{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A2FGXBEAFZZ5VPGWGFFQNC7E6R","short_pith_number":"pith:A2FGXBEA","canonical_record":{"source":{"id":"1307.6200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-23T19:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"a3ed9f0ea6b9d7c501112e21005d6f05c81f726f7fe263eda47141cd66087199","abstract_canon_sha256":"82145952f78af61067a791dc451798de2365056b946abd552b7d53c2604053fe"},"schema_version":"1.0"},"canonical_sha256":"068a6b84802e73dabcd6314b068be4f4443ff5b20c7d29efb2fa3f0f2f96d17c","source":{"kind":"arxiv","id":"1307.6200","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6200","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6200v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6200","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"A2FGXBEAFZZ5","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A2FGXBEAFZZ5VPGW","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A2FGXBEA","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A2FGXBEAFZZ5VPGWGFFQNC7E6R","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-23T19:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"a3ed9f0ea6b9d7c501112e21005d6f05c81f726f7fe263eda47141cd66087199","abstract_canon_sha256":"82145952f78af61067a791dc451798de2365056b946abd552b7d53c2604053fe"},"schema_version":"1.0"},"canonical_sha256":"068a6b84802e73dabcd6314b068be4f4443ff5b20c7d29efb2fa3f0f2f96d17c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:45.075367Z","signature_b64":"AS8/4lzpYKhDWGC0hqsWyReSRG/PW4yL3RKNZtI9Ioi4d4wFMxF9eTD6gKF9de6xRisNhhXBN9/6jeCHgdIVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"068a6b84802e73dabcd6314b068be4f4443ff5b20c7d29efb2fa3f0f2f96d17c","last_reissued_at":"2026-05-18T03:17:45.074774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:45.074774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6200","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":"5Tv3c3A88uae0AzmG8X/2kKWIeOWoTa8uOPsqQw8iYIiVKSD+Rj/xRcuoVLxLnzanIE6WHn801IKZ/eGy4huBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:32:28.609554Z"},"content_sha256":"cacaf8d23646f332904dbc09227f455af3fffb62ad817954f6ec458375424826","schema_version":"1.0","event_id":"sha256:cacaf8d23646f332904dbc09227f455af3fffb62ad817954f6ec458375424826"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A2FGXBEAFZZ5VPGWGFFQNC7E6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomials with integer coefficients and their zeros","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Pritsker","submitted_at":"2013-07-23T19:22:49Z","abstract_excerpt":"We study several related problems on polynomials with integer coefficients. This includes the integer Chebyshev problem, and the Schur problems on means of algebraic numbers. We also discuss interesting applications to approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets. The distribution of zeros for polynomials with integer coefficients plays an important role in all of these problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6200","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":"T4qfgayNJG/erijl6G9wTitxguMT2ZRqH+K5hNw27h/RO4Ko32zeKbKy41w9MbRpdt7cpLH/5f4eZ9X3AXpmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:32:28.609917Z"},"content_sha256":"06544ce475bb5630362755f488c9542dd358687ac803e6ebe15bb69d76781662","schema_version":"1.0","event_id":"sha256:06544ce475bb5630362755f488c9542dd358687ac803e6ebe15bb69d76781662"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A2FGXBEAFZZ5VPGWGFFQNC7E6R/bundle.json","state_url":"https://pith.science/pith/A2FGXBEAFZZ5VPGWGFFQNC7E6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A2FGXBEAFZZ5VPGWGFFQNC7E6R/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":"2026-06-23T10:32:28Z","links":{"resolver":"https://pith.science/pith/A2FGXBEAFZZ5VPGWGFFQNC7E6R","bundle":"https://pith.science/pith/A2FGXBEAFZZ5VPGWGFFQNC7E6R/bundle.json","state":"https://pith.science/pith/A2FGXBEAFZZ5VPGWGFFQNC7E6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A2FGXBEAFZZ5VPGWGFFQNC7E6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A2FGXBEAFZZ5VPGWGFFQNC7E6R","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":"82145952f78af61067a791dc451798de2365056b946abd552b7d53c2604053fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-23T19:22:49Z","title_canon_sha256":"a3ed9f0ea6b9d7c501112e21005d6f05c81f726f7fe263eda47141cd66087199"},"schema_version":"1.0","source":{"id":"1307.6200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6200","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6200v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6200","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"A2FGXBEAFZZ5","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A2FGXBEAFZZ5VPGW","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A2FGXBEA","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:06544ce475bb5630362755f488c9542dd358687ac803e6ebe15bb69d76781662","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 several related problems on polynomials with integer coefficients. This includes the integer Chebyshev problem, and the Schur problems on means of algebraic numbers. We also discuss interesting applications to approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets. The distribution of zeros for polynomials with integer coefficients plays an important role in all of these problems.","authors_text":"Igor E. Pritsker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-23T19:22:49Z","title":"Polynomials with integer coefficients and their zeros"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6200","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:cacaf8d23646f332904dbc09227f455af3fffb62ad817954f6ec458375424826","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":"82145952f78af61067a791dc451798de2365056b946abd552b7d53c2604053fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-23T19:22:49Z","title_canon_sha256":"a3ed9f0ea6b9d7c501112e21005d6f05c81f726f7fe263eda47141cd66087199"},"schema_version":"1.0","source":{"id":"1307.6200","kind":"arxiv","version":1}},"canonical_sha256":"068a6b84802e73dabcd6314b068be4f4443ff5b20c7d29efb2fa3f0f2f96d17c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"068a6b84802e73dabcd6314b068be4f4443ff5b20c7d29efb2fa3f0f2f96d17c","first_computed_at":"2026-05-18T03:17:45.074774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:45.074774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AS8/4lzpYKhDWGC0hqsWyReSRG/PW4yL3RKNZtI9Ioi4d4wFMxF9eTD6gKF9de6xRisNhhXBN9/6jeCHgdIVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:45.075367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cacaf8d23646f332904dbc09227f455af3fffb62ad817954f6ec458375424826","sha256:06544ce475bb5630362755f488c9542dd358687ac803e6ebe15bb69d76781662"],"state_sha256":"f0abd3c6136286da24b146bfa855d146c742dda7f5e6dc860d7a86159e61d973"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vJS044BGf+bwVimGm9yNbhlRaQBkfh7Z8tdDQks+QbKUq3s8pJALElpkSj1xry2qDRBoy8iqJgb//ysetMyNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T10:32:28.611853Z","bundle_sha256":"3f24c1b770dc2a0eb4ccc502924e3b4c413c0fccf1687561584ec485c58139b8"}}