{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NMOGBBJ3RXQZWHG7OXBXL5G3TE","short_pith_number":"pith:NMOGBBJ3","schema_version":"1.0","canonical_sha256":"6b1c60853b8de19b1cdf75c375f4db9914e0f333382b76f0b4f7e062204691cb","source":{"kind":"arxiv","id":"1401.6358","version":2},"attestation_state":"computed","paper":{"title":"$\\mathcal{A}$-quasiconvexity and weak lower semicontinuity of integral functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriel Path\\'o, Jan Kr\\\"amer, Martin Kru\\v{z}\\'ik, Stefan Kr\\\"omer","submitted_at":"2014-01-24T14:49:28Z","abstract_excerpt":"We state necessary and sufficient conditions for weak lower semicontinuity of $u\\mapsto\\int_\\Omega h(x,u(x))\\,d x$ where $|h(x,s)|\\le C(1+|s|^p)$ is continuous and possesses a recession function, and $u\\in L^p(\\Omega;\\mathbb{R}^m)$, $p>1$, lives in the kernel of a constant-rank first-order differential operator $\\mathcal{A}$ which admits an extension property. Our newly defined notion coincides for $\\mathcal{A}=\\operatorname{curl}$ with quasiconvexity at the boundary due to J.M. Ball and J. Marsden. Moreover, we give an equivalent condition for weak lower semicontinuity of the above functional"},"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":"1401.6358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T14:49:28Z","cross_cats_sorted":[],"title_canon_sha256":"0baa62d351205eeab8301598c3531f7fac3f28b684704c3b15a608dbeeead02e","abstract_canon_sha256":"4303b3cfc96e0fde47e5e864f58c85bdac5dd52f38f0a3346acee63819ee8b43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:08.493759Z","signature_b64":"cJhQBh6XdZzHOEF/OahDP0F1/SvlZP0gXzIM7mRoG2UwkM4hDqQAFl4MUUjQO6CYCnhIXISFuXuhc8ixPozeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b1c60853b8de19b1cdf75c375f4db9914e0f333382b76f0b4f7e062204691cb","last_reissued_at":"2026-05-18T02:30:08.493292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:08.493292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathcal{A}$-quasiconvexity and weak lower semicontinuity of integral functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriel Path\\'o, Jan Kr\\\"amer, Martin Kru\\v{z}\\'ik, Stefan Kr\\\"omer","submitted_at":"2014-01-24T14:49:28Z","abstract_excerpt":"We state necessary and sufficient conditions for weak lower semicontinuity of $u\\mapsto\\int_\\Omega h(x,u(x))\\,d x$ where $|h(x,s)|\\le C(1+|s|^p)$ is continuous and possesses a recession function, and $u\\in L^p(\\Omega;\\mathbb{R}^m)$, $p>1$, lives in the kernel of a constant-rank first-order differential operator $\\mathcal{A}$ which admits an extension property. Our newly defined notion coincides for $\\mathcal{A}=\\operatorname{curl}$ with quasiconvexity at the boundary due to J.M. Ball and J. Marsden. Moreover, we give an equivalent condition for weak lower semicontinuity of the above functional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6358","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":"1401.6358","created_at":"2026-05-18T02:30:08.493375+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6358v2","created_at":"2026-05-18T02:30:08.493375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6358","created_at":"2026-05-18T02:30:08.493375+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMOGBBJ3RXQZ","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMOGBBJ3RXQZWHG7","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMOGBBJ3","created_at":"2026-05-18T12:28:41.024544+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/NMOGBBJ3RXQZWHG7OXBXL5G3TE","json":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE.json","graph_json":"https://pith.science/api/pith-number/NMOGBBJ3RXQZWHG7OXBXL5G3TE/graph.json","events_json":"https://pith.science/api/pith-number/NMOGBBJ3RXQZWHG7OXBXL5G3TE/events.json","paper":"https://pith.science/paper/NMOGBBJ3"},"agent_actions":{"view_html":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE","download_json":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE.json","view_paper":"https://pith.science/paper/NMOGBBJ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6358&json=true","fetch_graph":"https://pith.science/api/pith-number/NMOGBBJ3RXQZWHG7OXBXL5G3TE/graph.json","fetch_events":"https://pith.science/api/pith-number/NMOGBBJ3RXQZWHG7OXBXL5G3TE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/action/storage_attestation","attest_author":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/action/author_attestation","sign_citation":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/action/citation_signature","submit_replication":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/action/replication_record"}},"created_at":"2026-05-18T02:30:08.493375+00:00","updated_at":"2026-05-18T02:30:08.493375+00:00"}