{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6IJ4MCKOVYRCG3LEHM3GVVBREE","short_pith_number":"pith:6IJ4MCKO","canonical_record":{"source":{"id":"1809.08496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-22T22:11:17Z","cross_cats_sorted":[],"title_canon_sha256":"64bf48d7d98dc06bfaaa175f45fdb44068384e9cd5121677e55d43fb1797d179","abstract_canon_sha256":"77d372423289fee5a717e68351d72f5a1ca533388812a30a4f7f061dec5c2ff4"},"schema_version":"1.0"},"canonical_sha256":"f213c6094eae22236d643b366ad43121146dd870b9fecb97eed6176c1715d6d7","source":{"kind":"arxiv","id":"1809.08496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08496","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08496v1","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08496","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"6IJ4MCKOVYRC","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6IJ4MCKOVYRCG3LE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6IJ4MCKO","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6IJ4MCKOVYRCG3LEHM3GVVBREE","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-22T22:11:17Z","cross_cats_sorted":[],"title_canon_sha256":"64bf48d7d98dc06bfaaa175f45fdb44068384e9cd5121677e55d43fb1797d179","abstract_canon_sha256":"77d372423289fee5a717e68351d72f5a1ca533388812a30a4f7f061dec5c2ff4"},"schema_version":"1.0"},"canonical_sha256":"f213c6094eae22236d643b366ad43121146dd870b9fecb97eed6176c1715d6d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:04.265767Z","signature_b64":"6ltqmaTLTP5eh7SmxErYxQ+zLLCd2Kt8StFu3H/QUqsJ0HEtJMC4KcYfjQZAkEyckPHEcVMxUpa9fF1UvkrjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f213c6094eae22236d643b366ad43121146dd870b9fecb97eed6176c1715d6d7","last_reissued_at":"2026-05-18T00:05:04.265200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:04.265200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08496","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":"2026-05-18T00:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k1sI1mpqoplWb+MEhpdQuTRwm1SQ8e95HhCHl7t9ueLTBtefBUQ6TzUzu3bBCCKk05QwLmHkRaIZTJxP0mBoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T03:18:46.628544Z"},"content_sha256":"b36abe3c3f544682785b3e6f474b930e7b3f792b90d1411ca39211d11b3de732","schema_version":"1.0","event_id":"sha256:b36abe3c3f544682785b3e6f474b930e7b3f792b90d1411ca39211d11b3de732"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6IJ4MCKOVYRCG3LEHM3GVVBREE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the relation of separability, bandwidth and embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\'alint V\\'as\\'arhelyi, B\\'ela Csaba","submitted_at":"2018-09-22T22:11:17Z","abstract_excerpt":"In this paper we construct a class of bounded degree bipartite graphs with a small separator and large bandwidth. Furthermore, we also prove that graphs from this class are spanning subgraphs of graphs with minimum degree just slightly larger than $n/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08496","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":"2026-05-18T00:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i8NAHHCnHBgn5bQMnWv9DKVFuo/6I1UNOjWdaccQ4LtdSImZYDNah43ox1h7Xkj5xS7YK3ZVS7NbBxafkopQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T03:18:46.629264Z"},"content_sha256":"296bd2455c8b21d5a442a6cfc032a831dcc178e89b47bfce367f379186e5798e","schema_version":"1.0","event_id":"sha256:296bd2455c8b21d5a442a6cfc032a831dcc178e89b47bfce367f379186e5798e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6IJ4MCKOVYRCG3LEHM3GVVBREE/bundle.json","state_url":"https://pith.science/pith/6IJ4MCKOVYRCG3LEHM3GVVBREE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6IJ4MCKOVYRCG3LEHM3GVVBREE/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":"2026-06-26T03:18:46Z","links":{"resolver":"https://pith.science/pith/6IJ4MCKOVYRCG3LEHM3GVVBREE","bundle":"https://pith.science/pith/6IJ4MCKOVYRCG3LEHM3GVVBREE/bundle.json","state":"https://pith.science/pith/6IJ4MCKOVYRCG3LEHM3GVVBREE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6IJ4MCKOVYRCG3LEHM3GVVBREE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6IJ4MCKOVYRCG3LEHM3GVVBREE","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":"77d372423289fee5a717e68351d72f5a1ca533388812a30a4f7f061dec5c2ff4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-22T22:11:17Z","title_canon_sha256":"64bf48d7d98dc06bfaaa175f45fdb44068384e9cd5121677e55d43fb1797d179"},"schema_version":"1.0","source":{"id":"1809.08496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08496","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08496v1","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08496","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"6IJ4MCKOVYRC","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6IJ4MCKOVYRCG3LE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6IJ4MCKO","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:296bd2455c8b21d5a442a6cfc032a831dcc178e89b47bfce367f379186e5798e","target":"graph","created_at":"2026-05-18T00:05:04Z","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 paper we construct a class of bounded degree bipartite graphs with a small separator and large bandwidth. Furthermore, we also prove that graphs from this class are spanning subgraphs of graphs with minimum degree just slightly larger than $n/2$.","authors_text":"B\\'alint V\\'as\\'arhelyi, B\\'ela Csaba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-22T22:11:17Z","title":"On the relation of separability, bandwidth and embedding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08496","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:b36abe3c3f544682785b3e6f474b930e7b3f792b90d1411ca39211d11b3de732","target":"record","created_at":"2026-05-18T00:05:04Z","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":"77d372423289fee5a717e68351d72f5a1ca533388812a30a4f7f061dec5c2ff4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-22T22:11:17Z","title_canon_sha256":"64bf48d7d98dc06bfaaa175f45fdb44068384e9cd5121677e55d43fb1797d179"},"schema_version":"1.0","source":{"id":"1809.08496","kind":"arxiv","version":1}},"canonical_sha256":"f213c6094eae22236d643b366ad43121146dd870b9fecb97eed6176c1715d6d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f213c6094eae22236d643b366ad43121146dd870b9fecb97eed6176c1715d6d7","first_computed_at":"2026-05-18T00:05:04.265200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:04.265200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ltqmaTLTP5eh7SmxErYxQ+zLLCd2Kt8StFu3H/QUqsJ0HEtJMC4KcYfjQZAkEyckPHEcVMxUpa9fF1UvkrjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:04.265767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b36abe3c3f544682785b3e6f474b930e7b3f792b90d1411ca39211d11b3de732","sha256:296bd2455c8b21d5a442a6cfc032a831dcc178e89b47bfce367f379186e5798e"],"state_sha256":"b95233eeb04abb763eeb1ec29f1c94871045bb233e6efcad90f10fc6db28fe8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZIUw3z9Hy4YlC9KcIO00U4rlrmozXD17b8zf+IZEGL2boz8sXEqGIs9dAYmL+wdihMjuKa+LQ3srq5BjEpdCCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T03:18:46.633688Z","bundle_sha256":"64c18d52d93f2cb44f6eed0d437f5d28a7886f23593d264251d7430695e7f064"}}