{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:XHD2H2APVH4BU7ASOB6MEXXPVN","short_pith_number":"pith:XHD2H2AP","schema_version":"1.0","canonical_sha256":"b9c7a3e80fa9f81a7c12707cc25eefab70b513ef43a10063200ad0e27b644025","source":{"kind":"arxiv","id":"2107.08571","version":5},"attestation_state":"computed","paper":{"title":"The space of non-extendable quasimorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GT","math.SG"],"primary_cat":"math.GR","authors_text":"Masato Mimura, Mitsuaki Kimura, Morimichi Kawasaki, Shuhei Maruyama, Takahiro Matsushita","submitted_at":"2021-07-19T01:17:34Z","abstract_excerpt":"For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov-hyperbolic groups.\n  Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length f"},"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":"2107.08571","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-07-19T01:17:34Z","cross_cats_sorted":["math.FA","math.GT","math.SG"],"title_canon_sha256":"777ec27f8fb2fce5b85d39f20ee163629792cf7685410440a887f4cd2fc84cd6","abstract_canon_sha256":"52c36894c944eecf497ebb86f0a14e462dac0e1da298d511970d4fc06752fc18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:06.225489Z","signature_b64":"LnFual8p4dY1AXB0CVrrrBs9KwMnVp4Q8KN/+IWSj4tCsCUC5L8frg222PLQNUn3VzxpWj3YHGFgtCXyVm50Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9c7a3e80fa9f81a7c12707cc25eefab70b513ef43a10063200ad0e27b644025","last_reissued_at":"2026-07-05T11:06:06.224909Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:06.224909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The space of non-extendable quasimorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GT","math.SG"],"primary_cat":"math.GR","authors_text":"Masato Mimura, Mitsuaki Kimura, Morimichi Kawasaki, Shuhei Maruyama, Takahiro Matsushita","submitted_at":"2021-07-19T01:17:34Z","abstract_excerpt":"For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov-hyperbolic groups.\n  Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.08571","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.08571/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2107.08571","created_at":"2026-07-05T11:06:06.224962+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.08571v5","created_at":"2026-07-05T11:06:06.224962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.08571","created_at":"2026-07-05T11:06:06.224962+00:00"},{"alias_kind":"pith_short_12","alias_value":"XHD2H2APVH4B","created_at":"2026-07-05T11:06:06.224962+00:00"},{"alias_kind":"pith_short_16","alias_value":"XHD2H2APVH4BU7AS","created_at":"2026-07-05T11:06:06.224962+00:00"},{"alias_kind":"pith_short_8","alias_value":"XHD2H2AP","created_at":"2026-07-05T11:06:06.224962+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.20462","citing_title":"Bounded cohomology, quotient extensions, and hierarchical hyperbolicity","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN","json":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN.json","graph_json":"https://pith.science/api/pith-number/XHD2H2APVH4BU7ASOB6MEXXPVN/graph.json","events_json":"https://pith.science/api/pith-number/XHD2H2APVH4BU7ASOB6MEXXPVN/events.json","paper":"https://pith.science/paper/XHD2H2AP"},"agent_actions":{"view_html":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN","download_json":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN.json","view_paper":"https://pith.science/paper/XHD2H2AP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.08571&json=true","fetch_graph":"https://pith.science/api/pith-number/XHD2H2APVH4BU7ASOB6MEXXPVN/graph.json","fetch_events":"https://pith.science/api/pith-number/XHD2H2APVH4BU7ASOB6MEXXPVN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN/action/storage_attestation","attest_author":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN/action/author_attestation","sign_citation":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN/action/citation_signature","submit_replication":"https://pith.science/pith/XHD2H2APVH4BU7ASOB6MEXXPVN/action/replication_record"}},"created_at":"2026-07-05T11:06:06.224962+00:00","updated_at":"2026-07-05T11:06:06.224962+00:00"}