{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YXPKJ7Q6KNAT2Q6TUVJFSMAJFM","short_pith_number":"pith:YXPKJ7Q6","canonical_record":{"source":{"id":"2506.07170","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-08T14:35:51Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1bfcd49a3bd9a2ccc274df1c7492814b9f8fe6fb8d74ca23841dae0d708f8fc0","abstract_canon_sha256":"dda79a87fb193f837267bcab91a78d041f38c95788763475ba6d21e2c157c95c"},"schema_version":"1.0"},"canonical_sha256":"c5dea4fe1e53413d43d3a5525930092b19308817e5a871769ac052c709e5bd4a","source":{"kind":"arxiv","id":"2506.07170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07170","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07170v1","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07170","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"YXPKJ7Q6KNAT","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"YXPKJ7Q6KNAT2Q6T","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"YXPKJ7Q6","created_at":"2026-07-05T11:18:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YXPKJ7Q6KNAT2Q6TUVJFSMAJFM","target":"record","payload":{"canonical_record":{"source":{"id":"2506.07170","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-08T14:35:51Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1bfcd49a3bd9a2ccc274df1c7492814b9f8fe6fb8d74ca23841dae0d708f8fc0","abstract_canon_sha256":"dda79a87fb193f837267bcab91a78d041f38c95788763475ba6d21e2c157c95c"},"schema_version":"1.0"},"canonical_sha256":"c5dea4fe1e53413d43d3a5525930092b19308817e5a871769ac052c709e5bd4a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:02.980234Z","signature_b64":"k4r3vEV+U5RuWxObeoNu0cV67cEkNIptXThbuIxt/OQ8Km/9aPALSi5nPVDiC6UkTnI+JBsxEEnq1YNsLoEsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5dea4fe1e53413d43d3a5525930092b19308817e5a871769ac052c709e5bd4a","last_reissued_at":"2026-07-05T11:18:02.979725Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:02.979725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.07170","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":"2026-07-05T11:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Pl1ocNb9Hciv6C0Kk6lkSJUOp2pr5hwP1JR7O1bzpLfdM0PLz6dgoalQa4TpnjNh6YK541bsXvvUZK39qsmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:28:12.926710Z"},"content_sha256":"e64e4e98be25443fc0a5827c4519bd3594a2c1afef8a3145cc2904cd227b1d7a","schema_version":"1.0","event_id":"sha256:e64e4e98be25443fc0a5827c4519bd3594a2c1afef8a3145cc2904cd227b1d7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YXPKJ7Q6KNAT2Q6TUVJFSMAJFM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rectangular Duals on the Cylinder and the Torus","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Jonathan Klawitter, Philipp Kindermann, Therese Biedl","submitted_at":"2025-06-08T14:35:51Z","abstract_excerpt":"A rectangular dual of a plane graph $G$ is a contact representation of $G$ by interior-disjoint rectangles such that (i) no four rectangles share a point, and (ii) the union of all rectangles is a rectangle. In this paper, we study rectangular duals of graphs that are embedded in surfaces other than the plane. In particular, we fully characterize when a graph embedded on a cylinder admits a cylindrical rectangular dual. For graphs embedded on the flat torus, we can test whether the graph has a toroidal rectangular dual if we are additionally given a \\textit{regular edge labeling}, i.e. a combi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07170","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07170/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hqjICnC4mf83ZAI/Vjc0m7UqUFyxVcFek8lG0VgDIn+rkXmnZLomKMZWUpI7AG3X3JiZKY/z0DQFZMs8R65VCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:28:12.927657Z"},"content_sha256":"fbce457301717f55f71592f37f6e6bc426df65d5d6f9d3c8edd434f53bd5c542","schema_version":"1.0","event_id":"sha256:fbce457301717f55f71592f37f6e6bc426df65d5d6f9d3c8edd434f53bd5c542"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXPKJ7Q6KNAT2Q6TUVJFSMAJFM/bundle.json","state_url":"https://pith