{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CTCXLYUD4P6HSQER3UE4RJMAKG","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":"f11daa419614bcd44c4ec45f97eb1b13f63f93b656eefa3467ff85a1f534216d","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-06-04T09:50:53Z","title_canon_sha256":"b28a137e5fbebe03914ba75d5708c23097a6ce4bc03c43d2ca1e0c1e04fa7255"},"schema_version":"1.0","source":{"id":"1206.0566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0566","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0566v1","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0566","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"CTCXLYUD4P6H","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CTCXLYUD4P6HSQER","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CTCXLYUD","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:ec8abdc68d31d3caa08927782dbd5846a62512b60dcabd9b7eb7d812bd885b4a","target":"graph","created_at":"2026-05-18T03:54:17Z","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":"The $S^2 \\times R$ geometry can be derived by the direct product of the spherical plane $\\bS^2$ and the real line $\\bR$. J. Z. Farkas has classified and given the complete list of the space groups of $S^2 \\times R$. The $S^2 \\times R$ manifolds were classified by E. Moln\\'ar and J. Z. Farkas by similarity and diffeomorphism. In Szirmai we have studied the geodesic balls and their volumes in $S^2 \\times R$ space, moreover we have introduced the notion of geodesic ball packing and its density and have determined the densest geodesic ball packing for generalized Coxeter space groups of $S^2 \\time","authors_text":"Jen\\H{o} Szirmai","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-06-04T09:50:53Z","title":"Simply transitive geodesic ball packings to $S^2 \\times R$ space groups generated by glide reflections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0566","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":"sha256:6a963df4b868d63a5127e711d581839ef365fbdb502021d7eb0f3ee983277357","target":"record","created_at":"2026-05-18T03:54:17Z","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":"f11daa419614bcd44c4ec45f97eb1b13f63f93b656eefa3467ff85a1f534216d","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-06-04T09:50:53Z","title_canon_sha256":"b28a137e5fbebe03914ba75d5708c23097a6ce4bc03c43d2ca1e0c1e04fa7255"},"schema_version":"1.0","source":{"id":"1206.0566","kind":"arxiv","version":1}},"canonical_sha256":"14c575e283e3fc794091dd09c8a58051b5d09943ab96588f219478765df45507","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14c575e283e3fc794091dd09c8a58051b5d09943ab96588f219478765df45507","first_computed_at":"2026-05-18T03:54:17.306671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:17.306671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Whmb8aVj6bzX0Y0tANm7xcE1mBmC+NVSW/xm/Pu1g/kGqNSfLLR21eT7+SDqKMCHiWx0c7DtXR7ezWK9f9AeBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:17.307200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a963df4b868d63a5127e711d581839ef365fbdb502021d7eb0f3ee983277357","sha256:ec8abdc68d31d3caa08927782dbd5846a62512b60dcabd9b7eb7d812bd885b4a"],"state_sha256":"1ac02ba5df252574d772cabff7097249e674e62d3a3d55676c509fe1efd38cc1"}