{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NMOGBBJ3RXQZWHG7OXBXL5G3TE","short_pith_number":"pith:NMOGBBJ3","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"},"canonical_sha256":"6b1c60853b8de19b1cdf75c375f4db9914e0f333382b76f0b4f7e062204691cb","source":{"kind":"arxiv","id":"1401.6358","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6358","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6358v2","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6358","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"NMOGBBJ3RXQZ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NMOGBBJ3RXQZWHG7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NMOGBBJ3","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NMOGBBJ3RXQZWHG7OXBXL5G3TE","target":"record","payload":{"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"},"canonical_sha256":"6b1c60853b8de19b1cdf75c375f4db9914e0f333382b76f0b4f7e062204691cb","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"},"source_kind":"arxiv","source_id":"1401.6358","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JM4mClzCcMZuRhpbXfaVZ/Uo1g8ZZLexB/rSOzvnTR2cO2gms3/bRL3LuGNyGGoNLlbrsUEbFUOKXvl0Buv7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:21:38.115187Z"},"content_sha256":"defb8a96cf5f66ab341eba4ba2d0e261f95b6f0b807ee77792ed301f90adccaa","schema_version":"1.0","event_id":"sha256:defb8a96cf5f66ab341eba4ba2d0e261f95b6f0b807ee77792ed301f90adccaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NMOGBBJ3RXQZWHG7OXBXL5G3TE","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3tEZ86wppFnDVfI6QzVp1AjkJRAwaJ7Uye3IDq3aGjyVgN6Fx1OoYF1oPHqxcooBFG+T22PEzZpODFxqvfyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:21:38.115549Z"},"content_sha256":"74bf5424e582f38c689694dd4928787ed06d8162b97bb0b36d73418e9031de31","schema_version":"1.0","event_id":"sha256:74bf5424e582f38c689694dd4928787ed06d8162b97bb0b36d73418e9031de31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/bundle.json","state_url":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T14:21:38Z","links":{"resolver":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE","bundle":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/bundle.json","state":"https://pith.science/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMOGBBJ3RXQZWHG7OXBXL5G3TE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NMOGBBJ3RXQZWHG7OXBXL5G3TE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4303b3cfc96e0fde47e5e864f58c85bdac5dd52f38f0a3346acee63819ee8b43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T14:49:28Z","title_canon_sha256":"0baa62d351205eeab8301598c3531f7fac3f28b684704c3b15a608dbeeead02e"},"schema_version":"1.0","source":{"id":"1401.6358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6358","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6358v2","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6358","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"NMOGBBJ3RXQZ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NMOGBBJ3RXQZWHG7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NMOGBBJ3","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:74bf5424e582f38c689694dd4928787ed06d8162b97bb0b36d73418e9031de31","target":"graph","created_at":"2026-05-18T02:30:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Gabriel Path\\'o, Jan Kr\\\"amer, Martin Kru\\v{z}\\'ik, Stefan Kr\\\"omer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T14:49:28Z","title":"$\\mathcal{A}$-quasiconvexity and weak lower semicontinuity of integral functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6358","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:defb8a96cf5f66ab341eba4ba2d0e261f95b6f0b807ee77792ed301f90adccaa","target":"record","created_at":"2026-05-18T02:30:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4303b3cfc96e0fde47e5e864f58c85bdac5dd52f38f0a3346acee63819ee8b43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T14:49:28Z","title_canon_sha256":"0baa62d351205eeab8301598c3531f7fac3f28b684704c3b15a608dbeeead02e"},"schema_version":"1.0","source":{"id":"1401.6358","kind":"arxiv","version":2}},"canonical_sha256":"6b1c60853b8de19b1cdf75c375f4db9914e0f333382b76f0b4f7e062204691cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b1c60853b8de19b1cdf75c375f4db9914e0f333382b76f0b4f7e062204691cb","first_computed_at":"2026-05-18T02:30:08.493292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:08.493292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cJhQBh6XdZzHOEF/OahDP0F1/SvlZP0gXzIM7mRoG2UwkM4hDqQAFl4MUUjQO6CYCnhIXISFuXuhc8ixPozeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:08.493759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:defb8a96cf5f66ab341eba4ba2d0e261f95b6f0b807ee77792ed301f90adccaa","sha256:74bf5424e582f38c689694dd4928787ed06d8162b97bb0b36d73418e9031de31"],"state_sha256":"f86a76e468511eb1ee0d7f0bd6adead770c8fc6bf55d11d559f0f44fce03cc9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8/2aX95WHC7iCEBvXrUCVZpSISBLOixY/nS3RalHqb3R1hRgr47jHaEWLyvV1DYW8ywEvHYzpMD7nHWUCMOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T14:21:38.118118Z","bundle_sha256":"48f0f9de36527dd3102f975f936470afb254e2e56696f8f58ad0e3eeb1f7ccd3"}}