{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TN5TEFKDWS6Y5C6BN55MZQ2SG3","short_pith_number":"pith:TN5TEFKD","canonical_record":{"source":{"id":"1012.0170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-01T12:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"03eed4ecf882fc6654dda2d3e663453144100ef881af7e87571bf95ef1a0d879","abstract_canon_sha256":"36d20cf8e3b7caa07262f5ef36f862fb7889291b92a3276573c784cb5b7918da"},"schema_version":"1.0"},"canonical_sha256":"9b7b321543b4bd8e8bc16f7accc35236fe3091cc5936f34b822ac89816acd58e","source":{"kind":"arxiv","id":"1012.0170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0170","created_at":"2026-05-18T02:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0170v1","created_at":"2026-05-18T02:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0170","created_at":"2026-05-18T02:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"TN5TEFKDWS6Y","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TN5TEFKDWS6Y5C6B","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TN5TEFKD","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TN5TEFKDWS6Y5C6BN55MZQ2SG3","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-01T12:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"03eed4ecf882fc6654dda2d3e663453144100ef881af7e87571bf95ef1a0d879","abstract_canon_sha256":"36d20cf8e3b7caa07262f5ef36f862fb7889291b92a3276573c784cb5b7918da"},"schema_version":"1.0"},"canonical_sha256":"9b7b321543b4bd8e8bc16f7accc35236fe3091cc5936f34b822ac89816acd58e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:36.734062Z","signature_b64":"G05nlCg3D0rX/iFP8Vcw9CLJwpb/axacqeJ9ItQ5LC9UTuUyCGX2xFS1KJ1YjFaFicomiO08zOcesmbhw27bAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b7b321543b4bd8e8bc16f7accc35236fe3091cc5936f34b822ac89816acd58e","last_reissued_at":"2026-05-18T02:04:36.733409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:36.733409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0170","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":"2026-05-18T02:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6YKB2wXcyoAnJSeM95xXzK5aJqBx5TeH1D5oGJLhobVAannIJrx8v+pkk6w1oOqD97gwlCuyEgOpwLLJ5+VBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:30:22.644094Z"},"content_sha256":"099fb260ce8fb27cc064b25aa506f79c111bda22fa5d112caa0bda230e41645d","schema_version":"1.0","event_id":"sha256:099fb260ce8fb27cc064b25aa506f79c111bda22fa5d112caa0bda230e41645d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TN5TEFKDWS6Y5C6BN55MZQ2SG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the convergence on nonlinear Pad\\'e--Chebyshev approximations to the multivalued analytic functions, variation of equilibrium energy and $S$-property of stationary compacts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrei A. Gonchar, Evguenii A. Rakhmanov, Sergey P. Suetin","submitted_at":"2010-12-01T12:02:49Z","abstract_excerpt":"Some new results on the convergence of nonlinear diagonal Pad\\'e--Chebyshev approximations to multivalued analytic function given on the segment $[-1,1]$, are proved. We show that these approximations converge to the given function in the \"maxmimal\" domain of its meromorphity and that the boundary of this maxmimal domain is an $S$-curve.\n  The results of the work have been announced in abs/1009.4813\n  Bibliography: 57 items."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0170","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":"2026-05-18T02:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vtI4w73prWA6rS0eGUYbudcfHS6OAuFE5ddM9UGqssq1lbj2OGawrK1V90HoK6BVAeAIdOWiQdy3bqt5woeABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:30:22.644465Z"},"content_sha256":"06af8ff3e20c263455580a36c8844986fb72599b4c5cf8af98d79a9d5e54fef3","schema_version":"1.0","event_id":"sha256:06af8ff3e20c263455580a36c8844986fb72599b4c5cf8af98d79a9d5e54fef3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TN5TEFKDWS6Y5C6BN55MZQ2SG3/bundle.json","state_url":"https://pith.science/pith/TN5TEFKDWS6Y5C6BN55MZQ2SG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TN5TEFKDWS6Y5C6BN55MZQ2SG3/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":"2026-06-22T18:30:22Z","links":{"resolver":"https://pith.science/pith/TN5TEFKDWS6Y5C6BN55MZQ2SG3","bundle":"https://pith.science/pith/TN5TEFKDWS6Y5C6BN55MZQ2SG3/bundle.json","state":"https://pith.science/pith/TN5TEFKDWS6Y5C6BN55MZQ2SG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TN5TEFKDWS6Y5C6BN55MZQ2SG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TN5TEFKDWS6Y5C6BN55MZQ2SG3","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":"36d20cf8e3b7caa07262f5ef36f862fb7889291b92a3276573c784cb5b7918da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-01T12:02:49Z","title_canon_sha256":"03eed4ecf882fc6654dda2d3e663453144100ef881af7e87571bf95ef1a0d879"},"schema_version":"1.0","source":{"id":"1012.0170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0170","created_at":"2026-05-18T02:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0170v1","created_at":"2026-05-18T02:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0170","created_at":"2026-05-18T02:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"TN5TEFKDWS6Y","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TN5TEFKDWS6Y5C6B","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TN5TEFKD","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:06af8ff3e20c263455580a36c8844986fb72599b4c5cf8af98d79a9d5e54fef3","target":"graph","created_at":"2026-05-18T02:04:36Z","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":"Some new results on the convergence of nonlinear diagonal Pad\\'e--Chebyshev approximations to multivalued analytic function given on the segment $[-1,1]$, are proved. We show that these approximations converge to the given function in the \"maxmimal\" domain of its meromorphity and that the boundary of this maxmimal domain is an $S$-curve.\n  The results of the work have been announced in abs/1009.4813\n  Bibliography: 57 items.","authors_text":"Andrei A. Gonchar, Evguenii A. Rakhmanov, Sergey P. Suetin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-01T12:02:49Z","title":"On the convergence on nonlinear Pad\\'e--Chebyshev approximations to the multivalued analytic functions, variation of equilibrium energy and $S$-property of stationary compacts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0170","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":"sha256:099fb260ce8fb27cc064b25aa506f79c111bda22fa5d112caa0bda230e41645d","target":"record","created_at":"2026-05-18T02:04:36Z","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":"36d20cf8e3b7caa07262f5ef36f862fb7889291b92a3276573c784cb5b7918da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-01T12:02:49Z","title_canon_sha256":"03eed4ecf882fc6654dda2d3e663453144100ef881af7e87571bf95ef1a0d879"},"schema_version":"1.0","source":{"id":"1012.0170","kind":"arxiv","version":1}},"canonical_sha256":"9b7b321543b4bd8e8bc16f7accc35236fe3091cc5936f34b822ac89816acd58e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b7b321543b4bd8e8bc16f7accc35236fe3091cc5936f34b822ac89816acd58e","first_computed_at":"2026-05-18T02:04:36.733409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:36.733409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G05nlCg3D0rX/iFP8Vcw9CLJwpb/axacqeJ9ItQ5LC9UTuUyCGX2xFS1KJ1YjFaFicomiO08zOcesmbhw27bAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:36.734062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:099fb260ce8fb27cc064b25aa506f79c111bda22fa5d112caa0bda230e41645d","sha256:06af8ff3e20c263455580a36c8844986fb72599b4c5cf8af98d79a9d5e54fef3"],"state_sha256":"c6478783d5e8359e7751f18d2c87779a7be8400be26eabbfacaa7e69605c1178"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQRdfqgP/0f0RnQsa9aabC6flL1ugFeUpkmUsbQOdQDo+2McJiVnd6oFzJ6ju6QZucwHgEb1e3Vr9EI4OIkhCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:30:22.646465Z","bundle_sha256":"7bd703fbba8cc9c811be6417071a769e98316938cf2b20619fb01cc4f8be989a"}}