{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TYDKTU6YMYIQ5DMP47GF6QTIKJ","short_pith_number":"pith:TYDKTU6Y","schema_version":"1.0","canonical_sha256":"9e06a9d3d866110e8d8fe7cc5f426852651dc0d3c08eff18c53f0dcd5e936279","source":{"kind":"arxiv","id":"1306.1542","version":2},"attestation_state":"computed","paper":{"title":"Bounded cohomology with coefficients in uniformly convex Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ken Bromberg, Koji Fujiwara, Mladen Bestvina","submitted_at":"2013-06-06T20:19:10Z","abstract_excerpt":"We show that for acylindrically hyperbolic groups $\\Gamma$ (with no nontrivial finite normal subgroups) and arbitrary unitary representation $\\rho$ of $\\Gamma$ in a (nonzero) uniformly convex Banach space the vector space $H^2_b(\\Gamma;\\rho)$ is infinite dimensional. The result was known for the regular representations on $\\ell^p(\\Gamma)$ with $1<p<\\infty$ by a different argument. But our result is new even for a non-abelian free group in this great generality for representations, and also the case for acylindrically hyperbolic groups follows as an application."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1306.1542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-06T20:19:10Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"4ee44f1ba2bb6f762910c3748dfb1df90256e07402feea2b025c3cc092cc6cd2","abstract_canon_sha256":"4f61269771b3dd07867796f9b46d71e421e1d7aabf8289a80d0f7a34e4d0e250"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:08.259172Z","signature_b64":"2rnJ0fyfi3UrqXiXs30raCmu0WsnFSFGmCK4uaVb7mWtGno2sTtBNtRmW6iWyOIgiOevPtiYjR+LlwSLCKxFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e06a9d3d866110e8d8fe7cc5f426852651dc0d3c08eff18c53f0dcd5e936279","last_reissued_at":"2026-05-18T02:27:08.258451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:08.258451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded cohomology with coefficients in uniformly convex Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ken Bromberg, Koji Fujiwara, Mladen Bestvina","submitted_at":"2013-06-06T20:19:10Z","abstract_excerpt":"We show that for acylindrically hyperbolic groups $\\Gamma$ (with no nontrivial finite normal subgroups) and arbitrary unitary representation $\\rho$ of $\\Gamma$ in a (nonzero) uniformly convex Banach space the vector space $H^2_b(\\Gamma;\\rho)$ is infinite dimensional. The result was known for the regular representations on $\\ell^p(\\Gamma)$ with $1<p<\\infty$ by a different argument. But our result is new even for a non-abelian free group in this great generality for representations, and also the case for acylindrically hyperbolic groups follows as an application."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1542","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1306.1542","created_at":"2026-05-18T02:27:08.258565+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.1542v2","created_at":"2026-05-18T02:27:08.258565+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1542","created_at":"2026-05-18T02:27:08.258565+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYDKTU6YMYIQ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYDKTU6YMYIQ5DMP","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYDKTU6Y","created_at":"2026-05-18T12:28:02.375192+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.11126","citing_title":"Connections between the topology of the Morse boundary, the Morse local-to-global property and acylindrical hyperbolicity","ref_index":69,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ","json":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ.json","graph_json":"https://pith.science/api/pith-number/TYDKTU6YMYIQ5DMP47GF6QTIKJ/graph.json","events_json":"https://pith.science/api/pith-number/TYDKTU6YMYIQ5DMP47GF6QTIKJ/events.json","paper":"https://pith.science/paper/TYDKTU6Y"},"agent_actions":{"view_html":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ","download_json":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ.json","view_paper":"https://pith.science/paper/TYDKTU6Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.1542&json=true","fetch_graph":"https://pith.science/api/pith-number/TYDKTU6YMYIQ5DMP47GF6QTIKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/TYDKTU6YMYIQ5DMP47GF6QTIKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ/action/storage_attestation","attest_author":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ/action/author_attestation","sign_citation":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ/action/citation_signature","submit_replication":"https://pith.science/pith/TYDKTU6YMYIQ5DMP47GF6QTIKJ/action/replication_record"}},"created_at":"2026-05-18T02:27:08.258565+00:00","updated_at":"2026-05-18T02:27:08.258565+00:00"}