{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YDJSI4IOASXBD5YAQAILS3K6JH","short_pith_number":"pith:YDJSI4IO","canonical_record":{"source":{"id":"1602.01750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-04T17:05:20Z","cross_cats_sorted":["math.CO","math.CV"],"title_canon_sha256":"cdc5c73a4968381750775d63138d5f96f74ca199d3e4da5d1f416ec68aff4fac","abstract_canon_sha256":"e3c0e7fefc4c462a86af50379a641d9f768679e77506a4dd39a085f55bf9b3f3"},"schema_version":"1.0"},"canonical_sha256":"c0d324710e04ae11f7008010b96d5e49c12c665f424b9deaf1c9e415cc86d156","source":{"kind":"arxiv","id":"1602.01750","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01750","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01750v1","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01750","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"YDJSI4IOASXB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YDJSI4IOASXBD5YA","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YDJSI4IO","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YDJSI4IOASXBD5YAQAILS3K6JH","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-04T17:05:20Z","cross_cats_sorted":["math.CO","math.CV"],"title_canon_sha256":"cdc5c73a4968381750775d63138d5f96f74ca199d3e4da5d1f416ec68aff4fac","abstract_canon_sha256":"e3c0e7fefc4c462a86af50379a641d9f768679e77506a4dd39a085f55bf9b3f3"},"schema_version":"1.0"},"canonical_sha256":"c0d324710e04ae11f7008010b96d5e49c12c665f424b9deaf1c9e415cc86d156","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:18.203633Z","signature_b64":"ZnhnHdDs3nqhENBp5VivzV/LPSjlZv4grXVTYsNF5mkHgwWSZPIMqJc8Se2DbiRerilhqgGUufQoajMSSqHQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0d324710e04ae11f7008010b96d5e49c12c665f424b9deaf1c9e415cc86d156","last_reissued_at":"2026-05-18T01:21:18.203083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:18.203083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01750","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":"2026-05-18T01:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XtiN7cJMrcDkpEqBuNG8jVVXlk72Y0Koiefv4A3GsHWzxoXcT5Adune0ScmqePZ/I2oussZs1rTT9KA6N9zFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T00:22:00.788471Z"},"content_sha256":"87df1730bad82e0ff0732a4669cce71baa57d60ec717c6924b9c67dba2116461","schema_version":"1.0","event_id":"sha256:87df1730bad82e0ff0732a4669cce71baa57d60ec717c6924b9c67dba2116461"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YDJSI4IOASXBD5YAQAILS3K6JH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^q$ norms of Fekete and related polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CV"],"primary_cat":"math.NT","authors_text":"Christian G\\\"unther, Kai-Uwe Schmidt","submitted_at":"2016-02-04T17:05:20Z","abstract_excerpt":"A Littlewood polynomial is a polynomial in $\\mathbb{C}[z]$ having all of its coefficients in $\\{-1,1\\}$. There are various old unsolved problems, mostly due to Littlewood and Erd\\H{o}s, that ask for Littlewood polynomials that provide a good approximation to a function that is constant on the complex unit circle, and in particular have small $L^q$ norm on the complex unit circle. We consider the Fekete polynomials \\[ f_p(z)=\\sum_{j=1}^{p-1}(j\\mid p)\\,z^j, \\] where $p$ is an odd prime and $(\\,\\cdot\\mid p)$ is the Legendre symbol (so that $z^{-1}f_p(z)$ is a Littlewood polynomial). We give expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01750","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":"2026-05-18T01:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NvLQAxVggawM364krUH4QEvJneiAXq4iD7PS2+mAqE0PJE0WgzWO+pvJkvCuwhz9qCkI/tK4dBlFHlGISSg7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T00:22:00.788816Z"},"content_sha256":"1bb949d94f9868347c73b2908f012550e8a5644f909cc1208cb5d5358c300712","schema_version":"1.0","event_id":"sha256:1bb949d94f9868347c73b2908f012550e8a5644f909cc1208cb5d5358c300712"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDJSI4IOASXBD5YAQAILS3K6JH/bundle.json","state_url":"https://pith.science/pith/YDJSI4IOASXBD5YAQAILS3K6JH