{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HMFK6PBDTK2SZW4QDTGLOL72HB","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":"e7010225d5fc077f4a20edcec71cfec75190a49a4fcf91bb06d7dede0754741d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-16T18:44:27Z","title_canon_sha256":"71ada5dbc8379f4e82a123730f925dd72931dd7e11bf9c16e3e2028a0e48e6df"},"schema_version":"1.0","source":{"id":"1510.04974","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04974","created_at":"2026-05-18T00:09:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04974v2","created_at":"2026-05-18T00:09:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04974","created_at":"2026-05-18T00:09:39Z"},{"alias_kind":"pith_short_12","alias_value":"HMFK6PBDTK2S","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HMFK6PBDTK2SZW4Q","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HMFK6PBD","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:9aefa46f94e58d020ba4c446e5446ab5d5626865aaa8365bf586baddb6c82258","target":"graph","created_at":"2026-05-18T00:09:39Z","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":"The paper deals with the three-dimensional Dirichlet boundary value problem (BVP) for a second order strongly elliptic self-adjoint system of partial differential equations in the divergence form with variable coefficients and develops the integral potential method based on a localized parametrix. Using Green's representation formula and properties of the localized layer and volume potentials, we reduce the Dirichlet BVP to a system of localized boundary-domain integral equations (LBDIEs). The equivalence between the Dirichlet BVP and the corresponding LBDIE system is studied. We establish tha","authors_text":"D. Natroshvili, O. Chkadua, S.E. Mikhailov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-16T18:44:27Z","title":"Localized Boundary-Domain Singular Integral Equations of Dirichlet Problem for Self-adjoint Second Order Strongly Elliptic PDE Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04974","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":"sha256:5dc582907a45b090325e795bdd65e353ac5c4b9779689c1a5a1185e728c9ea0e","target":"record","created_at":"2026-05-18T00:09:39Z","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":"e7010225d5fc077f4a20edcec71cfec75190a49a4fcf91bb06d7dede0754741d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-16T18:44:27Z","title_canon_sha256":"71ada5dbc8379f4e82a123730f925dd72931dd7e11bf9c16e3e2028a0e48e6df"},"schema_version":"1.0","source":{"id":"1510.04974","kind":"arxiv","version":2}},"canonical_sha256":"3b0aaf3c239ab52cdb901cccb72ffa3842d44759f03b983981cb600329947514","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b0aaf3c239ab52cdb901cccb72ffa3842d44759f03b983981cb600329947514","first_computed_at":"2026-05-18T00:09:39.614996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:39.614996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4pVdjTn3MVdqlTHWoYMA23O9nSy5swklY0qSPkN0R1KXVGolzr7ulBk7HxJjeZ1uW4+qOWWWsdfF9EXgLuVlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:39.615602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04974","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dc582907a45b090325e795bdd65e353ac5c4b9779689c1a5a1185e728c9ea0e","sha256:9aefa46f94e58d020ba4c446e5446ab5d5626865aaa8365bf586baddb6c82258"],"state_sha256":"ce622a121102a6260bb9b7a8a97557495a10843ad589e14b46138c42c017b044"}