{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:3ITGNXVOKJGK467JFORUS2ZD4A","short_pith_number":"pith:3ITGNXVO","schema_version":"1.0","canonical_sha256":"da2666deae524cae7be92ba3496b23e00aa93fe54df12199dbc494f1797a4525","source":{"kind":"arxiv","id":"1902.08613","version":2},"attestation_state":"computed","paper":{"title":"Sobolev embeddings with weights in complete riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eric Amar","submitted_at":"2019-02-21T08:23:38Z","abstract_excerpt":"We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold. We also get general Gaffney's inequality with weights. As a consequence, under a \"weak bounded geometry\" hypothesis, we improve classical Sobolev embedding Theorems for vector bundles in a complete riemannian manifold. We also improve known results on Gaffney's inequality in a complete riemannian manifold."},"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":"1902.08613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-21T08:23:38Z","cross_cats_sorted":[],"title_canon_sha256":"d605eb384eab52ed65160c2b0463e93ee8ed17ed259fd0a443fecc972764da09","abstract_canon_sha256":"57c6cd7cfe0ff4b8f16b0cbcd273b5397dd0bfe72a98403fc26aefeb117a1a69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:38.614715Z","signature_b64":"Ryt68DhRDgUy0i3ktLjlkukNv7AAdh+qCTil70KSqwutqbO7k2YJeEJt8awtgv4prGBM0hsOPIctq7CqaNLqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da2666deae524cae7be92ba3496b23e00aa93fe54df12199dbc494f1797a4525","last_reissued_at":"2026-05-17T23:44:38.614227Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:38.614227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sobolev embeddings with weights in complete riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eric Amar","submitted_at":"2019-02-21T08:23:38Z","abstract_excerpt":"We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold. We also get general Gaffney's inequality with weights. As a consequence, under a \"weak bounded geometry\" hypothesis, we improve classical Sobolev embedding Theorems for vector bundles in a complete riemannian manifold. We also improve known results on Gaffney's inequality in a complete riemannian manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08613","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":"1902.08613","created_at":"2026-05-17T23:44:38.614311+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.08613v2","created_at":"2026-05-17T23:44:38.614311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08613","created_at":"2026-05-17T23:44:38.614311+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ITGNXVOKJGK","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ITGNXVOKJGK467J","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ITGNXVO","created_at":"2026-05-18T12:33:07.085635+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/3ITGNXVOKJGK467JFORUS2ZD4A","json":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A.json","graph_json":"https://pith.science/api/pith-number/3ITGNXVOKJGK467JFORUS2ZD4A/graph.json","events_json":"https://pith.science/api/pith-number/3ITGNXVOKJGK467JFORUS2ZD4A/events.json","paper":"https://pith.science/paper/3ITGNXVO"},"agent_actions":{"view_html":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A","download_json":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A.json","view_paper":"https://pith.science/paper/3ITGNXVO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.08613&json=true","fetch_graph":"https://pith.science/api/pith-number/3ITGNXVOKJGK467JFORUS2ZD4A/graph.json","fetch_events":"https://pith.science/api/pith-number/3ITGNXVOKJGK467JFORUS2ZD4A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A/action/storage_attestation","attest_author":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A/action/author_attestation","sign_citation":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A/action/citation_signature","submit_replication":"https://pith.science/pith/3ITGNXVOKJGK467JFORUS2ZD4A/action/replication_record"}},"created_at":"2026-05-17T23:44:38.614311+00:00","updated_at":"2026-05-17T23:44:38.614311+00:00"}