{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NTCT63UHYFTPDDE6AVUR3SRI25","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":"84781798bae555e4856117db12525a8eb4af4c32bb3476f02a434b375823b3b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T16:55:24Z","title_canon_sha256":"c1f6f12321e87d3dafa1d6223a06ba6b1c4c744145e7a307a9454daa2f66cf40"},"schema_version":"1.0","source":{"id":"1704.03411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03411","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03411v1","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03411","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"NTCT63UHYFTP","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NTCT63UHYFTPDDE6","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NTCT63UH","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:af1ed26f66c397e308c89a33b2f88fcfd9b19f539af5f243851b9f94ea0d6983","target":"graph","created_at":"2026-05-18T00:46:32Z","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":"We introduce numerical methods for the approximation of the main (global) quantities in Pluripotential Theory as the \\emph{extremal plurisubharmonic function} $V_E^*$ of a compact $\\mathcal L$-regular set $E\\subset \\C^n$, its \\emph{transfinite diameter} $\\delta(E),$ and the \\emph{pluripotential equilibrium measure} $\\mu_E:=\\ddcn{V_E^*}.$\n  The methods rely on the computation of a \\emph{polynomial mesh} for $E$ and numerical orthonormalization of a suitable basis of polynomials. We prove the convergence of the approximation of $\\delta(E)$ and the uniform convergence of our approximation to $V_E","authors_text":"Federico Piazzon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T16:55:24Z","title":"Pluripotential Numerics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03411","kind":"arxiv","version":1},"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:b3ac29d7d4f8cf80bb756b953eaef2627ba2b912f772e79d16d140513b58deba","target":"record","created_at":"2026-05-18T00:46:32Z","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":"84781798bae555e4856117db12525a8eb4af4c32bb3476f02a434b375823b3b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T16:55:24Z","title_canon_sha256":"c1f6f12321e87d3dafa1d6223a06ba6b1c4c744145e7a307a9454daa2f66cf40"},"schema_version":"1.0","source":{"id":"1704.03411","kind":"arxiv","version":1}},"canonical_sha256":"6cc53f6e87c166f18c9e05691dca28d758d6cd0e49623390725c50dacde7aa19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cc53f6e87c166f18c9e05691dca28d758d6cd0e49623390725c50dacde7aa19","first_computed_at":"2026-05-18T00:46:32.557499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:32.557499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bkaaXAlaVYWxg7bTZhopK1UF3A94+KgY+zNweHkfOv9zlSiHjKkS1oY8xi26M/T8nDLunIGcjeTjuJRBw13ACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:32.558139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3ac29d7d4f8cf80bb756b953eaef2627ba2b912f772e79d16d140513b58deba","sha256:af1ed26f66c397e308c89a33b2f88fcfd9b19f539af5f243851b9f94ea0d6983"],"state_sha256":"d44642273726302fa19b0b655d5f124319b95e8236302a168bb008fc5f81d016"}