{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XHREFHQ5DWKS3VPMICB2AUCYDU","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":"d26990408b8d5fd72290c743e94d84b33f3bfe4c3f6aa7cad0bd7395a6352545","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-06T15:01:16Z","title_canon_sha256":"d27aeec554e59f1f288e76f6fda6a31d1ea7093b257830ce2e1d03f595201f2a"},"schema_version":"1.0","source":{"id":"1302.1392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1392","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1392v2","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1392","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"pith_short_12","alias_value":"XHREFHQ5DWKS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XHREFHQ5DWKS3VPM","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XHREFHQ5","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:a3c480228f381a02f0448fac31e0a8be9509d2ac8e21dc88417bc404026bdabe","target":"graph","created_at":"2026-05-18T03:34:02Z","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 initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu-Birkhoff decomposition theorem, this generalizes and complements theorems on continuous group cohomology by several authors.","authors_text":"Christian Rosendal, Roman Sauer, Uri Bader","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-06T15:01:16Z","title":"On the cohomology of weakly almost periodic group representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1392","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":"sha256:3dbbdc6a58cc6ad72a46b522a93e5824004794b090ac89626614362c20533791","target":"record","created_at":"2026-05-18T03:34:02Z","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":"d26990408b8d5fd72290c743e94d84b33f3bfe4c3f6aa7cad0bd7395a6352545","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-06T15:01:16Z","title_canon_sha256":"d27aeec554e59f1f288e76f6fda6a31d1ea7093b257830ce2e1d03f595201f2a"},"schema_version":"1.0","source":{"id":"1302.1392","kind":"arxiv","version":2}},"canonical_sha256":"b9e2429e1d1d952dd5ec4083a050581d14d2af595dff80130b51997e1014f70a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e2429e1d1d952dd5ec4083a050581d14d2af595dff80130b51997e1014f70a","first_computed_at":"2026-05-18T03:34:02.233226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:02.233226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QjfNT3Ob9ZOlkJVVwHb5hDA13+SkDXqdEt/uKZeRYwS9HjDaMX+HxulQYWaEwK2sBxQUhHUnZF2RG1hEwxQoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:02.234086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dbbdc6a58cc6ad72a46b522a93e5824004794b090ac89626614362c20533791","sha256:a3c480228f381a02f0448fac31e0a8be9509d2ac8e21dc88417bc404026bdabe"],"state_sha256":"324af5a8d0410b5f2a5427d21d17721b228c3c3523b5b96ae2aeb880701db7e3"}