{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R2ZWD4FLHWQGPASGIGRLM4TQEV","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":"e02431f1e74db88b4a6944d821d4f11800f52a52040ee67cbf1c7bb93c5dd751","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-11T11:32:01Z","title_canon_sha256":"20a7846bf418621ccbee8048d7d24965e9bbbf57ea14e614dc3a63fda77a115e"},"schema_version":"1.0","source":{"id":"1709.03335","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03335","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03335v2","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03335","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"R2ZWD4FLHWQG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2ZWD4FLHWQGPASG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2ZWD4FL","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:91b65680640fd36df7df7ea929f2cd9e14fdbfe311fd621cb35e276f83d8cdbf","target":"graph","created_at":"2026-05-18T00:33:29Z","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 orbit polytope for a finite group G acting linearly and freely on a sphere S is used to construct a cellularized fundamental domain for the action. A resolution of the integers over G results from the associated G-equivariant cellularization of S. This technique is applied to the generalized binary tetrahedral group family; the homology groups, the cohomology rings and the Reidemeister torsions of the related spherical space forms are determined.","authors_text":"Mauro Spreafico, Rocco Chirivi'","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-11T11:32:01Z","title":"Space Forms and Group Resolutions: the tetrahedral family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03335","kind":"arxiv","version":2},"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":"sha256:29676f5218fdbeefe8fc9db978fc27ea020ec1f638c675a56fdd44c3a53899a8","target":"record","created_at":"2026-05-18T00:33:29Z","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":"e02431f1e74db88b4a6944d821d4f11800f52a52040ee67cbf1c7bb93c5dd751","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-11T11:32:01Z","title_canon_sha256":"20a7846bf418621ccbee8048d7d24965e9bbbf57ea14e614dc3a63fda77a115e"},"schema_version":"1.0","source":{"id":"1709.03335","kind":"arxiv","version":2}},"canonical_sha256":"8eb361f0ab3da067824641a2b67270256947a1d2c15582f338b9d648a3aed372","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8eb361f0ab3da067824641a2b67270256947a1d2c15582f338b9d648a3aed372","first_computed_at":"2026-05-18T00:33:29.821618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:29.821618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7V9o9mfRTElJTG9VqLgZFTYArS1UMo3xlFW39rd/qqZxreyAZxFJRSVJUHvPgs5XlIPJb3BRgHEw1jaWuMxiDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:29.822141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03335","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29676f5218fdbeefe8fc9db978fc27ea020ec1f638c675a56fdd44c3a53899a8","sha256:91b65680640fd36df7df7ea929f2cd9e14fdbfe311fd621cb35e276f83d8cdbf"],"state_sha256":"14e1431dca34c08876721deb20ed3e291670c5b103b737e08ba10622efd2364c"}