{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KWQLTA2SPI63VBB3EZ5BSPS4FJ","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":"556b9cefaa63c9416206151b4e0a344ad745f0a1d8f993fb92afdb84f60c7f8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-08T17:28:53Z","title_canon_sha256":"b55dbe04bec37359e1147ec390539d36aea3ba81660ae2bbe059151ebf15ef1e"},"schema_version":"1.0","source":{"id":"1605.02340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02340","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02340v1","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02340","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"KWQLTA2SPI63","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KWQLTA2SPI63VBB3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KWQLTA2S","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:4f21f9cd661a13ea1adbf7bd96f3e9fdf0cb5b508f66733dcda16f0cccf700bb","target":"graph","created_at":"2026-05-18T01:15:21Z","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 study solutions of the first order partial differential inclusions of the form $\\nabla u\\in K$, where $u:\\Omega\\subset\\mathbb{R}^n\\to\\mathbb{R}^m$ and $K$ is a set of $m\\times n$ real matrices, and derive a companion version to the result of {M\\\"uller and \\v{S}ver\\'ak} [20], concerning a general linear constraint on the components of $\\nabla u$. We then consider two applications: the vectorial eikonal equation and a $T_4$-configuration both under linear constraints.","authors_text":"Seonghak Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-08T17:28:53Z","title":"Convex integration with linear constraints and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02340","kind":"arxiv","version":1},"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:ec382218a76c6d08887165637caf4d23cde4f4b32a0d52597e4670d3da5946ad","target":"record","created_at":"2026-05-18T01:15:21Z","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":"556b9cefaa63c9416206151b4e0a344ad745f0a1d8f993fb92afdb84f60c7f8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-08T17:28:53Z","title_canon_sha256":"b55dbe04bec37359e1147ec390539d36aea3ba81660ae2bbe059151ebf15ef1e"},"schema_version":"1.0","source":{"id":"1605.02340","kind":"arxiv","version":1}},"canonical_sha256":"55a0b983527a3dba843b267a193e5c2a57956aa4a59ec890bfd0e5fc734a1e3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55a0b983527a3dba843b267a193e5c2a57956aa4a59ec890bfd0e5fc734a1e3f","first_computed_at":"2026-05-18T01:15:21.249239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:21.249239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tuyvj4drTbN8z/yMSbFHPo7x6/qr4+tW9yoa3vcc0bwG+kyj1O26RFOdNe0DXCwiilwhgsjeVjXmXjEglJhJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:21.249939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec382218a76c6d08887165637caf4d23cde4f4b32a0d52597e4670d3da5946ad","sha256:4f21f9cd661a13ea1adbf7bd96f3e9fdf0cb5b508f66733dcda16f0cccf700bb"],"state_sha256":"df7e1c2357029691431018fb4458fbcd9e171cc23a236f736448074912f4600d"}