{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:JVALFMQUUBADDRIOHFV3RE3RRD","short_pith_number":"pith:JVALFMQU","canonical_record":{"source":{"id":"2501.01208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-01-02T11:37:16Z","cross_cats_sorted":[],"title_canon_sha256":"18da75228781a8530a6e8f57ec303cfee1eb5932a49e6a6d3418bb312851f62c","abstract_canon_sha256":"805a06ba84cdd41416c086aedc2c84e0d331ac58860a035eb3fd61eac0829771"},"schema_version":"1.0"},"canonical_sha256":"4d40b2b214a04031c50e396bb8937188d10bd32115362751def96d507bf1d533","source":{"kind":"arxiv","id":"2501.01208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01208","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01208v1","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01208","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"JVALFMQUUBAD","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"pith_short_16","alias_value":"JVALFMQUUBADDRIO","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"pith_short_8","alias_value":"JVALFMQU","created_at":"2026-07-05T09:56:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:JVALFMQUUBADDRIOHFV3RE3RRD","target":"record","payload":{"canonical_record":{"source":{"id":"2501.01208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-01-02T11:37:16Z","cross_cats_sorted":[],"title_canon_sha256":"18da75228781a8530a6e8f57ec303cfee1eb5932a49e6a6d3418bb312851f62c","abstract_canon_sha256":"805a06ba84cdd41416c086aedc2c84e0d331ac58860a035eb3fd61eac0829771"},"schema_version":"1.0"},"canonical_sha256":"4d40b2b214a04031c50e396bb8937188d10bd32115362751def96d507bf1d533","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:16.268736Z","signature_b64":"z7ee+arLC78IrbdLNLgbsyOj0RXrOF+WehkPrjWJHl6Et3VJbGoklwdFgIKYhqmLfX8BDAzm/wTqZETlQASpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d40b2b214a04031c50e396bb8937188d10bd32115362751def96d507bf1d533","last_reissued_at":"2026-07-05T09:56:16.268251Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:16.268251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.01208","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":"2026-07-05T09:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kFCBqccXNvQEoqjlk8YKOCWLvPa2dIczL8M68mll3HItsQPf0uupFz5NSbN4P41JUrCglqkBlABmdqAnM7rzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:15:01.609851Z"},"content_sha256":"efe6badb65b5683406709062526cdbfaf51bc30eaec924270968f1f429c22096","schema_version":"1.0","event_id":"sha256:efe6badb65b5683406709062526cdbfaf51bc30eaec924270968f1f429c22096"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:JVALFMQUUBADDRIOHFV3RE3RRD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riesz equilibrium on a ball in the external field of a point charge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eduard B. Saff, Franck Wielonsky, Peter D. Dragnev, Ramon Orive","submitted_at":"2025-01-02T11:37:16Z","abstract_excerpt":"We investigate the Riesz energy minimization problem on a $d$-dimensional ball in the presence of an external field created by a point charge above the ball in $\\R^{d+1}$, $d\\geq1$. Both cases of an attractive charge and a repulsive charge are considered. The notion of a signed equilibrium measure is one of the main tools in the present study. For the case of a positive (repulsive) charge, the determination of the support of the equilibrium measure is a nontrivial question. We solve it in the one-dimensional case by making use of iterated balayage, a method already applied in logarithmic poten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01208","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.01208/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BmqHdwGHzJDlzV9MAY0NAAxdFmYqA3WQxBdZ8SxQpBWKBHShldjxeihmx87Psl9YnpZboOeCJX7nx70aB4REBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:15:01.610886Z"},"content_sha256":"6204ad830d4afc50438cab0ab245696f0911def8ccec64cc4c334b1627b8bb1f","schema_version":"1.0","event_id":"sha256:6204ad830d4afc50438cab0ab245696f0911def8ccec64cc4c334b1627b8bb1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVALFMQUUBADDRIOHFV3RE3RRD/bundle.json","state_url":"https://pith.science/pith/JVALFMQUUBADDRIOHFV3RE3RRD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVALFMQUUBADDRIOHFV3RE3RRD/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":"2026-08-17T00:15:01Z","links":{"resolver":"https://pith.science/pith/JVALFMQUUBADDRIOHFV3RE3RRD","bundle":"https://pith.science/pith/JVALFMQUUBADDRIOHFV3RE3RRD/bundle.json","state":"https://pith.science/pith/JVALFMQUUBADDRIOHFV3RE3RRD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVALFMQUUBADDRIOHFV3RE3RRD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JVALFMQUUBADDRIOHFV3RE3RRD","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":"805a06ba84cdd41416c086aedc2c84e0d331ac58860a035eb3fd61eac0829771","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-01-02T11:37:16Z","title_canon_sha256":"18da75228781a8530a6e8f57ec303cfee1eb5932a49e6a6d3418bb312851f62c"},"schema_version":"1.0","source":{"id":"2501.01208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01208","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01208v1","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01208","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"JVALFMQUUBAD","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"pith_short_16","alias_value":"JVALFMQUUBADDRIO","created_at":"2026-07-05T09:56:16Z"},{"alias_kind":"pith_short_8","alias_value":"JVALFMQU","created_at":"2026-07-05T09:56:16Z"}],"graph_snapshots":[{"event_id":"sha256:6204ad830d4afc50438cab0ab245696f0911def8ccec64cc4c334b1627b8bb1f","target":"graph","created_at":"2026-07-05T09:56:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.01208/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the Riesz energy minimization problem on a $d$-dimensional ball in the presence of an external field created by a point charge above the ball in $\\R^{d+1}$, $d\\geq1$. Both cases of an attractive charge and a repulsive charge are considered. The notion of a signed equilibrium measure is one of the main tools in the present study. For the case of a positive (repulsive) charge, the determination of the support of the equilibrium measure is a nontrivial question. We solve it in the one-dimensional case by making use of iterated balayage, a method already applied in logarithmic poten","authors_text":"Eduard B. Saff, Franck Wielonsky, Peter D. Dragnev, Ramon Orive","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-01-02T11:37:16Z","title":"Riesz equilibrium on a ball in the external field of a point charge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01208","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:efe6badb65b5683406709062526cdbfaf51bc30eaec924270968f1f429c22096","target":"record","created_at":"2026-07-05T09:56:16Z","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":"805a06ba84cdd41416c086aedc2c84e0d331ac58860a035eb3fd61eac0829771","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-01-02T11:37:16Z","title_canon_sha256":"18da75228781a8530a6e8f57ec303cfee1eb5932a49e6a6d3418bb312851f62c"},"schema_version":"1.0","source":{"id":"2501.01208","kind":"arxiv","version":1}},"canonical_sha256":"4d40b2b214a04031c50e396bb8937188d10bd32115362751def96d507bf1d533","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d40b2b214a04031c50e396bb8937188d10bd32115362751def96d507bf1d533","first_computed_at":"2026-07-05T09:56:16.268251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:16.268251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z7ee+arLC78IrbdLNLgbsyOj0RXrOF+WehkPrjWJHl6Et3VJbGoklwdFgIKYhqmLfX8BDAzm/wTqZETlQASpBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:16.268736Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.01208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efe6badb65b5683406709062526cdbfaf51bc30eaec924270968f1f429c22096","sha256:6204ad830d4afc50438cab0ab245696f0911def8ccec64cc4c334b1627b8bb1f"],"state_sha256":"c6872f9d88914d3254077ad265e96f46bacfc588dbc2ac2440285a1b35f7f408"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTpyAKPs0SBQ9s1V2F5M3A4HrvXJuHuULBBAeH3OHWG0L7mKWugqDmbe2nFUFkoC0ZyaQFAievp3HjeizwjbCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T00:15:01.616122Z","bundle_sha256":"82596139793573d5eeffdab9f93e09a1942c4815cedfc88209e29ac2077bf085"}}