{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2TGCOYTVDSAXZCIWS4H64LEJVG","short_pith_number":"pith:2TGCOYTV","canonical_record":{"source":{"id":"1312.1820","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-06T10:08:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d72e1f4677cf2083d45136ee63b59d10b8c2ddf43e9fa9f826a588040e5cdede","abstract_canon_sha256":"9de5a6afc38202cfcdf9bcdbe443e65a61cbb4c26e6bd36a96874e4573ed8e7a"},"schema_version":"1.0"},"canonical_sha256":"d4cc2762751c817c8916970fee2c89a9a63f069d3a809294a20098e429f5a0f8","source":{"kind":"arxiv","id":"1312.1820","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1820","created_at":"2026-05-18T02:39:16Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1820v3","created_at":"2026-05-18T02:39:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1820","created_at":"2026-05-18T02:39:16Z"},{"alias_kind":"pith_short_12","alias_value":"2TGCOYTVDSAX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2TGCOYTVDSAXZCIW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2TGCOYTV","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2TGCOYTVDSAXZCIWS4H64LEJVG","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1820","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-06T10:08:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d72e1f4677cf2083d45136ee63b59d10b8c2ddf43e9fa9f826a588040e5cdede","abstract_canon_sha256":"9de5a6afc38202cfcdf9bcdbe443e65a61cbb4c26e6bd36a96874e4573ed8e7a"},"schema_version":"1.0"},"canonical_sha256":"d4cc2762751c817c8916970fee2c89a9a63f069d3a809294a20098e429f5a0f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:16.647827Z","signature_b64":"pxl0xEvHas876B/fAvz6nY7UoHvSTykLTVfl31U6KzeUG74fapekREVX0aDu5sfDC0yzjlQWfuR6+Rimf/PoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4cc2762751c817c8916970fee2c89a9a63f069d3a809294a20098e429f5a0f8","last_reissued_at":"2026-05-18T02:39:16.647305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:16.647305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1820","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJt5VQzOIMIYJcG22otSWdROKwbiMcrYxImOqfg+jZOicZXv89laM3t0f6lmSb6aFGgOCxVlw402F5AnlZBoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:21:55.933705Z"},"content_sha256":"d4dba6e206452e400fd1e3dc4193f353a5fb2ff264e6cfd02b53488b7ce1fc9f","schema_version":"1.0","event_id":"sha256:d4dba6e206452e400fd1e3dc4193f353a5fb2ff264e6cfd02b53488b7ce1fc9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2TGCOYTVDSAXZCIWS4H64LEJVG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential inclusions and Young measures involving prescribed Jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Emil Wiedemann, Filip Rindler, Konstantinos Koumatos","submitted_at":"2013-12-06T10:08:04Z","abstract_excerpt":"This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,p}$ with $p$ less than the space dimension, whose Jacobian determinant is subjected to a range of constraints. Two special cases are particularly important in the theories of elasticity and fluid dynamics: (a) the generating gradients have positive Jacobians that are uniformly bounded away from zero and (b) the underlying deformations are incompressible, corresponding to their Jacobian determinants being constantly o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1820","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9hFGd18wwpCBNdVR/KtwNGGF4N92sV1u9V17KCZ0A2pFBuAzvmHULVG+MfArEt9MqjOOMv32FchSlKu0vxFCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:21:55.934366Z"},"content_sha256":"4972d0864516e8c8f803a23f57cbf68f0590d725a39619ee277e888f299d9771","schema_version":"1.0","event_id":"sha256:4972d0864516e8c8f803a23f57cbf68f0590d725a39619ee277e888f299d9771"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2TGCOYTVDSAXZCIWS4H64LEJVG/bundle.json","state_url":"https://pith.science/pith/2TGCOYTVDSAXZCIWS4H64LEJVG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2TGCOYTVDSAXZCIWS4H64LEJVG/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":"2026-05-25T19:21:55Z","links":{"resolver":"https://pith.science/pith/2TGCOYTVDSAXZCIWS4H64LEJVG","bundle":"https://pith.science/pith/2TGCOYTVDSAXZCIWS4H64LEJVG/bundle.json","state":"https://pith.science/pith/2TGCOYTVDSAXZCIWS4H64LEJVG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2TGCOYTVDSAXZCIWS4H64LEJVG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2TGCOYTVDSAXZCIWS4H64LEJVG","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":"9de5a6afc38202cfcdf9bcdbe443e65a61cbb4c26e6bd36a96874e4573ed8e7a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-06T10:08:04Z","title_canon_sha256":"d72e1f4677cf2083d45136ee63b59d10b8c2ddf43e9fa9f826a588040e5cdede"},"schema_version":"1.0","source":{"id":"1312.1820","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1820","created_at":"2026-05-18T02:39:16Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1820v3","created_at":"2026-05-18T02:39:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1820","created_at":"2026-05-18T02:39:16Z"},{"alias_kind":"pith_short_12","alias_value":"2TGCOYTVDSAX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2TGCOYTVDSAXZCIW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2TGCOYTV","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:4972d0864516e8c8f803a23f57cbf68f0590d725a39619ee277e888f299d9771","target":"graph","created_at":"2026-05-18T02:39:16Z","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":"This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,p}$ with $p$ less than the space dimension, whose Jacobian determinant is subjected to a range of constraints. Two special cases are particularly important in the theories of elasticity and fluid dynamics: (a) the generating gradients have positive Jacobians that are uniformly bounded away from zero and (b) the underlying deformations are incompressible, corresponding to their Jacobian determinants being constantly o","authors_text":"Emil Wiedemann, Filip Rindler, Konstantinos Koumatos","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-06T10:08:04Z","title":"Differential inclusions and Young measures involving prescribed Jacobian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1820","kind":"arxiv","version":3},"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:d4dba6e206452e400fd1e3dc4193f353a5fb2ff264e6cfd02b53488b7ce1fc9f","target":"record","created_at":"2026-05-18T02:39:16Z","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":"9de5a6afc38202cfcdf9bcdbe443e65a61cbb4c26e6bd36a96874e4573ed8e7a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-06T10:08:04Z","title_canon_sha256":"d72e1f4677cf2083d45136ee63b59d10b8c2ddf43e9fa9f826a588040e5cdede"},"schema_version":"1.0","source":{"id":"1312.1820","kind":"arxiv","version":3}},"canonical_sha256":"d4cc2762751c817c8916970fee2c89a9a63f069d3a809294a20098e429f5a0f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4cc2762751c817c8916970fee2c89a9a63f069d3a809294a20098e429f5a0f8","first_computed_at":"2026-05-18T02:39:16.647305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:16.647305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pxl0xEvHas876B/fAvz6nY7UoHvSTykLTVfl31U6KzeUG74fapekREVX0aDu5sfDC0yzjlQWfuR6+Rimf/PoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:16.647827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1820","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4dba6e206452e400fd1e3dc4193f353a5fb2ff264e6cfd02b53488b7ce1fc9f","sha256:4972d0864516e8c8f803a23f57cbf68f0590d725a39619ee277e888f299d9771"],"state_sha256":"513d9272cbf9725caa1430b54dd72eafb8df9e3b6a1a5b17c6ce543779695059"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"glb89epR72xk1CR3nAjrxdjSXOfnXYHAZKlyUfvlNBSaRqc43RN1obH95tzKtnXrRZvf6A90F1/j3jn7xuRYAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:21:55.941211Z","bundle_sha256":"16c31a99bbe5dd7c55a1d193a46cd63768da6185279f8b774c28e357b9309b82"}}