.\n  The graphs we construct are snarks so we get the same upper bound for the shortness coefficient of snarks, and we prove that the constructed graphs have an oddness growing linearly with the number of vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3870","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":"2026-05-18T03:03:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jquAKD4L9Xpx39r4l8sx7b8UTiB1RZ51mdrdNTisO68h54w4tTJXPVRp1x0YxoCLeUJEfby7hpJSD2ReziRgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:09:52.617004Z"},"content_sha256":"c4dfd94a00c6883b3796341f1d8622914dd08b9754cff3cc4980db1bf6dc2a53","schema_version":"1.0","event_id":"sha256:c4dfd94a00c6883b3796341f1d8622914dd08b9754cff3cc4980db1bf6dc2a53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBTB6BCQYVOYMRT4RPWXH3GVPZ/bundle.json","state_url":"https://pith.science/pith/ZBTB6BCQYVOYMRT4RPWXH3GVPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBTB6BCQYVOYMRT4RPWXH3GVPZ/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":"2026-06-06T14:09:52Z","links":{"resolver":"https://pith.science/pith/ZBTB6BCQYVOYMRT4RPWXH3GVPZ","bundle":"https://pith.science/pith/ZBTB6BCQYVOYMRT4RPWXH3GVPZ/bundle.json","state":"https://pith.science/pith/ZBTB6BCQYVOYMRT4RPWXH3GVPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBTB6BCQYVOYMRT4RPWXH3GVPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZBTB6BCQYVOYMRT4RPWXH3GVPZ","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":"6ff90cde3389c49c7fe94811d745808537008240f8c98f8f1c413b8c2da4e5ac","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-16T09:18:53Z","title_canon_sha256":"0e194e749a67605a5269cd6ae9fa0aa476c2a0b2b8b77028b15bef2ec2d106f2"},"schema_version":"1.0","source":{"id":"1309.3870","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3870","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3870v2","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3870","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZBTB6BCQYVOY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBTB6BCQYVOYMRT4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBTB6BCQ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:c4dfd94a00c6883b3796341f1d8622914dd08b9754cff3cc4980db1bf6dc2a53","target":"graph","created_at":"2026-05-18T03:03:09Z","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 present a construction which shows that there is an infinite set of cyclically 4-edge connected cubic graphs on $n$ vertices with no cycle longer than $c_4 n$ for $c_4=\\frac{12}{13}$, and at the same time prove that a certain natural family of cubic graphs cannot be used to lower the shortness coefficient $c_4$ to 0.\n  The graphs we construct are snarks so we get the same upper bound for the shortness coefficient of snarks, and we prove that the constructed graphs have an oddness growing linearly with the number of vertices.","authors_text":"Klas Markstr\\\"om","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-16T09:18:53Z","title":"Improved bounds for the shortness coefficient of cyclically 4-edge connected cubic graphs and snarks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3870","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":"sha256:4ee56102e0c6b3eef5c5917c5cfe3f4ffab0bcf102ccbc7691aad55604bc29e0","target":"record","created_at":"2026-05-18T03:03:09Z","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":"6ff90cde3389c49c7fe94811d745808537008240f8c98f8f1c413b8c2da4e5ac","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-16T09:18:53Z","title_canon_sha256":"0e194e749a67605a5269cd6ae9fa0aa476c2a0b2b8b77028b15bef2ec2d106f2"},"schema_version":"1.0","source":{"id":"1309.3870","kind":"arxiv","version":2}},"canonical_sha256":"c8661f0450c55d86467c8bed73ecd57e6f2c4d0915b9fe5256d82c03c3acdd0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8661f0450c55d86467c8bed73ecd57e6f2c4d0915b9fe5256d82c03c3acdd0d","first_computed_at":"2026-05-18T03:03:09.708157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:09.708157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xA69hPg6LnK2drKPhET1VwGjI9V6FdSKj/5DNaUguBvVdSChMnSt9XGZXTd73ZByR8bIv06WvOnXdjnVcC6pBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:09.708860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3870","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ee56102e0c6b3eef5c5917c5cfe3f4ffab0bcf102ccbc7691aad55604bc29e0","sha256:c4dfd94a00c6883b3796341f1d8622914dd08b9754cff3cc4980db1bf6dc2a53"],"state_sha256":"cdb5b99f032fb6b3b008af9946702fad947131c4044171c15f52aac3c12f29a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OtJIIc1mc+wYUbsdoRMXbYQhvzbWD874e3AusyE75PNKI38shJacIdp2u35rQKY7RUcwIBaVLk+PGcYBNij+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:09:52.620486Z","bundle_sha256":"f1ace04e6abe3c5cbb6a82bd5c791218ecc7b7b475af202cea2d4141a7c05a96"}}