{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2M5AF443NETTJ2O6H5GO3AW2I4","short_pith_number":"pith:2M5AF443","schema_version":"1.0","canonical_sha256":"d33a02f39b692734e9de3f4ced82da473730fc1e27537d72d1623a1503be6783","source":{"kind":"arxiv","id":"1403.5518","version":2},"attestation_state":"computed","paper":{"title":"The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.MG"],"primary_cat":"math.AT","authors_text":"Ayato Mitsuishi","submitted_at":"2014-03-21T16:57:30Z","abstract_excerpt":"We consider the category of all locally Lipschitz contractible metric spaces and all locally Lipschitz maps, which is a wide class of metric spaces, including all finite dimensional Alexandrov spaces and all CAT spaces. We also consider the chain complex of normal currents with compact support in a metric space in the sense of Ambrosio and Kirchheim. In the present paper, its homology is proved to be a homotopy invariant on the category.\n  To prove this result, we define a new topology on a space of Lipschitz maps between arbitrary metric spaces. This topology is proved to coincide with the us"},"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":"1403.5518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-21T16:57:30Z","cross_cats_sorted":["math.GN","math.MG"],"title_canon_sha256":"577c013b4ffacd3bc28931e7aa0dd41fec283872b34c8808d2cee07d929c9ee0","abstract_canon_sha256":"f94b0ec6bdfe28e61d94d5a787353db6da720b21d5fdc872aa6f087703e20fa1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:21.858064Z","signature_b64":"RN8VhSdU3tD0HbYtS2hVJLBJ5Yd28W+doy7COPJtnWVnWPhmTq8dZxW+gpBwjJh89nuuGZ69vMojnmnICu5ODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d33a02f39b692734e9de3f4ced82da473730fc1e27537d72d1623a1503be6783","last_reissued_at":"2026-05-18T01:29:21.857348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:21.857348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.MG"],"primary_cat":"math.AT","authors_text":"Ayato Mitsuishi","submitted_at":"2014-03-21T16:57:30Z","abstract_excerpt":"We consider the category of all locally Lipschitz contractible metric spaces and all locally Lipschitz maps, which is a wide class of metric spaces, including all finite dimensional Alexandrov spaces and all CAT spaces. We also consider the chain complex of normal currents with compact support in a metric space in the sense of Ambrosio and Kirchheim. In the present paper, its homology is proved to be a homotopy invariant on the category.\n  To prove this result, we define a new topology on a space of Lipschitz maps between arbitrary metric spaces. This topology is proved to coincide with the us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5518","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":"1403.5518","created_at":"2026-05-18T01:29:21.857469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5518v2","created_at":"2026-05-18T01:29:21.857469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5518","created_at":"2026-05-18T01:29:21.857469+00:00"},{"alias_kind":"pith_short_12","alias_value":"2M5AF443NETT","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2M5AF443NETTJ2O6","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2M5AF443","created_at":"2026-05-18T12:28:11.866339+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/2M5AF443NETTJ2O6H5GO3AW2I4","json":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4.json","graph_json":"https://pith.science/api/pith-number/2M5AF443NETTJ2O6H5GO3AW2I4/graph.json","events_json":"https://pith.science/api/pith-number/2M5AF443NETTJ2O6H5GO3AW2I4/events.json","paper":"https://pith.science/paper/2M5AF443"},"agent_actions":{"view_html":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4","download_json":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4.json","view_paper":"https://pith.science/paper/2M5AF443","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5518&json=true","fetch_graph":"https://pith.science/api/pith-number/2M5AF443NETTJ2O6H5GO3AW2I4/graph.json","fetch_events":"https://pith.science/api/pith-number/2M5AF443NETTJ2O6H5GO3AW2I4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4/action/storage_attestation","attest_author":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4/action/author_attestation","sign_citation":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4/action/citation_signature","submit_replication":"https://pith.science/pith/2M5AF443NETTJ2O6H5GO3AW2I4/action/replication_record"}},"created_at":"2026-05-18T01:29:21.857469+00:00","updated_at":"2026-05-18T01:29:21.857469+00:00"}