{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5NEOP5MX2SYCJSIFNASERVVUSO","short_pith_number":"pith:5NEOP5MX","schema_version":"1.0","canonical_sha256":"eb48e7f597d4b024c905682448d6b4938aebaa5fcc8f223f7f0e28217c76f8bb","source":{"kind":"arxiv","id":"1705.08400","version":3},"attestation_state":"computed","paper":{"title":"Eigenvalue estimates and differential form Laplacians on Alexandrov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John Lott","submitted_at":"2017-05-23T16:37:54Z","abstract_excerpt":"We give upper bounds on the eigenvalues of the differential form Laplacian on a compact Riemannian manifold. The proof uses Alexandrov spaces with curvature bounded below. We also construct differential form Laplacians on Alexandrov spaces. Under a local biLipschitz assumption on the Alexandrov space, which is conjecturally always satisfied, we show that the differential form Laplacian has a compact resolvent. We identify its kernel with an intersection homology group."},"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":"1705.08400","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-23T16:37:54Z","cross_cats_sorted":[],"title_canon_sha256":"c219f08c5d26a01226cc45aac674e884c38bf84a0a1fe6eb81c6e5322a91b5b9","abstract_canon_sha256":"e4734d694b06a53bb957e6a2572babaaad5b845687ae925bf2708fe89b18946d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:21.349461Z","signature_b64":"En0ViDo4SlZafNovwwDGfOZ6E4tNmRrgLAtORx4M9QUAR5O59mWgB1DlpyuKidCQIcD5To4oeqngizglG2fIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb48e7f597d4b024c905682448d6b4938aebaa5fcc8f223f7f0e28217c76f8bb","last_reissued_at":"2026-05-18T00:26:21.348877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:21.348877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalue estimates and differential form Laplacians on Alexandrov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John Lott","submitted_at":"2017-05-23T16:37:54Z","abstract_excerpt":"We give upper bounds on the eigenvalues of the differential form Laplacian on a compact Riemannian manifold. The proof uses Alexandrov spaces with curvature bounded below. We also construct differential form Laplacians on Alexandrov spaces. Under a local biLipschitz assumption on the Alexandrov space, which is conjecturally always satisfied, we show that the differential form Laplacian has a compact resolvent. We identify its kernel with an intersection homology group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08400","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":"1705.08400","created_at":"2026-05-18T00:26:21.348952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.08400v3","created_at":"2026-05-18T00:26:21.348952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08400","created_at":"2026-05-18T00:26:21.348952+00:00"},{"alias_kind":"pith_short_12","alias_value":"5NEOP5MX2SYC","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5NEOP5MX2SYCJSIF","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5NEOP5MX","created_at":"2026-05-18T12:31:00.734936+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/5NEOP5MX2SYCJSIFNASERVVUSO","json":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO.json","graph_json":"https://pith.science/api/pith-number/5NEOP5MX2SYCJSIFNASERVVUSO/graph.json","events_json":"https://pith.science/api/pith-number/5NEOP5MX2SYCJSIFNASERVVUSO/events.json","paper":"https://pith.science/paper/5NEOP5MX"},"agent_actions":{"view_html":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO","download_json":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO.json","view_paper":"https://pith.science/paper/5NEOP5MX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.08400&json=true","fetch_graph":"https://pith.science/api/pith-number/5NEOP5MX2SYCJSIFNASERVVUSO/graph.json","fetch_events":"https://pith.science/api/pith-number/5NEOP5MX2SYCJSIFNASERVVUSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO/action/storage_attestation","attest_author":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO/action/author_attestation","sign_citation":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO/action/citation_signature","submit_replication":"https://pith.science/pith/5NEOP5MX2SYCJSIFNASERVVUSO/action/replication_record"}},"created_at":"2026-05-18T00:26:21.348952+00:00","updated_at":"2026-05-18T00:26:21.348952+00:00"}