{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5X4DPSMFXXL2OPJYMLO3FOOXOI","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":"f924e0da48e8127af8ce1d04029788482f2e688f6e10c874b0b530007b10edc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-11T04:47:33Z","title_canon_sha256":"d5733e8f136b1f2c10f464726d664e2f61462ae5410cee403eed69d5f71d9741"},"schema_version":"1.0","source":{"id":"1804.03808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03808","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03808v1","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03808","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"5X4DPSMFXXL2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5X4DPSMFXXL2OPJY","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5X4DPSMF","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:37a7452d0d7de62b7d0b6603b309b0b839db6d5f51c0a2baeb641a6a828048aa","target":"graph","created_at":"2026-05-18T00:18:43Z","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":"Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For $n \\equiv 1\\pmod 4$, we prove some cases of Schmidt's Conjecture for perfect binary sequences. (Des. Codes Cryptogr. 78 (2016), 237-267.) For $n \\equiv 2\\pmod 4$, Jungnickel and Pott (Discrete Appl. Math. 95 (1999) 331-359.) left four perfect binary sequences as open problem and we solve three of its. For $n \\equiv 3\\pmod 4$, we present some nonexistence of ","authors_text":"H. Cao, K. Feng, X. Niu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-11T04:47:33Z","title":"Non-existence of perfect binary sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03808","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:c5adc726d6f975fe226532203026e587be065e9e03ccdfe8cec504c422fd5a0a","target":"record","created_at":"2026-05-18T00:18:43Z","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":"f924e0da48e8127af8ce1d04029788482f2e688f6e10c874b0b530007b10edc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-11T04:47:33Z","title_canon_sha256":"d5733e8f136b1f2c10f464726d664e2f61462ae5410cee403eed69d5f71d9741"},"schema_version":"1.0","source":{"id":"1804.03808","kind":"arxiv","version":1}},"canonical_sha256":"edf837c985bdd7a73d3862ddb2b9d7722f4228fa69d5a2af7648280aff640a62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf837c985bdd7a73d3862ddb2b9d7722f4228fa69d5a2af7648280aff640a62","first_computed_at":"2026-05-18T00:18:43.015401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:43.015401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8RlFS1vijFKs5bbvoQJliNdIgS9RYNUWPQ58GkF4EiHzHzVA7uwq1SM+ZERNTSAWrm3yv7z+22r9getDDSP5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:43.016028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5adc726d6f975fe226532203026e587be065e9e03ccdfe8cec504c422fd5a0a","sha256:37a7452d0d7de62b7d0b6603b309b0b839db6d5f51c0a2baeb641a6a828048aa"],"state_sha256":"8c34c5f5a1770462ae4d98cbc5b5492cf36a29a6a68d5c075ee700d1142ccc86"}