{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4FCPWTPYHCJ4UVORF6EGT4HBPK","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":"8045fc213d107927d5a6986d80be28e61ab73cc26bfb3f6608696d0a8aab4a3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-21T19:11:55Z","title_canon_sha256":"975d7322685ae0343c97098a2c3705d63b08601e636d3f1218a95906b31e026c"},"schema_version":"1.0","source":{"id":"1701.06070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06070","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06070v2","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06070","created_at":"2026-05-17T23:59:58Z"},{"alias_kind":"pith_short_12","alias_value":"4FCPWTPYHCJ4","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FCPWTPYHCJ4UVOR","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FCPWTPY","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:f31dbddcf3033fa2be4da7d8407b4780b099bd7dc45310f1b128df935ccb6ed7","target":"graph","created_at":"2026-05-17T23:59:58Z","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 study the equivariant homotopy type of the poset of orthogonal decompositions of a finite-dimensional complex vector space. Suppose that n is a power of a prime p, and that D is an elementary abelian p-subgroup of U(n) acting on complex n-space by the regular representation. We prove that the fixed point space of D acting on the decomposition poset of complex n-space contains as a retract the unreduced suspension of the Tits building for GL(k), which a wedge of (k-1)-dimensional spheres. Let Gamma be the projective elementary abelian subgroup of U(n) that contains the center of U(n) and act","authors_text":"Gregory Arone, Kathryn Lesh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-21T19:11:55Z","title":"Fixed points of coisotropic subgroups of $\\Gamma_{k}$ on decomposition spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06070","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:b4a28761432f1c64f7faec23d4bbb332f6be82153385a3cb9f8cd3d31769c4da","target":"record","created_at":"2026-05-17T23:59:58Z","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":"8045fc213d107927d5a6986d80be28e61ab73cc26bfb3f6608696d0a8aab4a3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-21T19:11:55Z","title_canon_sha256":"975d7322685ae0343c97098a2c3705d63b08601e636d3f1218a95906b31e026c"},"schema_version":"1.0","source":{"id":"1701.06070","kind":"arxiv","version":2}},"canonical_sha256":"e144fb4df83893ca55d12f8869f0e17a9bef8eddd0862f2b9058105653b2e360","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e144fb4df83893ca55d12f8869f0e17a9bef8eddd0862f2b9058105653b2e360","first_computed_at":"2026-05-17T23:59:58.297239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:58.297239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+UW5r8Nf6N+XdKWm1gMPvo9PSbbkBhq2cWj5Y3JWDz+2YVhr+zxSEo4r1Znqz52LN2T/K+VNcy8tm0C2E2mKAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:58.297760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4a28761432f1c64f7faec23d4bbb332f6be82153385a3cb9f8cd3d31769c4da","sha256:f31dbddcf3033fa2be4da7d8407b4780b099bd7dc45310f1b128df935ccb6ed7"],"state_sha256":"f791ad29e2bd5ac30f1a76b0cb7f6f191e0c5bfdaf76c21dd4c196ed9deac0a6"}