{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YWWBIY2F276XUI3I5UKGJHNHS5","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":"1dba10f7df2f04f983f03b8ddcdc2253e1d0330e3b114a298d88716f0110d92d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-07T11:43:13Z","title_canon_sha256":"b3ba440f3c1b295b0920ebe3a85306e9ac1b6ed2a087e60690e3e36b1bcb7924"},"schema_version":"1.0","source":{"id":"1811.02845","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02845","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02845v3","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02845","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"YWWBIY2F276X","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YWWBIY2F276XUI3I","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YWWBIY2F","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:9fd71c03ae7ec9b5d2e40aadd26516a3761f48043ee9597edb19528e208cb830","target":"graph","created_at":"2026-05-17T23:56:12Z","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 utilise new methods of Calculus of Variations in $L^\\infty$ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a non-homogeneous linear elliptic equation, satisfying Dirichlet data on a domain. One of the advantages over the classical Tykhonov regularisation in $L^2$ is that the approximated solution of the PDE is uniformly close to the noisy measurements taken on a compact subset of the domain.","authors_text":"Nikos Katzourakis (Reading, UK)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-07T11:43:13Z","title":"An $L^\\infty$ regularisation strategy to the inverse source identification problem for elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02845","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:b1afcff8c6c7407f0cc05dae88560952a27c78e1cc764dae3bd76bc28ce309f6","target":"record","created_at":"2026-05-17T23:56:12Z","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":"1dba10f7df2f04f983f03b8ddcdc2253e1d0330e3b114a298d88716f0110d92d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-07T11:43:13Z","title_canon_sha256":"b3ba440f3c1b295b0920ebe3a85306e9ac1b6ed2a087e60690e3e36b1bcb7924"},"schema_version":"1.0","source":{"id":"1811.02845","kind":"arxiv","version":3}},"canonical_sha256":"c5ac146345d7fd7a2368ed14649da79771b74cc44d52943b0efb36913e843f64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5ac146345d7fd7a2368ed14649da79771b74cc44d52943b0efb36913e843f64","first_computed_at":"2026-05-17T23:56:12.570396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:12.570396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lK90NEMot12IbjicbYMlQkdHF4OjlRscDj+mf/ct48kbFxHmtEfAiyyhf1bLUJxbZe3vyZfJ0agOk1msU76SBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:12.571673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02845","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1afcff8c6c7407f0cc05dae88560952a27c78e1cc764dae3bd76bc28ce309f6","sha256:9fd71c03ae7ec9b5d2e40aadd26516a3761f48043ee9597edb19528e208cb830"],"state_sha256":"4836d1ed814b57239b8040ce403f1d227cf840cc880c9d6fb121b1adfd6182f3"}