{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:G5IYWUIJORS7ADNWMXVQTBOVZ6","short_pith_number":"pith:G5IYWUIJ","schema_version":"1.0","canonical_sha256":"37518b51097465f00db665eb0985d5cf98a295a989491bef6cfa5d7e362018b1","source":{"kind":"arxiv","id":"1607.01660","version":2},"attestation_state":"computed","paper":{"title":"Whitney-type extension theorems for jets generated by Sobolev functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pavel Shvartsman","submitted_at":"2016-07-06T15:09:45Z","abstract_excerpt":"Let $L^m_p(R^n)$, $p\\in [1,\\infty]$, be the homogeneous Sobolev space, and let $E\\subset R^n$ be a closed set. For each $p>n$ and each non-negative integer $m$ we give an intrinsic characterization of the restrictions to $E$ of $m$-jets generated by functions $F\\in L^{m+1}_p(R^n)$. Our trace criterion is expressed in terms of variations of corresponding Taylor remainders of $m$-jets evaluated on a certain family of \"well separated\" two point subsets of $E$. For $p=\\infty$ this result coincides with the classical Whitney-Glaeser extension theorem for $m$-jets.\n  Our approach is based on a repre"},"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":"1607.01660","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-06T15:09:45Z","cross_cats_sorted":[],"title_canon_sha256":"0494585a8a60375c9af9a7a811ca63d94986e0c3f23c5e42ae4c32aa772a681d","abstract_canon_sha256":"e357868fe4e0188d714ab1e70773e13494da6fc803b626e997c8c8b14e9fef5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:58.783334Z","signature_b64":"yCkTZ49wcSdPihdXq+BjXBk+QbVCMIh6TrGBeaW15dEmR1Sv+L+EamvNu8l7jbAwhtsaMnckOxIXDQpRV3jTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37518b51097465f00db665eb0985d5cf98a295a989491bef6cfa5d7e362018b1","last_reissued_at":"2026-05-18T01:10:58.782771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:58.782771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Whitney-type extension theorems for jets generated by Sobolev functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pavel Shvartsman","submitted_at":"2016-07-06T15:09:45Z","abstract_excerpt":"Let $L^m_p(R^n)$, $p\\in [1,\\infty]$, be the homogeneous Sobolev space, and let $E\\subset R^n$ be a closed set. For each $p>n$ and each non-negative integer $m$ we give an intrinsic characterization of the restrictions to $E$ of $m$-jets generated by functions $F\\in L^{m+1}_p(R^n)$. Our trace criterion is expressed in terms of variations of corresponding Taylor remainders of $m$-jets evaluated on a certain family of \"well separated\" two point subsets of $E$. For $p=\\infty$ this result coincides with the classical Whitney-Glaeser extension theorem for $m$-jets.\n  Our approach is based on a repre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01660","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":"1607.01660","created_at":"2026-05-18T01:10:58.782875+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01660v2","created_at":"2026-05-18T01:10:58.782875+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01660","created_at":"2026-05-18T01:10:58.782875+00:00"},{"alias_kind":"pith_short_12","alias_value":"G5IYWUIJORS7","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"G5IYWUIJORS7ADNW","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"G5IYWUIJ","created_at":"2026-05-18T12:30:15.759754+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/G5IYWUIJORS7ADNWMXVQTBOVZ6","json":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6.json","graph_json":"https://pith.science/api/pith-number/G5IYWUIJORS7ADNWMXVQTBOVZ6/graph.json","events_json":"https://pith.science/api/pith-number/G5IYWUIJORS7ADNWMXVQTBOVZ6/events.json","paper":"https://pith.science/paper/G5IYWUIJ"},"agent_actions":{"view_html":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6","download_json":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6.json","view_paper":"https://pith.science/paper/G5IYWUIJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01660&json=true","fetch_graph":"https://pith.science/api/pith-number/G5IYWUIJORS7ADNWMXVQTBOVZ6/graph.json","fetch_events":"https://pith.science/api/pith-number/G5IYWUIJORS7ADNWMXVQTBOVZ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6/action/storage_attestation","attest_author":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6/action/author_attestation","sign_citation":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6/action/citation_signature","submit_replication":"https://pith.science/pith/G5IYWUIJORS7ADNWMXVQTBOVZ6/action/replication_record"}},"created_at":"2026-05-18T01:10:58.782875+00:00","updated_at":"2026-05-18T01:10:58.782875+00:00"}