{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RKPFCQRYQLR6PCNTFABDBZQWU4","short_pith_number":"pith:RKPFCQRY","canonical_record":{"source":{"id":"1606.07662","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-24T12:44:49Z","cross_cats_sorted":[],"title_canon_sha256":"87d1a7111fca9329a685d55ddd216330ded473d0eb917609dc12b53be38459b8","abstract_canon_sha256":"bd58bb12f61e78c536143e911bd4dfc165b89ac8b7e6aacfca8604c56850be50"},"schema_version":"1.0"},"canonical_sha256":"8a9e51423882e3e789b3280230e616a73cc7e9c57d5adb0b8597037fe3ac4f29","source":{"kind":"arxiv","id":"1606.07662","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07662","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07662v3","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07662","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"RKPFCQRYQLR6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RKPFCQRYQLR6PCNT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RKPFCQRY","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RKPFCQRYQLR6PCNTFABDBZQWU4","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07662","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-24T12:44:49Z","cross_cats_sorted":[],"title_canon_sha256":"87d1a7111fca9329a685d55ddd216330ded473d0eb917609dc12b53be38459b8","abstract_canon_sha256":"bd58bb12f61e78c536143e911bd4dfc165b89ac8b7e6aacfca8604c56850be50"},"schema_version":"1.0"},"canonical_sha256":"8a9e51423882e3e789b3280230e616a73cc7e9c57d5adb0b8597037fe3ac4f29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:54.458805Z","signature_b64":"DvxzzkKwhfkz/5gFFUM32lWNk0NMjk5+0vV1crKPc/dfXkpx50a1WKmPSbEqJZxaM/WAMBxzZUQemW4gElD/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a9e51423882e3e789b3280230e616a73cc7e9c57d5adb0b8597037fe3ac4f29","last_reissued_at":"2026-05-18T00:48:54.458098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:54.458098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07662","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/Gy7ySjsM260I7F8gmeKOhD72xFoXFDbbvL9RdMuaEGLyFQPsJei1QViHNNc8Qh9QvcEmte9KozXIzL27HbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:42:25.037688Z"},"content_sha256":"4573581d02c7e0094fb48a2ca3f49f09b6c7f960d11f1545edf1e27751daea93","schema_version":"1.0","event_id":"sha256:4573581d02c7e0094fb48a2ca3f49f09b6c7f960d11f1545edf1e27751daea93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RKPFCQRYQLR6PCNTFABDBZQWU4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reducing quadrangulations of the sphere and the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elke Fuchs, Laura Gellert","submitted_at":"2016-06-24T12:44:49Z","abstract_excerpt":"We show that every quadrangulation of the sphere can be transformed into a $4$-cycle by deletions of degree-$2$ vertices and by $t$-contractions at degree-$3$ vertices. A $t$-contraction simultaneously contracts all incident edges at a vertex with stable neighbourhood. The operation is mainly used in the field of $t$-perfect graphs. \nWe further show that a non-bipartite quadrangulation of the projective plane can be transformed into an odd wheel by $t$-contractions and deletions of degree-$2$ vertices. \nWe deduce that a quadrangulation of the projective plane is (strongly) $t$-perfect if and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07662","kind":"arxiv","version":3},"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":"2026-05-18T00:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3c9BLwVdbMkR1mlTAfD1maR+dWXHhSj6EPLTqTMwdurGn2Lcdrq/nWGBL8SF2EvI6mFUPAFfu/749c8gsmsfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:42:25.038044Z"},"content_sha256":"3583ee34bacdf404f2ea22b7cfbc1fb0bdbadfe5b41286a7f109b4d6b8991bd7","schema_version":"1.0","event_id":"sha256:3583ee34bacdf404f2ea22b7cfbc1fb0bdbadfe5b41286a7f109b4d6b8991bd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKPFCQRYQLR6PCNTFABDBZQWU4/bundle.json","state_url":"https://pith.science/pith/RKPFCQRYQLR6PCNTFABDBZQWU4