{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GUCHEKUGQ7WUGTOQPFP37KM6K6","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":"4410b7db16e79880ff5fb64a87c6fdb172fbc7027d6b8b2d8609d95f3e42e7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T16:58:37Z","title_canon_sha256":"3de6846d38acc5a7b71930297011bbbda9633b99e8febc416d78cabfc73875b2"},"schema_version":"1.0","source":{"id":"1710.03193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03193","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03193v2","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03193","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"GUCHEKUGQ7WU","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GUCHEKUGQ7WUGTOQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GUCHEKUG","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:2b535b6eb53142f6ea01aafa2bb4dc64bc5e338cba2aa95879db11ee9e91d53a","target":"graph","created_at":"2026-05-17T23:58:14Z","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":"The theory of bounded cohomology of groups has many applications. A key open problem is to compute the full bounded cohomology $H_b^n(F, R)$ of a non-abelian free group $F$ with trivial real coefficients. It is known that $H_b^n(F,R)$ is trivial for $n=1$ and uncountable dimensional for $n=2,3$, but remains unknown for any $n \\geq 4$. For $n=4$, one may construct classes by taking the cup product $\\alpha \\cup \\beta \\in H_b^4(F, R)$ between two $2$-classes $\\alpha, \\beta \\in H^2_b(F, R)$. However, we show that all such cup products are trivial if $\\alpha$ and $\\beta$ are classes induced by the ","authors_text":"Nicolaus Heuer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T16:58:37Z","title":"Cup Product in Bounded Cohomology of the Free Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03193","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":"sha256:7b60d7539154402a39446df43f1bf409562538267c1c53a3352bab18625352f6","target":"record","created_at":"2026-05-17T23:58:14Z","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":"4410b7db16e79880ff5fb64a87c6fdb172fbc7027d6b8b2d8609d95f3e42e7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T16:58:37Z","title_canon_sha256":"3de6846d38acc5a7b71930297011bbbda9633b99e8febc416d78cabfc73875b2"},"schema_version":"1.0","source":{"id":"1710.03193","kind":"arxiv","version":2}},"canonical_sha256":"3504722a8687ed434dd0795fbfa99e57835c27c665c74ef18213725cc90836ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3504722a8687ed434dd0795fbfa99e57835c27c665c74ef18213725cc90836ea","first_computed_at":"2026-05-17T23:58:14.853469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:14.853469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vRfh5SD+xifbXINH8VLjC10B4IrVClhjKpPsQYAlGYv2l3dQBfgqUBth6Q5qJqUA9s1pDipeoj0FLTcv7xB8DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:14.853941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b60d7539154402a39446df43f1bf409562538267c1c53a3352bab18625352f6","sha256:2b535b6eb53142f6ea01aafa2bb4dc64bc5e338cba2aa95879db11ee9e91d53a"],"state_sha256":"48079019990d3c710414aee251e847fdf8973ba70d7c53449737f28cc14f5211"}