{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HYIVW63GWAMRQHI4AIHNIXAPIE","short_pith_number":"pith:HYIVW63G","canonical_record":{"source":{"id":"1307.6076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-07-22T14:53:41Z","cross_cats_sorted":[],"title_canon_sha256":"243dc7aeb6b7b956c9d3983056e23744241b82f9022de3b0f7275d20998f2a4f","abstract_canon_sha256":"99cfc1b51611f9ec51454c2dd72d0dc42bed3afc8970024b86304d897ed5ca5d"},"schema_version":"1.0"},"canonical_sha256":"3e115b7b66b019181d1c020ed45c0f4109838beae628d3ecbdf8559a0cf55944","source":{"kind":"arxiv","id":"1307.6076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6076","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6076v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6076","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"HYIVW63GWAMR","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HYIVW63GWAMRQHI4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HYIVW63G","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HYIVW63GWAMRQHI4AIHNIXAPIE","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-07-22T14:53:41Z","cross_cats_sorted":[],"title_canon_sha256":"243dc7aeb6b7b956c9d3983056e23744241b82f9022de3b0f7275d20998f2a4f","abstract_canon_sha256":"99cfc1b51611f9ec51454c2dd72d0dc42bed3afc8970024b86304d897ed5ca5d"},"schema_version":"1.0"},"canonical_sha256":"3e115b7b66b019181d1c020ed45c0f4109838beae628d3ecbdf8559a0cf55944","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:45.407701Z","signature_b64":"uXSV4GdMl/5ZO0vP/NLNiagA4XVZc6o9qfpZmEGeaXg5zTMvGm2uSnAdI0nieQmo8UDTWlMRbsawts9hhC0hCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e115b7b66b019181d1c020ed45c0f4109838beae628d3ecbdf8559a0cf55944","last_reissued_at":"2026-05-18T03:17:45.406938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:45.406938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6076","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":"2026-05-18T03:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmq6mp57epl/HS0ukl+UpXzIjSVoyCMQ2dwLeQSdIqWhdYFUUT6lyj3lmIJEW/TqgJEQjdDnSTfHxwB6eHgYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:55:05.507717Z"},"content_sha256":"972a89fd1386fe2784510b23e62f2afbeb71aadb0c21c91508e1f03ac4909a72","schema_version":"1.0","event_id":"sha256:972a89fd1386fe2784510b23e62f2afbeb71aadb0c21c91508e1f03ac4909a72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HYIVW63GWAMRQHI4AIHNIXAPIE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistribution of points via energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Igor E. Pritsker","submitted_at":"2013-07-22T14:53:41Z","abstract_excerpt":"We study the asymptotic equidistribution of points with discrete energy close to Robin's constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of this equidistribution. Applications include estimates of growth for the Fekete and Leja polynomials associated with large classes of compact sets, convergence rates of the discrete energy approximations to Robin's constant, and problems on the means of zeros of polynomials with integer coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6076","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":"2026-05-18T03:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mp7PhwOhK8V67+mkPIDgArr2JiXG8j0a0fceCxyDlhz2YsmCbaxluWEdpsR/FSysMuJzi0bFnDJ7jm4RNiUpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:55:05.508064Z"},"content_sha256":"68f8fc3a47000fb1aa77f389c53e166339e107e1ebdebc3b5522cfe874e0a31d","schema_version":"1.0","event_id":"sha256:68f8fc3a47000fb1aa77f389c53e166339e107e1ebdebc3b5522cfe874e0a31d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYIVW63GWAMRQHI4AIHNIXAPIE/bundle.json","state_url":"https://pith.science/pith/HYIVW63GWAMRQHI4AIHNIXAPIE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYIVW63GWAMRQHI4AIHNIXAPIE/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":"2026-06-22T21:55:05Z","links":{"resolver":"https://pith.science/pith/HYIVW63GWAMRQHI4AIHNIXAPIE","bundle":"https://pith.science/pith/HYIVW63GWAMRQHI4AIHNIXAPIE/bundle.json","state":"https://pith.science/pith/HYIVW63GWAMRQHI4AIHNIXAPIE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYIVW63GWAMRQHI4AIHNIXAPIE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HYIVW63GWAMRQHI4AIHNIXAPIE","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":"99cfc1b51611f9ec51454c2dd72d0dc42bed3afc8970024b86304d897ed5ca5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-07-22T14:53:41Z","title_canon_sha256":"243dc7aeb6b7b956c9d3983056e23744241b82f9022de3b0f7275d20998f2a4f"},"schema_version":"1.0","source":{"id":"1307.6076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6076","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6076v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6076","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"HYIVW63GWAMR","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HYIVW63GWAMRQHI4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HYIVW63G","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:68f8fc3a47000fb1aa77f389c53e166339e107e1ebdebc3b5522cfe874e0a31d","target":"graph","created_at":"2026-05-18T03:17:45Z","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 study the asymptotic equidistribution of points with discrete energy close to Robin's constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of this equidistribution. Applications include estimates of growth for the Fekete and Leja polynomials associated with large classes of compact sets, convergence rates of the discrete energy approximations to Robin's constant, and problems on the means of zeros of polynomials with integer coefficients.","authors_text":"Igor E. Pritsker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-07-22T14:53:41Z","title":"Equidistribution of points via energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6076","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":"sha256:972a89fd1386fe2784510b23e62f2afbeb71aadb0c21c91508e1f03ac4909a72","target":"record","created_at":"2026-05-18T03:17:45Z","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":"99cfc1b51611f9ec51454c2dd72d0dc42bed3afc8970024b86304d897ed5ca5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-07-22T14:53:41Z","title_canon_sha256":"243dc7aeb6b7b956c9d3983056e23744241b82f9022de3b0f7275d20998f2a4f"},"schema_version":"1.0","source":{"id":"1307.6076","kind":"arxiv","version":1}},"canonical_sha256":"3e115b7b66b019181d1c020ed45c0f4109838beae628d3ecbdf8559a0cf55944","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e115b7b66b019181d1c020ed45c0f4109838beae628d3ecbdf8559a0cf55944","first_computed_at":"2026-05-18T03:17:45.406938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:45.406938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uXSV4GdMl/5ZO0vP/NLNiagA4XVZc6o9qfpZmEGeaXg5zTMvGm2uSnAdI0nieQmo8UDTWlMRbsawts9hhC0hCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:45.407701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:972a89fd1386fe2784510b23e62f2afbeb71aadb0c21c91508e1f03ac4909a72","sha256:68f8fc3a47000fb1aa77f389c53e166339e107e1ebdebc3b5522cfe874e0a31d"],"state_sha256":"c89bb3efe668f7b40b7fc557027cba64291f87be6c59389cad597d60a40d32c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ubQ5jC2obtXTMBRVsEc3NuuVaEuyXv9ktytoJ/gAJ9V99VeIjXDkw7vYDJMhjtOhdKA7SUQcNR1Yzt3mACMiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:55:05.509991Z","bundle_sha256":"551a200eea77b714ca2d7df8ef630ef192e07758d0abcf9a4ab583856f7237a5"}}