{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RU42ZBMFIMGPLZKYAIOYMBKFRI","short_pith_number":"pith:RU42ZBMF","schema_version":"1.0","canonical_sha256":"8d39ac8585430cf5e558021d8605458a339ebaca7b82a5b90346dd8f30d49fcd","source":{"kind":"arxiv","id":"1901.05081","version":1},"attestation_state":"computed","paper":{"title":"The adiabatic groupoid and the Higson-Roe exact sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Vito Felice Zenobi","submitted_at":"2019-01-15T22:59:22Z","abstract_excerpt":"Let $\\widetilde{X}$ be a smooth Riemannian manifold equipped with a proper, free, isometric and cocompact action of a discrete group $\\Gamma$. In this paper we prove that the analytic surgery exact sequence of Higson-Roe for $\\widetilde{X}$ is isomorphic to the exact sequence associated to the adiabatic deformation of the Lie groupoid $\\widetilde{X}\\times_\\Gamma\\widetilde{X}$. We then generalize this result to the context of smoothly stratified manifolds. Finally, we show, by means of the aforementioned isomorphism, that the $\\varrho$-classes associated to a metric with positive scalar curvatu"},"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":"1901.05081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-01-15T22:59:22Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"662dffc18d41edc92eb59eb4e9eb44ceed122adf2425052745e431f35bc02eeb","abstract_canon_sha256":"f213e19b8295152e360818d9826812a265161f274f2439ee7e7c212672b36fdc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:12.001264Z","signature_b64":"TwBm5XBzH0bOuEpF4Do8iOG6K5754cfDlKlD9JL0FoEvSc9hyPO0hJkq9A6AlsNHb0mR8p+pIRUJlfx9lHOjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d39ac8585430cf5e558021d8605458a339ebaca7b82a5b90346dd8f30d49fcd","last_reissued_at":"2026-05-17T23:56:12.000645Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:12.000645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The adiabatic groupoid and the Higson-Roe exact sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Vito Felice Zenobi","submitted_at":"2019-01-15T22:59:22Z","abstract_excerpt":"Let $\\widetilde{X}$ be a smooth Riemannian manifold equipped with a proper, free, isometric and cocompact action of a discrete group $\\Gamma$. In this paper we prove that the analytic surgery exact sequence of Higson-Roe for $\\widetilde{X}$ is isomorphic to the exact sequence associated to the adiabatic deformation of the Lie groupoid $\\widetilde{X}\\times_\\Gamma\\widetilde{X}$. We then generalize this result to the context of smoothly stratified manifolds. Finally, we show, by means of the aforementioned isomorphism, that the $\\varrho$-classes associated to a metric with positive scalar curvatu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05081","kind":"arxiv","version":1},"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":"1901.05081","created_at":"2026-05-17T23:56:12.000736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.05081v1","created_at":"2026-05-17T23:56:12.000736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05081","created_at":"2026-05-17T23:56:12.000736+00:00"},{"alias_kind":"pith_short_12","alias_value":"RU42ZBMFIMGP","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"RU42ZBMFIMGPLZKY","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"RU42ZBMF","created_at":"2026-05-18T12:33:27.125529+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.05258","citing_title":"Lie groupoids, pseudodifferential calculus and index theory","ref_index":119,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI","json":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI.json","graph_json":"https://pith.science/api/pith-number/RU42ZBMFIMGPLZKYAIOYMBKFRI/graph.json","events_json":"https://pith.science/api/pith-number/RU42ZBMFIMGPLZKYAIOYMBKFRI/events.json","paper":"https://pith.science/paper/RU42ZBMF"},"agent_actions":{"view_html":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI","download_json":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI.json","view_paper":"https://pith.science/paper/RU42ZBMF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.05081&json=true","fetch_graph":"https://pith.science/api/pith-number/RU42ZBMFIMGPLZKYAIOYMBKFRI/graph.json","fetch_events":"https://pith.science/api/pith-number/RU42ZBMFIMGPLZKYAIOYMBKFRI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI/action/storage_attestation","attest_author":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI/action/author_attestation","sign_citation":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI/action/citation_signature","submit_replication":"https://pith.science/pith/RU42ZBMFIMGPLZKYAIOYMBKFRI/action/replication_record"}},"created_at":"2026-05-17T23:56:12.000736+00:00","updated_at":"2026-05-17T23:56:12.000736+00:00"}