{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FIDBQE2EDCWWROCBKHFTBVK3O5","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":"e6881a5df38234fc748885f0b39ba808ab3fce58241f807f2125e5733c35ba85","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-12T12:57:53Z","title_canon_sha256":"4d51fdd4b35deeb0b6d413607730fb68722ab371178502841a92de5714199131"},"schema_version":"1.0","source":{"id":"1802.04857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04857","created_at":"2026-05-18T00:23:22Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04857v1","created_at":"2026-05-18T00:23:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04857","created_at":"2026-05-18T00:23:22Z"},{"alias_kind":"pith_short_12","alias_value":"FIDBQE2EDCWW","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FIDBQE2EDCWWROCB","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FIDBQE2E","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:f5dcd342de7232447ef8e4c24228946015b79b591e07beae5128f48caa7dcbc3","target":"graph","created_at":"2026-05-18T00:23:22Z","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":"In this paper we study the isotropic realizability of a given non smooth gradient field $\\nabla u$ defined in $\\mathbb{R}^d$, namely when one can reconstruct an isotropic conductivity $\\sigma>0$ such that $\\sigma\\nabla u$ is divergence free in $\\mathbb{R}^d$. On the one hand, in the case where $\\nabla u$ is non-vanishing, uniformly continuous in $\\mathbb{R}^d$ and $\\triangle u$ is a bounded function in $\\mathbb{R}^d$, we prove the isotropic realizability of $\\nabla u$ using the associated gradient flow combined with the DiPerna, Lions approach for solving ordinary differential equations in sui","authors_text":"Marc Briane (IRMAR)","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-12T12:57:53Z","title":"Reconstruction of isotropic conductivities from non smooth electric fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04857","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":"sha256:29b44657a903e9b65d10e3fd9d5e738f4d45fedf5b70011fd8913b40c875e323","target":"record","created_at":"2026-05-18T00:23:22Z","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":"e6881a5df38234fc748885f0b39ba808ab3fce58241f807f2125e5733c35ba85","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-12T12:57:53Z","title_canon_sha256":"4d51fdd4b35deeb0b6d413607730fb68722ab371178502841a92de5714199131"},"schema_version":"1.0","source":{"id":"1802.04857","kind":"arxiv","version":1}},"canonical_sha256":"2a0618134418ad68b84151cb30d55b7741579b816d6444dff45b5e2667406949","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a0618134418ad68b84151cb30d55b7741579b816d6444dff45b5e2667406949","first_computed_at":"2026-05-18T00:23:22.421781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:22.421781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/CkJd5IYnnTHQhgxtJyQiml4W5UHYD4hmOlktkZ9y6X1O0BRHle5f74XN6iZoZl+ga4wOb/FCFN4Gf6T4oseBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:22.422526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29b44657a903e9b65d10e3fd9d5e738f4d45fedf5b70011fd8913b40c875e323","sha256:f5dcd342de7232447ef8e4c24228946015b79b591e07beae5128f48caa7dcbc3"],"state_sha256":"9ec5931a69224ec09a0f62c13627d07d45a560ea63c3c57be5d58218800e7063"}