{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GB5WSYVGKHGJEPBJRCWSTPLWHP","short_pith_number":"pith:GB5WSYVG","schema_version":"1.0","canonical_sha256":"307b6962a651cc923c2988ad29bd763bea4d15c7ad54924d38af99828bbfc858","source":{"kind":"arxiv","id":"1504.08205","version":1},"attestation_state":"computed","paper":{"title":"Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anders Bj\\\"orn, Jana Bj\\\"orn, Visa Latvala","submitted_at":"2015-04-30T13:01:16Z","abstract_excerpt":"We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\\'e inequality with 1<p<\\infty, and connect them to the Sobolev theory in R^n. In particular, we show that for quasiopen subsets of R^n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpel\\\"ainen and Mal\\'y in 1992. As a by-product, we establish the quasi-Lindel\\\"of principle of the fine topology in metric spaces and study several vari"},"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":"1504.08205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-30T13:01:16Z","cross_cats_sorted":[],"title_canon_sha256":"e5bd453ec0ecd43f3843ed12f3b2eb845dabfcb505aff3dd98ce10f6eb6c09f7","abstract_canon_sha256":"3fbe933d6e9c720b38c41dcd24d4b7828a89fc2f9a938e0787cffaca36f06d71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:01.577296Z","signature_b64":"FDtE0d+juNDEbc4M4kaCExJo5PgVBTiB7Q64jr8g82nRrqEtsQmGyhJ24V1bzVTISNoCGkygEnIt/t1TdYsSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"307b6962a651cc923c2988ad29bd763bea4d15c7ad54924d38af99828bbfc858","last_reissued_at":"2026-05-18T00:51:01.576779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:01.576779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anders Bj\\\"orn, Jana Bj\\\"orn, Visa Latvala","submitted_at":"2015-04-30T13:01:16Z","abstract_excerpt":"We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\\'e inequality with 1<p<\\infty, and connect them to the Sobolev theory in R^n. In particular, we show that for quasiopen subsets of R^n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpel\\\"ainen and Mal\\'y in 1992. As a by-product, we establish the quasi-Lindel\\\"of principle of the fine topology in metric spaces and study several vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08205","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":"1504.08205","created_at":"2026-05-18T00:51:01.576864+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.08205v1","created_at":"2026-05-18T00:51:01.576864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08205","created_at":"2026-05-18T00:51:01.576864+00:00"},{"alias_kind":"pith_short_12","alias_value":"GB5WSYVGKHGJ","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GB5WSYVGKHGJEPBJ","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GB5WSYVG","created_at":"2026-05-18T12:29:22.688609+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/GB5WSYVGKHGJEPBJRCWSTPLWHP","json":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP.json","graph_json":"https://pith.science/api/pith-number/GB5WSYVGKHGJEPBJRCWSTPLWHP/graph.json","events_json":"https://pith.science/api/pith-number/GB5WSYVGKHGJEPBJRCWSTPLWHP/events.json","paper":"https://pith.science/paper/GB5WSYVG"},"agent_actions":{"view_html":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP","download_json":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP.json","view_paper":"https://pith.science/paper/GB5WSYVG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.08205&json=true","fetch_graph":"https://pith.science/api/pith-number/GB5WSYVGKHGJEPBJRCWSTPLWHP/graph.json","fetch_events":"https://pith.science/api/pith-number/GB5WSYVGKHGJEPBJRCWSTPLWHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP/action/storage_attestation","attest_author":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP/action/author_attestation","sign_citation":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP/action/citation_signature","submit_replication":"https://pith.science/pith/GB5WSYVGKHGJEPBJRCWSTPLWHP/action/replication_record"}},"created_at":"2026-05-18T00:51:01.576864+00:00","updated_at":"2026-05-18T00:51:01.576864+00:00"}