{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7DV2KYOMYYM7O7WDPODITSF2LB","short_pith_number":"pith:7DV2KYOM","schema_version":"1.0","canonical_sha256":"f8eba561ccc619f77ec37b8689c8ba587dec2a6bcb08016f80375ee0bd860c2d","source":{"kind":"arxiv","id":"1604.03068","version":3},"attestation_state":"computed","paper":{"title":"Existence of 1D vectorial Absolute Minimisers in $L^\\infty$ under minimal assumptions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hussien Abugirda (Reading, Nikos Katzourakis (Reading, UK)","submitted_at":"2016-04-11T18:59:36Z","abstract_excerpt":"We prove the existence of vectorial Absolute Minimisers in the sense of Aronsson to the supremal functional $E_\\infty(u,\\Omega') = \\|\\mathscr{L}(\\cdot,u,D u)\\|_{L^\\infty(\\Omega')}$, $\\Omega'\\Subset \\Omega$, applied to $W^{1,\\infty}$ maps $u:\\Omega\\subseteq \\mathbb{R}\\longrightarrow \\mathbb{R}^N$ with given boundary values. The assumptions on $\\mathscr{L}($ are minimal, improving earlier existence results previously established by Barron-Jensen-Wang and by the second author."},"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":"1604.03068","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-11T18:59:36Z","cross_cats_sorted":[],"title_canon_sha256":"d05391b97c780b468cfb3f78c3655b187f55625696ef58bf6e2334a0febd7c13","abstract_canon_sha256":"baacad32dd2f1d8396b80c326fad5b601a61fad92387847874280db2510c0e00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:19.888220Z","signature_b64":"jhtkSLrcL6RIeJ4+6Ll5rPWmTpPFuSG0Ovtwk9Je3/EmCRSK3FgbrUoF3nonKP5zsjw6/TB9YtmNwJA6XE7UCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8eba561ccc619f77ec37b8689c8ba587dec2a6bcb08016f80375ee0bd860c2d","last_reissued_at":"2026-05-18T01:10:19.887779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:19.887779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of 1D vectorial Absolute Minimisers in $L^\\infty$ under minimal assumptions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hussien Abugirda (Reading, Nikos Katzourakis (Reading, UK)","submitted_at":"2016-04-11T18:59:36Z","abstract_excerpt":"We prove the existence of vectorial Absolute Minimisers in the sense of Aronsson to the supremal functional $E_\\infty(u,\\Omega') = \\|\\mathscr{L}(\\cdot,u,D u)\\|_{L^\\infty(\\Omega')}$, $\\Omega'\\Subset \\Omega$, applied to $W^{1,\\infty}$ maps $u:\\Omega\\subseteq \\mathbb{R}\\longrightarrow \\mathbb{R}^N$ with given boundary values. The assumptions on $\\mathscr{L}($ are minimal, improving earlier existence results previously established by Barron-Jensen-Wang and by the second author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03068","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":"1604.03068","created_at":"2026-05-18T01:10:19.887840+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.03068v3","created_at":"2026-05-18T01:10:19.887840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03068","created_at":"2026-05-18T01:10:19.887840+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DV2KYOMYYM7","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DV2KYOMYYM7O7WD","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DV2KYOM","created_at":"2026-05-18T12:30:04.600751+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/7DV2KYOMYYM7O7WDPODITSF2LB","json":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB.json","graph_json":"https://pith.science/api/pith-number/7DV2KYOMYYM7O7WDPODITSF2LB/graph.json","events_json":"https://pith.science/api/pith-number/7DV2KYOMYYM7O7WDPODITSF2LB/events.json","paper":"https://pith.science/paper/7DV2KYOM"},"agent_actions":{"view_html":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB","download_json":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB.json","view_paper":"https://pith.science/paper/7DV2KYOM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.03068&json=true","fetch_graph":"https://pith.science/api/pith-number/7DV2KYOMYYM7O7WDPODITSF2LB/graph.json","fetch_events":"https://pith.science/api/pith-number/7DV2KYOMYYM7O7WDPODITSF2LB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB/action/storage_attestation","attest_author":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB/action/author_attestation","sign_citation":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB/action/citation_signature","submit_replication":"https://pith.science/pith/7DV2KYOMYYM7O7WDPODITSF2LB/action/replication_record"}},"created_at":"2026-05-18T01:10:19.887840+00:00","updated_at":"2026-05-18T01:10:19.887840+00:00"}