{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NTCT63UHYFTPDDE6AVUR3SRI25","short_pith_number":"pith:NTCT63UH","canonical_record":{"source":{"id":"1704.03411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T16:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"c1f6f12321e87d3dafa1d6223a06ba6b1c4c744145e7a307a9454daa2f66cf40","abstract_canon_sha256":"84781798bae555e4856117db12525a8eb4af4c32bb3476f02a434b375823b3b8"},"schema_version":"1.0"},"canonical_sha256":"6cc53f6e87c166f18c9e05691dca28d758d6cd0e49623390725c50dacde7aa19","source":{"kind":"arxiv","id":"1704.03411","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NTCT63UHYFTPDDE6AVUR3SRI25","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T16:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"c1f6f12321e87d3dafa1d6223a06ba6b1c4c744145e7a307a9454daa2f66cf40","abstract_canon_sha256":"84781798bae555e4856117db12525a8eb4af4c32bb3476f02a434b375823b3b8"},"schema_version":"1.0"},"canonical_sha256":"6cc53f6e87c166f18c9e05691dca28d758d6cd0e49623390725c50dacde7aa19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:32.558139Z","signature_b64":"bkaaXAlaVYWxg7bTZhopK1UF3A94+KgY+zNweHkfOv9zlSiHjKkS1oY8xi26M/T8nDLunIGcjeTjuJRBw13ACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cc53f6e87c166f18c9e05691dca28d758d6cd0e49623390725c50dacde7aa19","last_reissued_at":"2026-05-18T00:46:32.557499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:32.557499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03411","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k++lDxnkWuDipceMQSCxFwtxb+UTzN1sUtT+JxFm9b0r2mHfOA7+urZqUqHBsjetQtqQly+l/F07rT/K9kSrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:31:20.587845Z"},"content_sha256":"b3ac29d7d4f8cf80bb756b953eaef2627ba2b912f772e79d16d140513b58deba","schema_version":"1.0","event_id":"sha256:b3ac29d7d4f8cf80bb756b953eaef2627ba2b912f772e79d16d140513b58deba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NTCT63UHYFTPDDE6AVUR3SRI25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pluripotential Numerics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Federico Piazzon","submitted_at":"2017-04-11T16:55:24Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03411","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzHfBjpUrAmTzCzix+FT6s0JpP5Ztw9vpS7l8trOvU5NrpqSgXgBmgxhz+Hm4VHIDqNRpY8IdkrFF0/MiJC8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:31:20.588195Z"},"content_sha256":"af1ed26f66c397e308c89a33b2f88fcfd9b19f539af5f243851b9f94ea0d6983","schema_version":"1.0","event_id":"sha256:af1ed26f66c397e308c89a33b2f88fcfd9b19f539af5f243851b9f94ea0d6983"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTCT63UHYFTPDDE6AVUR3SRI25/bundle.json","state_url":"https://pith.science/pith/NTCT63UHYFTPDDE6AVUR3SRI25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTCT63UHYFTPDDE6AVUR3SRI25/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T07:31:20Z","links":{"resolver":"https://pith.science/pith/NTCT63UHYFTPDDE6AVUR3SRI25","bundle":"https://pith.science/pith/NTCT63UHYFTPDDE6AVUR3SRI25/bundle.json","state":"https://pith.science/pith/NTCT63UHYFTPDDE6AVUR3SRI25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTCT63UHYFTPDDE6AVUR3SRI25/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3i34eeqeKLcTqMx7N5yMGt/cATR0DcSv2oygoYHlku+hngWpjPhu9UfjBUdCW2USXMEllXiWZTcvanzCy2uzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:31:20.590433Z","bundle_sha256":"fecda0b07ee78fa0d1326a336a19b61061659d595597c7c7bb75f29aaf5a0635"}}