{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZMN44NDPWRHAOE6Q5BZ43Q2MXS","short_pith_number":"pith:ZMN44NDP","canonical_record":{"source":{"id":"1201.1869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-09T18:45:36Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1c8cea085f03f4dc4573f0dead2c239730fd73c349f3e2943db8fe66f418cfa4","abstract_canon_sha256":"4f71239cb90998dc81428ebd3cac54b92fcc186ac20dd96e021000fe1710cb67"},"schema_version":"1.0"},"canonical_sha256":"cb1bce346fb44e0713d0e873cdc34cbcbd78cc5e5010dbd684c4fafc0cd02e4d","source":{"kind":"arxiv","id":"1201.1869","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1869","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1869v1","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1869","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZMN44NDPWRHA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZMN44NDPWRHAOE6Q","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZMN44NDP","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZMN44NDPWRHAOE6Q5BZ43Q2MXS","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-09T18:45:36Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1c8cea085f03f4dc4573f0dead2c239730fd73c349f3e2943db8fe66f418cfa4","abstract_canon_sha256":"4f71239cb90998dc81428ebd3cac54b92fcc186ac20dd96e021000fe1710cb67"},"schema_version":"1.0"},"canonical_sha256":"cb1bce346fb44e0713d0e873cdc34cbcbd78cc5e5010dbd684c4fafc0cd02e4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:55.475382Z","signature_b64":"6tkbR394/sgJ4tQZLS8S+/hn9hY79igoKO6KvDLbuDI0TPWSJUqD/YwMgrAVkSY686DRjFpniF4VH/8FBsfRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb1bce346fb44e0713d0e873cdc34cbcbd78cc5e5010dbd684c4fafc0cd02e4d","last_reissued_at":"2026-05-18T04:04:55.474747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:55.474747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1869","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":"2026-05-18T04:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkpuHPmB3aPFcJeGj2eCcCl6k7UaxIBlRvwpej/wrtLGSNsxgaYABtlsF5mhGrB/hrJMscYok8mO0p4/d7F+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:30:39.247712Z"},"content_sha256":"60604101dca29510de8c15cafcc0427bdbaabe3985ba74b9a71849c007a1e999","schema_version":"1.0","event_id":"sha256:60604101dca29510de8c15cafcc0427bdbaabe3985ba74b9a71849c007a1e999"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZMN44NDPWRHAOE6Q5BZ43Q2MXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sitting closer to friends than enemies, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Jakub Onufry Wojtaszczyk, Marcin Pilipczuk, Marek Cygan, Micha{\\l} Pilipczuk","submitted_at":"2012-01-09T18:45:36Z","abstract_excerpt":"Signed graphs, i.e., undirected graphs with edges labelled with a plus or minus sign, are commonly used to model relationships in social networks. Recently, Kermarrec and Thraves initiated the study of the problem of appropriately visualising the network: They asked whether any signed graph can be embedded into the metric space R^l in such a manner that every vertex is closer to all its friends (neighbours via positive edges) than to all its enemies (neighbours via negative edges). Interestingly, embeddability into R^1 can be expressed as a purely combinatorial problem. In this paper we pursue"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1869","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":"2026-05-18T04:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8CX4iQLpVCJP8wAa6SlTyaeHN/SErJD0BvYZyQTFYoHxsHbBD6CxW4/7ifbrIu87jmuaNK2ubbv65do/Vr8WBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:30:39.248394Z"},"content_sha256":"f23e913716fbed00ddeb32cc0a5ba70613b9851f5f0f1f74079b6a6dd7bfc451","schema_version":"1.0","event_id":"sha256:f23e913716fbed00ddeb32cc0a5ba70613b9851f5f0f1f74079b6a6dd7bfc451"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMN44NDPWRHAOE6Q5BZ43Q2MXS/bundle.json","state_url":"https://pith.science/pith/ZMN