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKPFCQRYQLR6PCNTFABDBZQWU4/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":"2026-06-25T22:42:25Z","links":{"resolver":"https://pith.science/pith/RKPFCQRYQLR6PCNTFABDBZQWU4","bundle":"https://pith.science/pith/RKPFCQRYQLR6PCNTFABDBZQWU4/bundle.json","state":"https://pith.science/pith/RKPFCQRYQLR6PCNTFABDBZQWU4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKPFCQRYQLR6PCNTFABDBZQWU4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RKPFCQRYQLR6PCNTFABDBZQWU4","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":"bd58bb12f61e78c536143e911bd4dfc165b89ac8b7e6aacfca8604c56850be50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-24T12:44:49Z","title_canon_sha256":"87d1a7111fca9329a685d55ddd216330ded473d0eb917609dc12b53be38459b8"},"schema_version":"1.0","source":{"id":"1606.07662","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07662","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07662v3","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07662","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"RKPFCQRYQLR6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RKPFCQRYQLR6PCNT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RKPFCQRY","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:3583ee34bacdf404f2ea22b7cfbc1fb0bdbadfe5b41286a7f109b4d6b8991bd7","target":"graph","created_at":"2026-05-18T00:48:54Z","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 show that every quadrangulation of the sphere can be transformed into a $4$-cycle by deletions of degree-$2$ vertices and by $t$-contractions at degree-$3$ vertices. A $t$-contraction simultaneously contracts all incident edges at a vertex with stable neighbourhood. The operation is mainly used in the field of $t$-perfect graphs. \nWe further show that a non-bipartite quadrangulation of the projective plane can be transformed into an odd wheel by $t$-contractions and deletions of degree-$2$ vertices. \nWe deduce that a quadrangulation of the projective plane is (strongly) $t$-perfect if and o","authors_text":"Elke Fuchs, Laura Gellert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-24T12:44:49Z","title":"Reducing quadrangulations of the sphere and the projective plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07662","kind":"arxiv","version":3},"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":"sha256:4573581d02c7e0094fb48a2ca3f49f09b6c7f960d11f1545edf1e27751daea93","target":"record","created_at":"2026-05-18T00:48:54Z","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":"bd58bb12f61e78c536143e911bd4dfc165b89ac8b7e6aacfca8604c56850be50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-24T12:44:49Z","title_canon_sha256":"87d1a7111fca9329a685d55ddd216330ded473d0eb917609dc12b53be38459b8"},"schema_version":"1.0","source":{"id":"1606.07662","kind":"arxiv","version":3}},"canonical_sha256":"8a9e51423882e3e789b3280230e616a73cc7e9c57d5adb0b8597037fe3ac4f29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a9e51423882e3e789b3280230e616a73cc7e9c57d5adb0b8597037fe3ac4f29","first_computed_at":"2026-05-18T00:48:54.458098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:54.458098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DvxzzkKwhfkz/5gFFUM32lWNk0NMjk5+0vV1crKPc/dfXkpx50a1WKmPSbEqJZxaM/WAMBxzZUQemW4gElD/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:54.458805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07662","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4573581d02c7e0094fb48a2ca3f49f09b6c7f960d11f1545edf1e27751daea93","sha256:3583ee34bacdf404f2ea22b7cfbc1fb0bdbadfe5b41286a7f109b4d6b8991bd7"],"state_sha256":"7b435cd345f44096b3749ff721fb39bbfac01f8be8001e3a4de1dfac17ef1619"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zRRsRxXEENVGMLZDlf058nJwBTHHD0u9O2EkqC1XWfvAQ+GqSJvIy4ATXm0DHoTeSnHWLEuDWUkZil23EMa/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:42:25.039992Z","bundle_sha256":"b6326af4d7b94eca7e16a72c5ddd8678bf4b75c4d97fcf4ca68a1f8eec94d1cb"}}