{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XVQBZLG4G26RH64EETLMW2DLQJ","short_pith_number":"pith:XVQBZLG4","schema_version":"1.0","canonical_sha256":"bd601cacdc36bd13fb8424d6cb686b8241bb47ccf7f0ae1fb66502f3516536df","source":{"kind":"arxiv","id":"1205.1375","version":3},"attestation_state":"computed","paper":{"title":"Simplicial volume of compact manifolds with amenable boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Sungwoon Kim, Thilo Kuessner","submitted_at":"2012-05-07T13:20:07Z","abstract_excerpt":"Let $M$ be the interior of a connected, oriented, compact manifold $V$ of dimension at least 2. If each path component of $\\partial V$ has amenable fundamental group, then we prove that the simplicial volume of $M$ is equal to the relative simplicial volume of $V$ and also to the geometric (Lipschitz) simplicial volume of any Riemannian metric on $M$ whenever the latter is finite. As an application we establish the proportionality principle for the simplicial volume of complete, pinched negatively curved manifolds of finite volume."},"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":"1205.1375","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-05-07T13:20:07Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"9e665859ca85929692a07e154946067cf957f0341950a2d6adc9812d248a64c2","abstract_canon_sha256":"db9fd9dcbf1a916dbfe0dce33b0a920981cb25f480f3a8c2294c47ea50aa4f7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:56.978186Z","signature_b64":"m97KvrxhFapsRlTpvAB8QOOTXSoQmKJ9aCXBCULTx2vFVUPeRM6/5klwS2GFMGe+x0Bx/E3+Wk3SEzXN44I/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd601cacdc36bd13fb8424d6cb686b8241bb47ccf7f0ae1fb66502f3516536df","last_reissued_at":"2026-05-18T03:19:56.977546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:56.977546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simplicial volume of compact manifolds with amenable boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Sungwoon Kim, Thilo Kuessner","submitted_at":"2012-05-07T13:20:07Z","abstract_excerpt":"Let $M$ be the interior of a connected, oriented, compact manifold $V$ of dimension at least 2. If each path component of $\\partial V$ has amenable fundamental group, then we prove that the simplicial volume of $M$ is equal to the relative simplicial volume of $V$ and also to the geometric (Lipschitz) simplicial volume of any Riemannian metric on $M$ whenever the latter is finite. As an application we establish the proportionality principle for the simplicial volume of complete, pinched negatively curved manifolds of finite volume."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1375","kind":"arxiv","version":3},"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":"1205.1375","created_at":"2026-05-18T03:19:56.977642+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1375v3","created_at":"2026-05-18T03:19:56.977642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1375","created_at":"2026-05-18T03:19:56.977642+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVQBZLG4G26R","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVQBZLG4G26RH64E","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVQBZLG4","created_at":"2026-05-18T12:27:27.928770+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ","json":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ.json","graph_json":"https://pith.science/api/pith-number/XVQBZLG4G26RH64EETLMW2DLQJ/graph.json","events_json":"https://pith.science/api/pith-number/XVQBZLG4G26RH64EETLMW2DLQJ/events.json","paper":"https://pith.science/paper/XVQBZLG4"},"agent_actions":{"view_html":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ","download_json":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ.json","view_paper":"https://pith.science/paper/XVQBZLG4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1375&json=true","fetch_graph":"https://pith.science/api/pith-number/XVQBZLG4G26RH64EETLMW2DLQJ/graph.json","fetch_events":"https://pith.science/api/pith-number/XVQBZLG4G26RH64EETLMW2DLQJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ/action/storage_attestation","attest_author":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ/action/author_attestation","sign_citation":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ/action/citation_signature","submit_replication":"https://pith.science/pith/XVQBZLG4G26RH64EETLMW2DLQJ/action/replication_record"}},"created_at":"2026-05-18T03:19:56.977642+00:00","updated_at":"2026-05-18T03:19:56.977642+00:00"}