44NDPWRHAOE6Q5BZ43Q2MXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMN44NDPWRHAOE6Q5BZ43Q2MXS/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":"2026-05-26T07:30:39Z","links":{"resolver":"https://pith.science/pith/ZMN44NDPWRHAOE6Q5BZ43Q2MXS","bundle":"https://pith.science/pith/ZMN44NDPWRHAOE6Q5BZ43Q2MXS/bundle.json","state":"https://pith.science/pith/ZMN44NDPWRHAOE6Q5BZ43Q2MXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMN44NDPWRHAOE6Q5BZ43Q2MXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZMN44NDPWRHAOE6Q5BZ43Q2MXS","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":"4f71239cb90998dc81428ebd3cac54b92fcc186ac20dd96e021000fe1710cb67","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-09T18:45:36Z","title_canon_sha256":"1c8cea085f03f4dc4573f0dead2c239730fd73c349f3e2943db8fe66f418cfa4"},"schema_version":"1.0","source":{"id":"1201.1869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1869","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1869v1","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1869","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZMN44NDPWRHA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZMN44NDPWRHAOE6Q","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZMN44NDP","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:f23e913716fbed00ddeb32cc0a5ba70613b9851f5f0f1f74079b6a6dd7bfc451","target":"graph","created_at":"2026-05-18T04:04:55Z","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":"Signed graphs, i.e., undirected graphs with edges labelled with a plus or minus sign, are commonly used to model relationships in social networks. Recently, Kermarrec and Thraves initiated the study of the problem of appropriately visualising the network: They asked whether any signed graph can be embedded into the metric space R^l in such a manner that every vertex is closer to all its friends (neighbours via positive edges) than to all its enemies (neighbours via negative edges). Interestingly, embeddability into R^1 can be expressed as a purely combinatorial problem. In this paper we pursue","authors_text":"Jakub Onufry Wojtaszczyk, Marcin Pilipczuk, Marek Cygan, Micha{\\l} Pilipczuk","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-09T18:45:36Z","title":"Sitting closer to friends than enemies, revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1869","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":"sha256:60604101dca29510de8c15cafcc0427bdbaabe3985ba74b9a71849c007a1e999","target":"record","created_at":"2026-05-18T04:04:55Z","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":"4f71239cb90998dc81428ebd3cac54b92fcc186ac20dd96e021000fe1710cb67","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-09T18:45:36Z","title_canon_sha256":"1c8cea085f03f4dc4573f0dead2c239730fd73c349f3e2943db8fe66f418cfa4"},"schema_version":"1.0","source":{"id":"1201.1869","kind":"arxiv","version":1}},"canonical_sha256":"cb1bce346fb44e0713d0e873cdc34cbcbd78cc5e5010dbd684c4fafc0cd02e4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb1bce346fb44e0713d0e873cdc34cbcbd78cc5e5010dbd684c4fafc0cd02e4d","first_computed_at":"2026-05-18T04:04:55.474747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:55.474747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6tkbR394/sgJ4tQZLS8S+/hn9hY79igoKO6KvDLbuDI0TPWSJUqD/YwMgrAVkSY686DRjFpniF4VH/8FBsfRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:55.475382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60604101dca29510de8c15cafcc0427bdbaabe3985ba74b9a71849c007a1e999","sha256:f23e913716fbed00ddeb32cc0a5ba70613b9851f5f0f1f74079b6a6dd7bfc451"],"state_sha256":"59be0b339ec041aaf18d4b8e8d8fa7a84b21dcaa1e535fb318a5c7ba9ade8c7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eW/RpqChb049yDRxE1ujxt11f1CFVjw7w5f/H2d6IlDCBY3kYCEDLlpjVggCwI7sfcnb2zIhtx3Hqp+JLUsrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:30:39.252031Z","bundle_sha256":"30ce4c848731b15742080389bf1645801c6d063b61da8dca638e0d58522160e6"}}