{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XNH77QZDZ64Q3LDJOSVJAAOPQU","short_pith_number":"pith:XNH77QZD","schema_version":"1.0","canonical_sha256":"bb4fffc323cfb90dac6974aa9001cf853a05c6739ef0c2dccb288ad55e3a61cd","source":{"kind":"arxiv","id":"1711.05484","version":2},"attestation_state":"computed","paper":{"title":"Condensers with touching plates and constrained minimum Riesz and Green energy problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B. Fuglede, D.P. Hardin, E.B. Saff, N. Zorii, P.D. Dragnev","submitted_at":"2017-11-15T10:13:30Z","abstract_excerpt":"We study minimum energy problems relative to the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, $\\alpha\\in(0,2]$, over signed Radon measures $\\mu$ on $\\mathbb R^n$, $n\\geqslant3$, associated with a generalized condenser $(A_1,A_2)$, where $A_1$ is a relatively closed subset of a domain $D$ and $A_2=\\mathbb R^n\\setminus D$. We show that, though $A_2\\cap\\mathrm{Cl}_{\\mathbb R^n}A_1$ may have nonzero capacity, this minimum energy problem is uniquely solvable (even in the presence of an external field) if we restrict ourselves to $\\mu$ with $\\mu^+\\leqslant\\xi$, where a constraint $\\xi$ is properly chos"},"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":"1711.05484","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-15T10:13:30Z","cross_cats_sorted":[],"title_canon_sha256":"821485990af4a8e14dc22a785d074f73f6e4a40d2ff492c03e4d044778d56808","abstract_canon_sha256":"053b25430290ab9daf900f06fe84b13fbe138a3f673ebbd5222d3e15b9cedd35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:19.497845Z","signature_b64":"apkPIXRp0wLxTOLLg20ZGO7gB2Jok/dInmqOrUEiytSKbXI7Jxy3XxYxR2q+UR+Y1pEuFKOACSI+iRy34BQdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb4fffc323cfb90dac6974aa9001cf853a05c6739ef0c2dccb288ad55e3a61cd","last_reissued_at":"2026-05-18T00:02:19.497443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:19.497443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Condensers with touching plates and constrained minimum Riesz and Green energy problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B. Fuglede, D.P. Hardin, E.B. Saff, N. Zorii, P.D. Dragnev","submitted_at":"2017-11-15T10:13:30Z","abstract_excerpt":"We study minimum energy problems relative to the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, $\\alpha\\in(0,2]$, over signed Radon measures $\\mu$ on $\\mathbb R^n$, $n\\geqslant3$, associated with a generalized condenser $(A_1,A_2)$, where $A_1$ is a relatively closed subset of a domain $D$ and $A_2=\\mathbb R^n\\setminus D$. We show that, though $A_2\\cap\\mathrm{Cl}_{\\mathbb R^n}A_1$ may have nonzero capacity, this minimum energy problem is uniquely solvable (even in the presence of an external field) if we restrict ourselves to $\\mu$ with $\\mu^+\\leqslant\\xi$, where a constraint $\\xi$ is properly chos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05484","kind":"arxiv","version":2},"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":"1711.05484","created_at":"2026-05-18T00:02:19.497498+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05484v2","created_at":"2026-05-18T00:02:19.497498+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05484","created_at":"2026-05-18T00:02:19.497498+00:00"},{"alias_kind":"pith_short_12","alias_value":"XNH77QZDZ64Q","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XNH77QZDZ64Q3LDJ","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XNH77QZD","created_at":"2026-05-18T12:31:56.362134+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/XNH77QZDZ64Q3LDJOSVJAAOPQU","json":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU.json","graph_json":"https://pith.science/api/pith-number/XNH77QZDZ64Q3LDJOSVJAAOPQU/graph.json","events_json":"https://pith.science/api/pith-number/XNH77QZDZ64Q3LDJOSVJAAOPQU/events.json","paper":"https://pith.science/paper/XNH77QZD"},"agent_actions":{"view_html":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU","download_json":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU.json","view_paper":"https://pith.science/paper/XNH77QZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05484&json=true","fetch_graph":"https://pith.science/api/pith-number/XNH77QZDZ64Q3LDJOSVJAAOPQU/graph.json","fetch_events":"https://pith.science/api/pith-number/XNH77QZDZ64Q3LDJOSVJAAOPQU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU/action/storage_attestation","attest_author":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU/action/author_attestation","sign_citation":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU/action/citation_signature","submit_replication":"https://pith.science/pith/XNH77QZDZ64Q3LDJOSVJAAOPQU/action/replication_record"}},"created_at":"2026-05-18T00:02:19.497498+00:00","updated_at":"2026-05-18T00:02:19.497498+00:00"}