{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KQL557KNZO56W7K3DHXYPV7J6L","short_pith_number":"pith:KQL557KN","canonical_record":{"source":{"id":"1904.08707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-18T11:46:33Z","cross_cats_sorted":[],"title_canon_sha256":"c21030df0b02ee3e46e37c9ed3a560aec48fd5f157ecbc74f99a531defd349a9","abstract_canon_sha256":"1333f4958f413b30199025f01cc96b22d8ef738e902cbbffcb894b59b6aecc60"},"schema_version":"1.0"},"canonical_sha256":"5417defd4dcbbbeb7d5b19ef87d7e9f2c6ad9b08fe091932d6a87ca6680008c1","source":{"kind":"arxiv","id":"1904.08707","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08707","created_at":"2026-05-17T23:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08707v1","created_at":"2026-05-17T23:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08707","created_at":"2026-05-17T23:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"KQL557KNZO56","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KQL557KNZO56W7K3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KQL557KN","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KQL557KNZO56W7K3DHXYPV7J6L","target":"record","payload":{"canonical_record":{"source":{"id":"1904.08707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-18T11:46:33Z","cross_cats_sorted":[],"title_canon_sha256":"c21030df0b02ee3e46e37c9ed3a560aec48fd5f157ecbc74f99a531defd349a9","abstract_canon_sha256":"1333f4958f413b30199025f01cc96b22d8ef738e902cbbffcb894b59b6aecc60"},"schema_version":"1.0"},"canonical_sha256":"5417defd4dcbbbeb7d5b19ef87d7e9f2c6ad9b08fe091932d6a87ca6680008c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:13.299800Z","signature_b64":"49ONIoOWfqprBZ3hT1NNZakjd9JpsmESKYkIZdf19EG2amMdoWRtiDo5UP0nuERZtXAgwJbhS1apvplTb5OJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5417defd4dcbbbeb7d5b19ef87d7e9f2c6ad9b08fe091932d6a87ca6680008c1","last_reissued_at":"2026-05-17T23:48:13.299106Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:13.299106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.08707","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":"2026-05-17T23:48:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yKSi73Px2rMRnDikmLzsMSzjob/PwrnI8qXOYjzWxgzYBylQ2rlbmmF4XhSUY2rJI7bkgYBf8yky7QrYtefBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:24:15.691808Z"},"content_sha256":"1798557c6f8c65e4ef57068d5324aab1958e474872c950f9fbf4bc943444fd24","schema_version":"1.0","event_id":"sha256:1798557c6f8c65e4ef57068d5324aab1958e474872c950f9fbf4bc943444fd24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KQL557KNZO56W7K3DHXYPV7J6L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper bounds for bar visibility of subgraphs and n-vertex graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Douglas B. West, Yan Yang, Yuanrui Feng","submitted_at":"2019-04-18T11:46:33Z","abstract_excerpt":"A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical channel of positive width. The least $t$ such that $G$ has a $t$-bar visibility representation is the bar visibility number of $G$, denoted by $b(G)$. We show that if $H$ is a spanning subgraph of $G$, then $b(H)\\le b(G)+1$. It follows that $b(G)\\le \\lceil n/6\\rceil+1$ when $G$ is an $n$-vertex graph. This improves the upper bound obtained by Chang et al. (SI"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08707","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":"2026-05-17T23:48:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TkEajYkerhp3vH6p1/ORWG2UPHOomwkgJE9qb6G97ZGi59EN26yw2bGnmnXfAaSONOOinwjsyZvLql9N6ZTrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:24:15.692368Z"},"content_sha256":"256d3d7b2463e0b3b4e36ec150de90c7409f2029dab681bf682633535536507e","schema_version":"1.0","event_id":"sha256:256d3d7b2463e0b3b4e36ec150de90c7409f2029dab681bf682633535536507e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQL557KNZO56W7K3DHXYPV7J6L/bundle.json","state_url":"https://pith.science/pith/KQL557KNZO56W7K3DHXYPV7J6L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQL557KNZO56W7K3DHXYPV7J6L/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":"2026-05-26T21:24:15Z","links":{"resolver":"https://pith.science/pith/KQL557KNZO56W7K3DHXYPV7J6L","bundle":"https://pith.science/pith/KQL557KNZO56W7K3DHXYPV7J6L/bundle.json","state":"https://pith.science/pith/KQL557KNZO56W7K3DHXYPV7J6L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQL557KNZO56W7K3DHXYPV7J6L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KQL557KNZO56W7K3DHXYPV7J6L","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":"1333f4958f413b30199025f01cc96b22d8ef738e902cbbffcb894b59b6aecc60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-18T11:46:33Z","title_canon_sha256":"c21030df0b02ee3e46e37c9ed3a560aec48fd5f157ecbc74f99a531defd349a9"},"schema_version":"1.0","source":{"id":"1904.08707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08707","created_at":"2026-05-17T23:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08707v1","created_at":"2026-05-17T23:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08707","created_at":"2026-05-17T23:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"KQL557KNZO56","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KQL557KNZO56W7K3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KQL557KN","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:256d3d7b2463e0b3b4e36ec150de90c7409f2029dab681bf682633535536507e","target":"graph","created_at":"2026-05-17T23:48:13Z","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":"A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical channel of positive width. The least $t$ such that $G$ has a $t$-bar visibility representation is the bar visibility number of $G$, denoted by $b(G)$. We show that if $H$ is a spanning subgraph of $G$, then $b(H)\\le b(G)+1$. It follows that $b(G)\\le \\lceil n/6\\rceil+1$ when $G$ is an $n$-vertex graph. This improves the upper bound obtained by Chang et al. (SI","authors_text":"Douglas B. West, Yan Yang, Yuanrui Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-18T11:46:33Z","title":"Upper bounds for bar visibility of subgraphs and n-vertex graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08707","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":"sha256:1798557c6f8c65e4ef57068d5324aab1958e474872c950f9fbf4bc943444fd24","target":"record","created_at":"2026-05-17T23:48:13Z","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":"1333f4958f413b30199025f01cc96b22d8ef738e902cbbffcb894b59b6aecc60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-18T11:46:33Z","title_canon_sha256":"c21030df0b02ee3e46e37c9ed3a560aec48fd5f157ecbc74f99a531defd349a9"},"schema_version":"1.0","source":{"id":"1904.08707","kind":"arxiv","version":1}},"canonical_sha256":"5417defd4dcbbbeb7d5b19ef87d7e9f2c6ad9b08fe091932d6a87ca6680008c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5417defd4dcbbbeb7d5b19ef87d7e9f2c6ad9b08fe091932d6a87ca6680008c1","first_computed_at":"2026-05-17T23:48:13.299106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:13.299106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49ONIoOWfqprBZ3hT1NNZakjd9JpsmESKYkIZdf19EG2amMdoWRtiDo5UP0nuERZtXAgwJbhS1apvplTb5OJCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:13.299800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1798557c6f8c65e4ef57068d5324aab1958e474872c950f9fbf4bc943444fd24","sha256:256d3d7b2463e0b3b4e36ec150de90c7409f2029dab681bf682633535536507e"],"state_sha256":"14c6c74308d5e9e13acfdc87680a94b824434817d9fcc3379044ebf26203d02c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DP+B8MfOt7KzHvjT7VihgS3W+pDDkHqCCaBX+O7M/NDTIdncm2X7NR0Bo23sRdOxjG7CcSoACUYUZkbumFcAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:24:15.695154Z","bundle_sha256":"b973fa54d4ac497b8f04e2b348459bebeabd2565390bea804d48f3c49842ea71"}}