{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BTXJBWU6IEGYFRJ7GTYB4PCY5I","short_pith_number":"pith:BTXJBWU6","schema_version":"1.0","canonical_sha256":"0cee90da9e410d82c53f34f01e3c58ea240baa1e004f2bd48bad9423f45d9447","source":{"kind":"arxiv","id":"1907.10776","version":1},"attestation_state":"computed","paper":{"title":"$C-$Robin Functions and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Norm Levenberg, Sione Ma`u","submitted_at":"2019-07-25T00:34:25Z","abstract_excerpt":"We continue the study in the setting of pluripotential theory arising from polynomials associated to a convex body $C$ in $({\\bf R}^+)^d$. Here we discuss $C-$Robin functions and their applications. In the particular case where $C$ is a simplex in $({\\bf R}^+)^2$ with vertices $(0,0),(b,0),(a,0)$, $a,b>0$, we generalize results of T. Bloom to construct families of polynomials which recover the $C-$extremal function $V_{C,K}$ of a nonpluripolar compact set $K\\subset {\\bf C}^d$."},"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":"1907.10776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-07-25T00:34:25Z","cross_cats_sorted":[],"title_canon_sha256":"432ad02a71d5978f56d96f6b783d3cbc2efde1dd974d863eebc56b5a1bacc89c","abstract_canon_sha256":"3c5dc51eb5be76600887d7747625d78f1675c8d8d3eb2f515779cfb7cd436745"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:34.521247Z","signature_b64":"XuRxEVOY36LEr5VnOISGMuBlc8yRW680T4L2DgkibyQWVisDHYAtWRz/FrSZblr/k4B6gnGsxY8x1fKW8AIZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cee90da9e410d82c53f34f01e3c58ea240baa1e004f2bd48bad9423f45d9447","last_reissued_at":"2026-05-17T23:39:34.520785Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:34.520785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$C-$Robin Functions and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Norm Levenberg, Sione Ma`u","submitted_at":"2019-07-25T00:34:25Z","abstract_excerpt":"We continue the study in the setting of pluripotential theory arising from polynomials associated to a convex body $C$ in $({\\bf R}^+)^d$. Here we discuss $C-$Robin functions and their applications. In the particular case where $C$ is a simplex in $({\\bf R}^+)^2$ with vertices $(0,0),(b,0),(a,0)$, $a,b>0$, we generalize results of T. Bloom to construct families of polynomials which recover the $C-$extremal function $V_{C,K}$ of a nonpluripolar compact set $K\\subset {\\bf C}^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10776","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":"1907.10776","created_at":"2026-05-17T23:39:34.520843+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.10776v1","created_at":"2026-05-17T23:39:34.520843+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10776","created_at":"2026-05-17T23:39:34.520843+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTXJBWU6IEGY","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTXJBWU6IEGYFRJ7","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTXJBWU6","created_at":"2026-05-18T12:33:12.712433+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/BTXJBWU6IEGYFRJ7GTYB4PCY5I","json":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I.json","graph_json":"https://pith.science/api/pith-number/BTXJBWU6IEGYFRJ7GTYB4PCY5I/graph.json","events_json":"https://pith.science/api/pith-number/BTXJBWU6IEGYFRJ7GTYB4PCY5I/events.json","paper":"https://pith.science/paper/BTXJBWU6"},"agent_actions":{"view_html":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I","download_json":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I.json","view_paper":"https://pith.science/paper/BTXJBWU6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.10776&json=true","fetch_graph":"https://pith.science/api/pith-number/BTXJBWU6IEGYFRJ7GTYB4PCY5I/graph.json","fetch_events":"https://pith.science/api/pith-number/BTXJBWU6IEGYFRJ7GTYB4PCY5I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I/action/storage_attestation","attest_author":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I/action/author_attestation","sign_citation":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I/action/citation_signature","submit_replication":"https://pith.science/pith/BTXJBWU6IEGYFRJ7GTYB4PCY5I/action/replication_record"}},"created_at":"2026-05-17T23:39:34.520843+00:00","updated_at":"2026-05-17T23:39:34.520843+00:00"}