{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NNYMERZQHGEKO3FOFRKJ7UTSBT","short_pith_number":"pith:NNYMERZQ","canonical_record":{"source":{"id":"1509.03447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-09-11T10:03:35Z","cross_cats_sorted":[],"title_canon_sha256":"cffdbe67c892ffd8b7525335c66aba342f7bf80a585adbef6745eb9c50afe7d1","abstract_canon_sha256":"818df6a99bbfe7ea0669ecb29559581305b57bc7f076a850464939add2a71db7"},"schema_version":"1.0"},"canonical_sha256":"6b70c247303988a76cae2c549fd2720cf42c18fdf9d74fbbfb0b8a7eb1e0d83d","source":{"kind":"arxiv","id":"1509.03447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03447","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03447v1","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03447","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"NNYMERZQHGEK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNYMERZQHGEKO3FO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNYMERZQ","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NNYMERZQHGEKO3FOFRKJ7UTSBT","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-09-11T10:03:35Z","cross_cats_sorted":[],"title_canon_sha256":"cffdbe67c892ffd8b7525335c66aba342f7bf80a585adbef6745eb9c50afe7d1","abstract_canon_sha256":"818df6a99bbfe7ea0669ecb29559581305b57bc7f076a850464939add2a71db7"},"schema_version":"1.0"},"canonical_sha256":"6b70c247303988a76cae2c549fd2720cf42c18fdf9d74fbbfb0b8a7eb1e0d83d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:23.174398Z","signature_b64":"j5cN/2lQAJG/ID+OP6HFWbZVjdykfLH2k0/0aw//9GOkjiaw24YCk10fSvnl858eGqiqi8yB8cfp+i0DpIgeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b70c247303988a76cae2c549fd2720cf42c18fdf9d74fbbfb0b8a7eb1e0d83d","last_reissued_at":"2026-05-18T01:33:23.173736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:23.173736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03447","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":"2026-05-18T01:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNSom3Zz8xZKXpE+n+fe+LgtMykToevt7YTDHDmS/yThwFXfc4Z5B+Z/HLu+dTheujn8GcJZY5UEWI7VkYs0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T16:57:54.279438Z"},"content_sha256":"477fc97ae5d642d7c2196779547638279de94f88fb344a3c0cd262ff08a68b99","schema_version":"1.0","event_id":"sha256:477fc97ae5d642d7c2196779547638279de94f88fb344a3c0cd262ff08a68b99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NNYMERZQHGEKO3FOFRKJ7UTSBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On 4-Map Graphs and 1-Planar Graphs and their Recognition Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Franz J. Brandenburg","submitted_at":"2015-09-11T10:03:35Z","abstract_excerpt":"We establish a one-to-one correspondence between 1-planar graphs and general and hole-free 4-map graphs and show that 1-planar graphs can be recognized in polynomial time if they are crossing-augmented, fully triangulated, and maximal 1-planar, respectively, with a polynomial of degree 120, 3, and 5, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03447","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":"2026-05-18T01:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5VfPl25PNEm8DgxHaXhjckicWRWPZAkU9JjJ/T2IpqFGXBxPNmuS21Uh1c9Cdxl0myJj9tnqy3hQy/3TuHEyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T16:57:54.279792Z"},"content_sha256":"6f132774b523b186cbd35d33044a14b9c1da0adfcdc6e11c1e0521d53478234b","schema_version":"1.0","event_id":"sha256:6f132774b523b186cbd35d33044a14b9c1da0adfcdc6e11c1e0521d53478234b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNYMERZQHGEKO3FOFRKJ7UTSBT/bundle.json","state_url":"https://pith.science/pith/NNYMERZQHGEKO3FOFRKJ7UTSBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNYMERZQHGEKO3FOFRKJ7UTSBT/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":"2026-05-21T16:57:54Z","links":{"resolver":"https://pith.science/pith/NNYMERZQHGEKO3FOFRKJ7UTSBT","bundle":"https://pith.science/pith/NNYMERZQHGEKO3FOFRKJ7UTSBT/bundle.json","state":"https://pith.science/pith/NNYMERZQHGEKO3FOFRKJ7UTSBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNYMERZQHGEKO3FOFRKJ7UTSBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NNYMERZQHGEKO3FOFRKJ7UTSBT","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":"818df6a99bbfe7ea0669ecb29559581305b57bc7f076a850464939add2a71db7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-09-11T10:03:35Z","title_canon_sha256":"cffdbe67c892ffd8b7525335c66aba342f7bf80a585adbef6745eb9c50afe7d1"},"schema_version":"1.0","source":{"id":"1509.03447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03447","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03447v1","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03447","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"NNYMERZQHGEK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNYMERZQHGEKO3FO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNYMERZQ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:6f132774b523b186cbd35d33044a14b9c1da0adfcdc6e11c1e0521d53478234b","target":"graph","created_at":"2026-05-18T01:33:23Z","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 establish a one-to-one correspondence between 1-planar graphs and general and hole-free 4-map graphs and show that 1-planar graphs can be recognized in polynomial time if they are crossing-augmented, fully triangulated, and maximal 1-planar, respectively, with a polynomial of degree 120, 3, and 5, respectively.","authors_text":"Franz J. Brandenburg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-09-11T10:03:35Z","title":"On 4-Map Graphs and 1-Planar Graphs and their Recognition Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03447","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":"sha256:477fc97ae5d642d7c2196779547638279de94f88fb344a3c0cd262ff08a68b99","target":"record","created_at":"2026-05-18T01:33:23Z","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":"818df6a99bbfe7ea0669ecb29559581305b57bc7f076a850464939add2a71db7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-09-11T10:03:35Z","title_canon_sha256":"cffdbe67c892ffd8b7525335c66aba342f7bf80a585adbef6745eb9c50afe7d1"},"schema_version":"1.0","source":{"id":"1509.03447","kind":"arxiv","version":1}},"canonical_sha256":"6b70c247303988a76cae2c549fd2720cf42c18fdf9d74fbbfb0b8a7eb1e0d83d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b70c247303988a76cae2c549fd2720cf42c18fdf9d74fbbfb0b8a7eb1e0d83d","first_computed_at":"2026-05-18T01:33:23.173736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:23.173736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j5cN/2lQAJG/ID+OP6HFWbZVjdykfLH2k0/0aw//9GOkjiaw24YCk10fSvnl858eGqiqi8yB8cfp+i0DpIgeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:23.174398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:477fc97ae5d642d7c2196779547638279de94f88fb344a3c0cd262ff08a68b99","sha256:6f132774b523b186cbd35d33044a14b9c1da0adfcdc6e11c1e0521d53478234b"],"state_sha256":"00d566aebf29360cc3c56500fc2cfec0b12699db88901b9bfd7cfa815ae53911"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HkOtmau+9Xga/Vjqs9ABX3r8xsfAFMASwUeX5KTZGzhEDF/S38cdO88Yp4apvszaZq7+/QDr3hv10WbIcmIDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T16:57:54.282571Z","bundle_sha256":"62d722cec784a6d60c1b32691bdd05e6c0266e9a7c17bf985e23c4f35a7197c6"}}