{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7RCTQHB5NIH7355CBM7VNMPKEO","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":"18dd9b7ca35b10fc711ab18b25b4f158a7b2a3006966548017642142668f59cc","cross_cats_sorted":["math.IT","math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-03T08:54:25Z","title_canon_sha256":"95198336470831792ef47d6e41947ec409782745d252acd7159aeb7b5ac997c7"},"schema_version":"1.0","source":{"id":"1703.01080","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01080","created_at":"2026-05-18T00:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01080v2","created_at":"2026-05-18T00:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01080","created_at":"2026-05-18T00:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"7RCTQHB5NIH7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7RCTQHB5NIH7355C","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7RCTQHB5","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:c52e798a0c62ffdd798746a25ce8449bfa640191e6691f7883e81f15d9b729af","target":"graph","created_at":"2026-05-18T00:46:12Z","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 long standing problem in the area of error correcting codes asks whether there exist good cyclic codes. Most of the known results point in the direction of a negative answer.\n  The uncertainty principle is a classical result of harmonic analysis asserting that given a non-zero function $f$ on some abelian group, either $f$ or its Fourier transform $\\hat{f}$ has large support.\n  In this note, we observe a connection between these two subjects. We point out that even a weak version of the uncertainty principle for fields of positive characteristic would imply that good cyclic codes do exist. W","authors_text":"Alexander Lubotzky, Emmanuel Kowalski, Shai Evra","cross_cats":["math.IT","math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-03T08:54:25Z","title":"Good cyclic codes and the uncertainty principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01080","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":"sha256:37dcf176988807e90ab3ae7cdbf91aa9f049adc09df7723f979a65d173d784c6","target":"record","created_at":"2026-05-18T00:46:12Z","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":"18dd9b7ca35b10fc711ab18b25b4f158a7b2a3006966548017642142668f59cc","cross_cats_sorted":["math.IT","math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-03T08:54:25Z","title_canon_sha256":"95198336470831792ef47d6e41947ec409782745d252acd7159aeb7b5ac997c7"},"schema_version":"1.0","source":{"id":"1703.01080","kind":"arxiv","version":2}},"canonical_sha256":"fc45381c3d6a0ffdf7a20b3f56b1ea23bad8e62f1aad925e13afc39935a05675","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc45381c3d6a0ffdf7a20b3f56b1ea23bad8e62f1aad925e13afc39935a05675","first_computed_at":"2026-05-18T00:46:12.473835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:12.473835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"00bVfbFHYZkL3yYyJQQAyP4brduwnGwgHjIouiI4jaL5O6IMOZCSOPi5ce5GOW+pNT3IadvXZtd2X6Pi4dj9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:12.474414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01080","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37dcf176988807e90ab3ae7cdbf91aa9f049adc09df7723f979a65d173d784c6","sha256:c52e798a0c62ffdd798746a25ce8449bfa640191e6691f7883e81f15d9b729af"],"state_sha256":"e62d3f0e34de1aa060764b247be544c0d8f016c27b11962e458f18e9d0e92bc0"}