{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Y62Z2B5UZ3COHFCHSFDD5B4ZQL","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":"348820a34fe8f1de823031b155e0eab38bbee5d6c514061f8447886ffff93ed0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-14T12:40:07Z","title_canon_sha256":"ce2662393c975c9d084bdc9da2e7178a5398562283b83bf32face08e686f19e9"},"schema_version":"1.0","source":{"id":"1009.2640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2640","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2640v1","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2640","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"Y62Z2B5UZ3CO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Y62Z2B5UZ3COHFCH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Y62Z2B5U","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:791ed114fa9202a36cae13b9c95e03dc5392861cd312881c8cec028e489d8b51","target":"graph","created_at":"2026-05-18T04:40:56Z","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 present a constructive proof, that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope \\beta^k into closed surfaces of genus \\leq 1, each with a transitive automorphism group given by the vertex transitive Z_{2k}-action on \\beta^k. Furthermore we show, that for each k \\equiv 1,5(6) the 2-skeleton of the (k-1)-simplex is a union of highly symmetric tori and M\\\"obius strips.","authors_text":"Jonathan Spreer","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-14T12:40:07Z","title":"Supplemental material to the article \"Partitions of the triangles of the cross polytope into surfaces''"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2640","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":"sha256:7799ab82f5ec15a2a8a1b9f05b53a188563c7f452b9420f3d46fa93b2b014bc6","target":"record","created_at":"2026-05-18T04:40:56Z","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":"348820a34fe8f1de823031b155e0eab38bbee5d6c514061f8447886ffff93ed0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-14T12:40:07Z","title_canon_sha256":"ce2662393c975c9d084bdc9da2e7178a5398562283b83bf32face08e686f19e9"},"schema_version":"1.0","source":{"id":"1009.2640","kind":"arxiv","version":1}},"canonical_sha256":"c7b59d07b4cec4e3944791463e879982f406db3d9d653293899d7feaeadc2cf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7b59d07b4cec4e3944791463e879982f406db3d9d653293899d7feaeadc2cf5","first_computed_at":"2026-05-18T04:40:56.661989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:56.661989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0LEDvCeoo8bc/SKaBYJKlJtj1KAhZMuPQl1jtUVX8gMxJRMStdl7Yl450+aDwM78ZoSvaWqIxHy+uegnPVrHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:56.662606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7799ab82f5ec15a2a8a1b9f05b53a188563c7f452b9420f3d46fa93b2b014bc6","sha256:791ed114fa9202a36cae13b9c95e03dc5392861cd312881c8cec028e489d8b51"],"state_sha256":"18ae1dccc515ce297afe218e458290af7114bc79aa8decc0f135f260c7e9c8de"}