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDJSI4IOASXBD5YAQAILS3K6JH/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":"2026-06-28T00:22:00Z","links":{"resolver":"https://pith.science/pith/YDJSI4IOASXBD5YAQAILS3K6JH","bundle":"https://pith.science/pith/YDJSI4IOASXBD5YAQAILS3K6JH/bundle.json","state":"https://pith.science/pith/YDJSI4IOASXBD5YAQAILS3K6JH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDJSI4IOASXBD5YAQAILS3K6JH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YDJSI4IOASXBD5YAQAILS3K6JH","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":"e3c0e7fefc4c462a86af50379a641d9f768679e77506a4dd39a085f55bf9b3f3","cross_cats_sorted":["math.CO","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-04T17:05:20Z","title_canon_sha256":"cdc5c73a4968381750775d63138d5f96f74ca199d3e4da5d1f416ec68aff4fac"},"schema_version":"1.0","source":{"id":"1602.01750","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01750","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01750v1","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01750","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"YDJSI4IOASXB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YDJSI4IOASXBD5YA","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YDJSI4IO","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:1bb949d94f9868347c73b2908f012550e8a5644f909cc1208cb5d5358c300712","target":"graph","created_at":"2026-05-18T01:21:18Z","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":"A Littlewood polynomial is a polynomial in $\\mathbb{C}[z]$ having all of its coefficients in $\\{-1,1\\}$. There are various old unsolved problems, mostly due to Littlewood and Erd\\H{o}s, that ask for Littlewood polynomials that provide a good approximation to a function that is constant on the complex unit circle, and in particular have small $L^q$ norm on the complex unit circle. We consider the Fekete polynomials \\[ f_p(z)=\\sum_{j=1}^{p-1}(j\\mid p)\\,z^j, \\] where $p$ is an odd prime and $(\\,\\cdot\\mid p)$ is the Legendre symbol (so that $z^{-1}f_p(z)$ is a Littlewood polynomial). We give expli","authors_text":"Christian G\\\"unther, Kai-Uwe Schmidt","cross_cats":["math.CO","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-04T17:05:20Z","title":"$L^q$ norms of Fekete and related polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01750","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":"sha256:87df1730bad82e0ff0732a4669cce71baa57d60ec717c6924b9c67dba2116461","target":"record","created_at":"2026-05-18T01:21:18Z","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":"e3c0e7fefc4c462a86af50379a641d9f768679e77506a4dd39a085f55bf9b3f3","cross_cats_sorted":["math.CO","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-04T17:05:20Z","title_canon_sha256":"cdc5c73a4968381750775d63138d5f96f74ca199d3e4da5d1f416ec68aff4fac"},"schema_version":"1.0","source":{"id":"1602.01750","kind":"arxiv","version":1}},"canonical_sha256":"c0d324710e04ae11f7008010b96d5e49c12c665f424b9deaf1c9e415cc86d156","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0d324710e04ae11f7008010b96d5e49c12c665f424b9deaf1c9e415cc86d156","first_computed_at":"2026-05-18T01:21:18.203083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:18.203083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZnhnHdDs3nqhENBp5VivzV/LPSjlZv4grXVTYsNF5mkHgwWSZPIMqJc8Se2DbiRerilhqgGUufQoajMSSqHQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:18.203633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01750","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87df1730bad82e0ff0732a4669cce71baa57d60ec717c6924b9c67dba2116461","sha256:1bb949d94f9868347c73b2908f012550e8a5644f909cc1208cb5d5358c300712"],"state_sha256":"2488b667de4c481271e12e51af776bbad76a67730a2dc85c6ed3776cd0d4a1e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Xx4QNr1XT/Ep1mZNtWI/NKuuWANMVWgxPqqHFSI+NATK7+z/NKCGNPB0h2yf2VfpeCCl8QCI1bYM7OF1NodDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T00:22:00.790763Z","bundle_sha256":"66dcd77b249a86e57f182f9affe84efe40aa5bcf1bb084ca0f9f2a728596a1d5"}}