.science/pith/YXPKJ7Q6KNAT2Q6TUVJFSMAJFM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXPKJ7Q6KNAT2Q6TUVJFSMAJFM/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":"2026-08-14T08:28:12Z","links":{"resolver":"https://pith.science/pith/YXPKJ7Q6KNAT2Q6TUVJFSMAJFM","bundle":"https://pith.science/pith/YXPKJ7Q6KNAT2Q6TUVJFSMAJFM/bundle.json","state":"https://pith.science/pith/YXPKJ7Q6KNAT2Q6TUVJFSMAJFM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXPKJ7Q6KNAT2Q6TUVJFSMAJFM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YXPKJ7Q6KNAT2Q6TUVJFSMAJFM","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":"dda79a87fb193f837267bcab91a78d041f38c95788763475ba6d21e2c157c95c","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-08T14:35:51Z","title_canon_sha256":"1bfcd49a3bd9a2ccc274df1c7492814b9f8fe6fb8d74ca23841dae0d708f8fc0"},"schema_version":"1.0","source":{"id":"2506.07170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07170","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07170v1","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07170","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"YXPKJ7Q6KNAT","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"YXPKJ7Q6KNAT2Q6T","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"YXPKJ7Q6","created_at":"2026-07-05T11:18:02Z"}],"graph_snapshots":[{"event_id":"sha256:fbce457301717f55f71592f37f6e6bc426df65d5d6f9d3c8edd434f53bd5c542","target":"graph","created_at":"2026-07-05T11:18:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.07170/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A rectangular dual of a plane graph $G$ is a contact representation of $G$ by interior-disjoint rectangles such that (i) no four rectangles share a point, and (ii) the union of all rectangles is a rectangle. In this paper, we study rectangular duals of graphs that are embedded in surfaces other than the plane. In particular, we fully characterize when a graph embedded on a cylinder admits a cylindrical rectangular dual. For graphs embedded on the flat torus, we can test whether the graph has a toroidal rectangular dual if we are additionally given a \\textit{regular edge labeling}, i.e. a combi","authors_text":"Jonathan Klawitter, Philipp Kindermann, Therese Biedl","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-08T14:35:51Z","title":"Rectangular Duals on the Cylinder and the Torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07170","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:e64e4e98be25443fc0a5827c4519bd3594a2c1afef8a3145cc2904cd227b1d7a","target":"record","created_at":"2026-07-05T11:18:02Z","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":"dda79a87fb193f837267bcab91a78d041f38c95788763475ba6d21e2c157c95c","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-08T14:35:51Z","title_canon_sha256":"1bfcd49a3bd9a2ccc274df1c7492814b9f8fe6fb8d74ca23841dae0d708f8fc0"},"schema_version":"1.0","source":{"id":"2506.07170","kind":"arxiv","version":1}},"canonical_sha256":"c5dea4fe1e53413d43d3a5525930092b19308817e5a871769ac052c709e5bd4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5dea4fe1e53413d43d3a5525930092b19308817e5a871769ac052c709e5bd4a","first_computed_at":"2026-07-05T11:18:02.979725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:02.979725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k4r3vEV+U5RuWxObeoNu0cV67cEkNIptXThbuIxt/OQ8Km/9aPALSi5nPVDiC6UkTnI+JBsxEEnq1YNsLoEsCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:02.980234Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e64e4e98be25443fc0a5827c4519bd3594a2c1afef8a3145cc2904cd227b1d7a","sha256:fbce457301717f55f71592f37f6e6bc426df65d5d6f9d3c8edd434f53bd5c542"],"state_sha256":"5afb772a7cc692dd94ff5666e43ddcbd273459669619b903241f9cc9abf99564"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PwWFTbJlXj0pUaF4wzw9CCH8VK81J50VL8DvLhZK9XgmcVh9ZpLoA7h/v6NNJXGecvhPZB3xu2Hebo5h9PkkCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:28:12.945283Z","bundle_sha256":"7c65e19821cd4d0a85f96d01be852721e52141c4fb513f9b9ec7f9256f0104b0"}}