{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AU5PSKPXU4NVTDALH7FCOHQWXN","short_pith_number":"pith:AU5PSKPX","schema_version":"1.0","canonical_sha256":"053af929f7a71b598c0b3fca271e16bb4580882401b0fdaae96c41f2dc143f35","source":{"kind":"arxiv","id":"1610.02637","version":1},"attestation_state":"computed","paper":{"title":"Two- and Multi-phase Quadrature Surfaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Avetik Arakelyan, Henrik Shahgholian, Jyotshana V. Prajapat","submitted_at":"2016-10-09T07:27:42Z","abstract_excerpt":"In this paper we shall initiate the study of the two- and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The problem is studied mostly from a potential theoretic point of view that (for two-phase case) relates to integral representation $$ \\int_{\\partial \\Omega^+} g h (x) \\ d\\sigma_x - \\int_{\\partial \\Omega^-} g h (x) \\ d\\sigma_x= \\int h d\\mu \\ , $$ where $d\\sigma_x$ is the surface measure, $\\mu= \\mu^+ - \\mu^-$ is given measure with support in (a priori unknown domain) $\\Omega$, $g$ is a given smooth positive function, and the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.02637","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2016-10-09T07:27:42Z","cross_cats_sorted":[],"title_canon_sha256":"c406ea0c7aaa79ab276982e6e903d0df9e9d7cc75e6c986e188655c7a2d5070c","abstract_canon_sha256":"99be1a067cac01009a4bbe5b77ca31f45b8d952cba71fbadbb33780f3ba3206b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:51.062905Z","signature_b64":"qLDnG4fpXQYJn4T6UINb8NSSugHaWYERo6au9v/OqC2ZYaZ+VAwNXv17ToU9yaphhscGSoj5V0BY7H4/i0V0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"053af929f7a71b598c0b3fca271e16bb4580882401b0fdaae96c41f2dc143f35","last_reissued_at":"2026-05-18T01:02:51.062530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:51.062530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two- and Multi-phase Quadrature Surfaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Avetik Arakelyan, Henrik Shahgholian, Jyotshana V. Prajapat","submitted_at":"2016-10-09T07:27:42Z","abstract_excerpt":"In this paper we shall initiate the study of the two- and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The problem is studied mostly from a potential theoretic point of view that (for two-phase case) relates to integral representation $$ \\int_{\\partial \\Omega^+} g h (x) \\ d\\sigma_x - \\int_{\\partial \\Omega^-} g h (x) \\ d\\sigma_x= \\int h d\\mu \\ , $$ where $d\\sigma_x$ is the surface measure, $\\mu= \\mu^+ - \\mu^-$ is given measure with support in (a priori unknown domain) $\\Omega$, $g$ is a given smooth positive function, and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02637","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.02637","created_at":"2026-05-18T01:02:51.062590+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.02637v1","created_at":"2026-05-18T01:02:51.062590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02637","created_at":"2026-05-18T01:02:51.062590+00:00"},{"alias_kind":"pith_short_12","alias_value":"AU5PSKPXU4NV","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AU5PSKPXU4NVTDAL","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AU5PSKPX","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN","json":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN.json","graph_json":"https://pith.science/api/pith-number/AU5PSKPXU4NVTDALH7FCOHQWXN/graph.json","events_json":"https://pith.science/api/pith-number/AU5PSKPXU4NVTDALH7FCOHQWXN/events.json","paper":"https://pith.science/paper/AU5PSKPX"},"agent_actions":{"view_html":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN","download_json":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN.json","view_paper":"https://pith.science/paper/AU5PSKPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.02637&json=true","fetch_graph":"https://pith.science/api/pith-number/AU5PSKPXU4NVTDALH7FCOHQWXN/graph.json","fetch_events":"https://pith.science/api/pith-number/AU5PSKPXU4NVTDALH7FCOHQWXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN/action/storage_attestation","attest_author":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN/action/author_attestation","sign_citation":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN/action/citation_signature","submit_replication":"https://pith.science/pith/AU5PSKPXU4NVTDALH7FCOHQWXN/action/replication_record"}},"created_at":"2026-05-18T01:02:51.062590+00:00","updated_at":"2026-05-18T01:02:51.062590+00:00"}