{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XT2QUFWHYGROM4ZMZJRTBW6734","short_pith_number":"pith:XT2QUFWH","canonical_record":{"source":{"id":"1006.5153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-06-26T16:52:09Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"1896ae4b3fdf75e6cdf00c1fc6132042df3f76e4f9fae46bada2bf5fe9a98237","abstract_canon_sha256":"eed034386123d3f6b37a32f8988d3522dd92ba28b1b2ab0931fa805f8096ac79"},"schema_version":"1.0"},"canonical_sha256":"bcf50a16c7c1a2e6732cca6330dbdfdf0212e4ffed794d3f90efd07a95c4d11f","source":{"kind":"arxiv","id":"1006.5153","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5153","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5153v2","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5153","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"XT2QUFWHYGRO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XT2QUFWHYGROM4ZM","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XT2QUFWH","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XT2QUFWHYGROM4ZMZJRTBW6734","target":"record","payload":{"canonical_record":{"source":{"id":"1006.5153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-06-26T16:52:09Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"1896ae4b3fdf75e6cdf00c1fc6132042df3f76e4f9fae46bada2bf5fe9a98237","abstract_canon_sha256":"eed034386123d3f6b37a32f8988d3522dd92ba28b1b2ab0931fa805f8096ac79"},"schema_version":"1.0"},"canonical_sha256":"bcf50a16c7c1a2e6732cca6330dbdfdf0212e4ffed794d3f90efd07a95c4d11f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:02.056004Z","signature_b64":"YmzcWDTnNtO7NsVr85WJVHbLMZ4J+ViJwLv3PS4Ir5f9lPVTQi1wC8pevyFXeTVwzCK5MmcNKJ3BfUWKqc6rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcf50a16c7c1a2e6732cca6330dbdfdf0212e4ffed794d3f90efd07a95c4d11f","last_reissued_at":"2026-05-18T02:58:02.055519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:02.055519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.5153","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqfrcbgbmSL3G+z4SCD3SHNgwX4rHDS/n75yNT4Sg1o0X9LkPFASK7Ma1FaurQ5KYEEMRARpeG4efYIieUI1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:56:01.665539Z"},"content_sha256":"b2192f549c0802a9986bd5c6746fd45c6bd52e37dd7aa4f5ef6a2b305495edcf","schema_version":"1.0","event_id":"sha256:b2192f549c0802a9986bd5c6746fd45c6bd52e37dd7aa4f5ef6a2b305495edcf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XT2QUFWHYGROM4ZMZJRTBW6734","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chebyshev constants for the unit circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.MG","authors_text":"Gergely Ambrus, Keith M. Ball, T. Erd\\'elyi","submitted_at":"2010-06-26T16:52:09Z","abstract_excerpt":"It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that\n  $$\\sum 1/|z-z_k|^2 \\leq n^2/4.$$ Equality holds iff the point system is a rotated copy of the nth unit roots.\n  Two proofs are presented: one uses a characterisation of equioscillating rational functions, while the other is based on Bernstein's inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5153","kind":"arxiv","version":2},"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":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4qx3KkVfeeQ88AEEKpMfsm1z0KUhgI8GMelz8F0S0OYVn4LYx6JDc5Q5CFrQVcmzuPoRuOBWppiSmlevPqwzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:56:01.666468Z"},"content_sha256":"a199ad81b09b5140716388c72eac7bb9a32e06bb69363edc385f79e292b82c45","schema_version":"1.0","event_id":"sha256:a199ad81b09b5140716388c72eac7bb9a32e06bb69363edc385f79e292b82c45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XT2QUFWHYGROM4ZMZJRTBW6734/bundle.json","state_url":"https://pith.science/pith/XT2QUFWHYGROM4ZMZJRTBW6734/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XT2QUFWHYGROM4ZMZJRTBW6734/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":"2026-06-10T16:56:01Z","links":{"resolver":"https://pith.science/pith/XT2QUFWHYGROM4ZMZJRTBW6734","bundle":"https://pith.science/pith/XT2QUFWHYGROM4ZMZJRTBW6734/bundle.json","state":"https://pith.science/pith/XT2QUFWHYGROM4ZMZJRTBW6734/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XT2QUFWHYGROM4ZMZJRTBW6734/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XT2QUFWHYGROM4ZMZJRTBW6734","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":"eed034386123d3f6b37a32f8988d3522dd92ba28b1b2ab0931fa805f8096ac79","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-06-26T16:52:09Z","title_canon_sha256":"1896ae4b3fdf75e6cdf00c1fc6132042df3f76e4f9fae46bada2bf5fe9a98237"},"schema_version":"1.0","source":{"id":"1006.5153","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5153","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5153v2","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5153","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"XT2QUFWHYGRO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XT2QUFWHYGROM4ZM","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XT2QUFWH","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:a199ad81b09b5140716388c72eac7bb9a32e06bb69363edc385f79e292b82c45","target":"graph","created_at":"2026-05-18T02:58:02Z","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":"It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that\n  $$\\sum 1/|z-z_k|^2 \\leq n^2/4.$$ Equality holds iff the point system is a rotated copy of the nth unit roots.\n  Two proofs are presented: one uses a characterisation of equioscillating rational functions, while the other is based on Bernstein's inequality.","authors_text":"Gergely Ambrus, Keith M. Ball, T. Erd\\'elyi","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-06-26T16:52:09Z","title":"Chebyshev constants for the unit circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5153","kind":"arxiv","version":2},"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:b2192f549c0802a9986bd5c6746fd45c6bd52e37dd7aa4f5ef6a2b305495edcf","target":"record","created_at":"2026-05-18T02:58:02Z","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":"eed034386123d3f6b37a32f8988d3522dd92ba28b1b2ab0931fa805f8096ac79","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-06-26T16:52:09Z","title_canon_sha256":"1896ae4b3fdf75e6cdf00c1fc6132042df3f76e4f9fae46bada2bf5fe9a98237"},"schema_version":"1.0","source":{"id":"1006.5153","kind":"arxiv","version":2}},"canonical_sha256":"bcf50a16c7c1a2e6732cca6330dbdfdf0212e4ffed794d3f90efd07a95c4d11f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcf50a16c7c1a2e6732cca6330dbdfdf0212e4ffed794d3f90efd07a95c4d11f","first_computed_at":"2026-05-18T02:58:02.055519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:02.055519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YmzcWDTnNtO7NsVr85WJVHbLMZ4J+ViJwLv3PS4Ir5f9lPVTQi1wC8pevyFXeTVwzCK5MmcNKJ3BfUWKqc6rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:02.056004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5153","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2192f549c0802a9986bd5c6746fd45c6bd52e37dd7aa4f5ef6a2b305495edcf","sha256:a199ad81b09b5140716388c72eac7bb9a32e06bb69363edc385f79e292b82c45"],"state_sha256":"501e3e55f49352251549bce150c25f6f65e3677788e2fdabbd313c2c717f695a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKKx4tJITOVg2iJr7ECaC0t6r2lMqLixkT1r+8HAEATbxY9/TUBDcgABd6U5hcVDHghp+qKdZ6sr0jao/V/DBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T16:56:01.670366Z","bundle_sha256":"bf19d06ee6ba3b74c3fb273a0e418791e1de3f5a8758bca7ed1c2ee0cfbd8d5c"}}