{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IIS2RMENVJGPKXMWBHIUPM32OA","short_pith_number":"pith:IIS2RMEN","schema_version":"1.0","canonical_sha256":"4225a8b08daa4cf55d9609d147b37a702b9cfc6841dbb902a40f9d057fc3e1b0","source":{"kind":"arxiv","id":"1203.0373","version":4},"attestation_state":"computed","paper":{"title":"The Kato square root problem on vector bundles with generalised bounded geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alan McIntosh, Lashi Bandara","submitted_at":"2012-03-02T05:17:54Z","abstract_excerpt":"We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions."},"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":"1203.0373","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-02T05:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"51d7acb515043960c71b2d609d5e2c6db1fcc7d30e394f2e7de2fac19cb3b2c5","abstract_canon_sha256":"b756b8aee98a19d798872502b0a61fd3896d637bd61279eaeea165ab8d10a2eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:31.154302Z","signature_b64":"11kY2fIRU8s/0fOIKsRIYZb7NQkJ/oXg3zO5pdX0KXaMqoyPx/CIwAj0DqRo3VI+KIGUe4ER53mTe1BjSAVXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4225a8b08daa4cf55d9609d147b37a702b9cfc6841dbb902a40f9d057fc3e1b0","last_reissued_at":"2026-05-18T01:19:31.153565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:31.153565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Kato square root problem on vector bundles with generalised bounded geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alan McIntosh, Lashi Bandara","submitted_at":"2012-03-02T05:17:54Z","abstract_excerpt":"We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0373","kind":"arxiv","version":4},"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":"1203.0373","created_at":"2026-05-18T01:19:31.153667+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.0373v4","created_at":"2026-05-18T01:19:31.153667+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0373","created_at":"2026-05-18T01:19:31.153667+00:00"},{"alias_kind":"pith_short_12","alias_value":"IIS2RMENVJGP","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IIS2RMENVJGPKXMW","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IIS2RMEN","created_at":"2026-05-18T12:27:09.501522+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/IIS2RMENVJGPKXMWBHIUPM32OA","json":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA.json","graph_json":"https://pith.science/api/pith-number/IIS2RMENVJGPKXMWBHIUPM32OA/graph.json","events_json":"https://pith.science/api/pith-number/IIS2RMENVJGPKXMWBHIUPM32OA/events.json","paper":"https://pith.science/paper/IIS2RMEN"},"agent_actions":{"view_html":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA","download_json":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA.json","view_paper":"https://pith.science/paper/IIS2RMEN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.0373&json=true","fetch_graph":"https://pith.science/api/pith-number/IIS2RMENVJGPKXMWBHIUPM32OA/graph.json","fetch_events":"https://pith.science/api/pith-number/IIS2RMENVJGPKXMWBHIUPM32OA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA/action/storage_attestation","attest_author":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA/action/author_attestation","sign_citation":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA/action/citation_signature","submit_replication":"https://pith.science/pith/IIS2RMENVJGPKXMWBHIUPM32OA/action/replication_record"}},"created_at":"2026-05-18T01:19:31.153667+00:00","updated_at":"2026-05-18T01:19:31.153667+00:00"}