{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B6IXQXG6RC24ZDBSR2S57GEH7Q","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":"54a0db3874342f5cb02b8a7bb0ed24ab8308d59827de934e690286527f330a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-12-09T22:34:28Z","title_canon_sha256":"7cc30cfbb361fb5c03b922ad853c5c73b44470887ba1fe26d95e875d5e90f971"},"schema_version":"1.0","source":{"id":"1412.3141","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3141","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3141v3","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3141","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"B6IXQXG6RC24","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B6IXQXG6RC24ZDBS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B6IXQXG6","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:e4ae20a7f2317e5d1591e0f47f6f5f13cac42ac0e07f6e194cc1fbfd7e814b91","target":"graph","created_at":"2026-05-18T00:44:28Z","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":"Let p be an odd prime. We prove that every rank three p-group acts freely and smoothly on a product of three spheres. To construct this action, we first prove a generalization of a theorem of L\\\" uck and Oliver on constructions of G-equivariant vector bundles. We also give some other applications of this generalization.","authors_text":"Ergun Yalcin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-12-09T22:34:28Z","title":"Rank Three p-Group Actions on Products of Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3141","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:b39ef443caaff0f2ec067bd51271dd1b6b08f4c4d74db232c7f7ff35ae0439e3","target":"record","created_at":"2026-05-18T00:44:28Z","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":"54a0db3874342f5cb02b8a7bb0ed24ab8308d59827de934e690286527f330a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-12-09T22:34:28Z","title_canon_sha256":"7cc30cfbb361fb5c03b922ad853c5c73b44470887ba1fe26d95e875d5e90f971"},"schema_version":"1.0","source":{"id":"1412.3141","kind":"arxiv","version":3}},"canonical_sha256":"0f91785cde88b5cc8c328ea5df9887fc2a99cf7b306a9ea85ed4bdbcb5839ef8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f91785cde88b5cc8c328ea5df9887fc2a99cf7b306a9ea85ed4bdbcb5839ef8","first_computed_at":"2026-05-18T00:44:28.600415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.600415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WhRLH6GjWbsPAwEY/r4tM2Wc6DGghFGBFixcShpf6OlU+AkudyIoMW0AXM3rSgSPifpopUSZDOkQnyYeCbgUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.601053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3141","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b39ef443caaff0f2ec067bd51271dd1b6b08f4c4d74db232c7f7ff35ae0439e3","sha256:e4ae20a7f2317e5d1591e0f47f6f5f13cac42ac0e07f6e194cc1fbfd7e814b91"],"state_sha256":"eb2c0cb9fa3325405e8edc0515e0355b94e2eab9d4675208fc4602a7f0fcf0da"}