{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GQ7ECOMIPXTB55ORUC5LUVXO6B","short_pith_number":"pith:GQ7ECOMI","canonical_record":{"source":{"id":"1307.5456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:56:39Z","cross_cats_sorted":[],"title_canon_sha256":"69e157a90d3a566e0132b7f39092e00ad88c96b974cd8e71e1e0600f7576b271","abstract_canon_sha256":"4c3a9a0552e99191a530225f39993aeaae04ecf478bb884cc84509a6a21e6c0c"},"schema_version":"1.0"},"canonical_sha256":"343e4139887de61ef5d1a0baba56eef07e75798e9236023fe1cd4d3469d90614","source":{"kind":"arxiv","id":"1307.5456","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5456","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5456v1","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5456","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"GQ7ECOMIPXTB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GQ7ECOMIPXTB55OR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GQ7ECOMI","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GQ7ECOMIPXTB55ORUC5LUVXO6B","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:56:39Z","cross_cats_sorted":[],"title_canon_sha256":"69e157a90d3a566e0132b7f39092e00ad88c96b974cd8e71e1e0600f7576b271","abstract_canon_sha256":"4c3a9a0552e99191a530225f39993aeaae04ecf478bb884cc84509a6a21e6c0c"},"schema_version":"1.0"},"canonical_sha256":"343e4139887de61ef5d1a0baba56eef07e75798e9236023fe1cd4d3469d90614","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:55.647007Z","signature_b64":"BFvikYW411ljfjHasCPua8VLWx4tzWZasTyiRe+7HQ8s7gw6izuK2BazFKCuYSuzKDh1SDUxyeXN9ETUSmCLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"343e4139887de61ef5d1a0baba56eef07e75798e9236023fe1cd4d3469d90614","last_reissued_at":"2026-05-18T03:17:55.644581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:55.644581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5456","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":"2026-05-18T03:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Csihb+363zJxPIqobNaVfKlAjWIkTx4dbOaE++sJhqATrqQcTvKx7VnoL64fyRxGgi968RDeoqcxQnnXx18XCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:52:57.179598Z"},"content_sha256":"e20eb41d7c6fe1606b7b6db2ee3e2940acf1a3211ea488058fdb8e88de0cd3bb","schema_version":"1.0","event_id":"sha256:e20eb41d7c6fe1606b7b6db2ee3e2940acf1a3211ea488058fdb8e88de0cd3bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GQ7ECOMIPXTB55ORUC5LUVXO6B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The multivariate integer Chebyshev problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"I. E. Pritsker, P. B. Borwein","submitted_at":"2013-07-20T19:56:39Z","abstract_excerpt":"The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in $\\C^d.$ We study this problem on general sets, but devote special attention to product sets such as cube and polydisk. We also establish a multivariate analog of the Hilbert-Fekete upper bound for the integer Chebyshev constant, which depends on the dimension of space. In the case of single variable polynomials in the complex plane, our estimate coincides with the Hilbert-Fekete result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5456","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":"2026-05-18T03:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1UytWQZJWrVHyLriS6uSvfKXdxqhxWeTS4uCeB4B+ai23RNvcixwR/qjJ4PjSCheFSd3VJ4A2CcuaWruSRDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:52:57.179939Z"},"content_sha256":"d14cdc1dcfe894eeda3c051f0252ccca4a45f8e348f73f93344d03924af55795","schema_version":"1.0","event_id":"sha256:d14cdc1dcfe894eeda3c051f0252ccca4a45f8e348f73f93344d03924af55795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQ7ECOMIPXTB55ORUC5LUVXO6B/bundle.json","state_url":"https://pith.science/pith/GQ7ECOMIPXTB55ORUC5LUVXO6B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQ7ECOMIPXTB55ORUC5LUVXO6B/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":"2026-06-24T04:52:57Z","links":{"resolver":"https://pith.science/pith/GQ7ECOMIPXTB55ORUC5LUVXO6B","bundle":"https://pith.science/pith/GQ7ECOMIPXTB55ORUC5LUVXO6B/bundle.json","state":"https://pith.science/pith/GQ7ECOMIPXTB55ORUC5LUVXO6B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQ7ECOMIPXTB55ORUC5LUVXO6B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GQ7ECOMIPXTB55ORUC5LUVXO6B","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":"4c3a9a0552e99191a530225f39993aeaae04ecf478bb884cc84509a6a21e6c0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:56:39Z","title_canon_sha256":"69e157a90d3a566e0132b7f39092e00ad88c96b974cd8e71e1e0600f7576b271"},"schema_version":"1.0","source":{"id":"1307.5456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5456","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5456v1","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5456","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"GQ7ECOMIPXTB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GQ7ECOMIPXTB55OR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GQ7ECOMI","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:d14cdc1dcfe894eeda3c051f0252ccca4a45f8e348f73f93344d03924af55795","target":"graph","created_at":"2026-05-18T03:17:55Z","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":"The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in $\\C^d.$ We study this problem on general sets, but devote special attention to product sets such as cube and polydisk. We also establish a multivariate analog of the Hilbert-Fekete upper bound for the integer Chebyshev constant, which depends on the dimension of space. In the case of single variable polynomials in the complex plane, our estimate coincides with the Hilbert-Fekete result.","authors_text":"I. E. Pritsker, P. B. Borwein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:56:39Z","title":"The multivariate integer Chebyshev problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5456","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:e20eb41d7c6fe1606b7b6db2ee3e2940acf1a3211ea488058fdb8e88de0cd3bb","target":"record","created_at":"2026-05-18T03:17:55Z","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":"4c3a9a0552e99191a530225f39993aeaae04ecf478bb884cc84509a6a21e6c0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:56:39Z","title_canon_sha256":"69e157a90d3a566e0132b7f39092e00ad88c96b974cd8e71e1e0600f7576b271"},"schema_version":"1.0","source":{"id":"1307.5456","kind":"arxiv","version":1}},"canonical_sha256":"343e4139887de61ef5d1a0baba56eef07e75798e9236023fe1cd4d3469d90614","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"343e4139887de61ef5d1a0baba56eef07e75798e9236023fe1cd4d3469d90614","first_computed_at":"2026-05-18T03:17:55.644581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:55.644581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BFvikYW411ljfjHasCPua8VLWx4tzWZasTyiRe+7HQ8s7gw6izuK2BazFKCuYSuzKDh1SDUxyeXN9ETUSmCLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:55.647007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e20eb41d7c6fe1606b7b6db2ee3e2940acf1a3211ea488058fdb8e88de0cd3bb","sha256:d14cdc1dcfe894eeda3c051f0252ccca4a45f8e348f73f93344d03924af55795"],"state_sha256":"404046e0c5b0e09b39fcfcf9fee36c4db25b2c578698de57e26364036e107e69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"912H4l72TMFqw+RdF35rIedmSwWs62+Mi1sBqHPztrWoBMMbsntfvKctVdRGYhOaI6AC6ZKo1WVnoNbIxvwvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:52:57.181837Z","bundle_sha256":"c86888236e1f911aeec8d87e3cb7a43c5c040d3b0e7f3ee9e5bc36537fb4658c"}}