{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NSBSMABY5DU6C2SAHRA2WL3MGS","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":"3ae173b4309b289a077a3342085789e347d2d5dbc006c3ca07051e8ce989765e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-04T11:12:57Z","title_canon_sha256":"a82b3f7e0c740ba8e5ffd39c08f14ad6488040deafc3e62817955cde16c2114c"},"schema_version":"1.0","source":{"id":"1708.01451","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01451","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01451v3","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01451","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"NSBSMABY5DU6","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NSBSMABY5DU6C2SA","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NSBSMABY","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:de57786e41071406a024d654e9f9d2461f42d55fd9e7e3da7349fa849111ef4a","target":"graph","created_at":"2026-05-17T23:43:28Z","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 $f\\colon M \\to M$ be a uniformly quasiregular self-mapping of a compact, connected, and oriented Riemannian $n$-manifold $M$ without boundary, $n\\ge 2$. We show that, for $k \\in \\{0,\\ldots, n\\}$, the induced homomorphism $f^* \\colon H^k(M;\\mathbb{R}) \\to H^k(M;\\mathbb{R})$, where $H^k(M;\\mathbb{R})$ is the $k$:th singular cohomology of $M$, is complex diagonalizable and the eigenvalues of $f^*$ have modulus $(\\mathrm{deg}\\ f)^{k/n}$. As an application, we obtain a degree restriction for uniformly quasiregular self-mappings of closed manifolds. In the proof of the main theorem, we use a Sob","authors_text":"Ilmari Kangasniemi, Pekka Pankka","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-04T11:12:57Z","title":"Uniform cohomological expansion of uniformly quasiregular mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01451","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":"sha256:6188f52a32125e8b903369255b3bc9141106c185ce7b1da772d357e3c4b497fe","target":"record","created_at":"2026-05-17T23:43:28Z","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":"3ae173b4309b289a077a3342085789e347d2d5dbc006c3ca07051e8ce989765e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-04T11:12:57Z","title_canon_sha256":"a82b3f7e0c740ba8e5ffd39c08f14ad6488040deafc3e62817955cde16c2114c"},"schema_version":"1.0","source":{"id":"1708.01451","kind":"arxiv","version":3}},"canonical_sha256":"6c83260038e8e9e16a403c41ab2f6c348752903f0e3ad9cc6f5f57ca72264f0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c83260038e8e9e16a403c41ab2f6c348752903f0e3ad9cc6f5f57ca72264f0d","first_computed_at":"2026-05-17T23:43:28.663722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:28.663722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Q2FVnfYF6ZGKfOtPZ/yUNfkhlt3WNZSE+mk3LOVxo62IPRY2QK+PeNT5jA18cnxV8s6EAMMf7AUFMNENzqlBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:28.664222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01451","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6188f52a32125e8b903369255b3bc9141106c185ce7b1da772d357e3c4b497fe","sha256:de57786e41071406a024d654e9f9d2461f42d55fd9e7e3da7349fa849111ef4a"],"state_sha256":"27a122d2649585865ab253be0fd2a5cc2de129b4a4e7a37a0fd929ad273924eb"}