{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2KBW6L76SGISWF7QXBGILJKWZO","short_pith_number":"pith:2KBW6L76","schema_version":"1.0","canonical_sha256":"d2836f2ffe91912b17f0b84c85a556cb85872687dbb588d07f34121f05a1c4f0","source":{"kind":"arxiv","id":"1402.4590","version":1},"attestation_state":"computed","paper":{"title":"On the distinctness of binary sequences derived from $2$-adic expansion of m-sequences over finite prime fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dongdai Lin, Yupeng Jiang","submitted_at":"2014-02-19T08:42:52Z","abstract_excerpt":"Let $p$ be an odd prime with $2$-adic expansion $\\sum_{i=0}^kp_i\\cdot2^i$. For a sequence $\\underline{a}=(a(t))_{t\\ge 0}$ over $\\mathbb{F}_{p}$, each $a(t)$ belongs to $\\{0,1,\\ldots, p-1\\}$ and has a unique $2$-adic expansion $$a(t)=a_0(t)+a_1(t)\\cdot 2+\\cdots+a_{k}(t)\\cdot2^k,$$ with $a_i(t)\\in\\{0, 1\\}$. Let $\\underline{a_i}$ denote the binary sequence $(a_i(t))_{t\\ge 0}$ for $0\\le i\\le k$. Assume $i_0$ is the smallest index $i$ such that $p_{i}=0$ and $\\underline{a}$ and $\\underline{b}$ are two different m-sequences generated by a same primitive characteristic polynomial over $\\mathbb{F}_p$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.4590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-02-19T08:42:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"2ceead3d6a44cef914cbd74526c2f7318875fc007bdcc060ab6b234ffe5e8a0f","abstract_canon_sha256":"fc9f49e465122630de9901c43555005ce56c8f6f8089887e3ea4296b81c0990d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:33.781288Z","signature_b64":"htAcgCGgXWmVGyijIa6CzygFXX6au03yGLFMrbQJvTkGm5wmAZ94Pt2/7TZYKeb8vZoPKMkTOKiuBURpVI38Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2836f2ffe91912b17f0b84c85a556cb85872687dbb588d07f34121f05a1c4f0","last_reissued_at":"2026-05-18T02:58:33.780658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:33.780658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the distinctness of binary sequences derived from $2$-adic expansion of m-sequences over finite prime fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dongdai Lin, Yupeng Jiang","submitted_at":"2014-02-19T08:42:52Z","abstract_excerpt":"Let $p$ be an odd prime with $2$-adic expansion $\\sum_{i=0}^kp_i\\cdot2^i$. For a sequence $\\underline{a}=(a(t))_{t\\ge 0}$ over $\\mathbb{F}_{p}$, each $a(t)$ belongs to $\\{0,1,\\ldots, p-1\\}$ and has a unique $2$-adic expansion $$a(t)=a_0(t)+a_1(t)\\cdot 2+\\cdots+a_{k}(t)\\cdot2^k,$$ with $a_i(t)\\in\\{0, 1\\}$. Let $\\underline{a_i}$ denote the binary sequence $(a_i(t))_{t\\ge 0}$ for $0\\le i\\le k$. Assume $i_0$ is the smallest index $i$ such that $p_{i}=0$ and $\\underline{a}$ and $\\underline{b}$ are two different m-sequences generated by a same primitive characteristic polynomial over $\\mathbb{F}_p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4590","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.4590","created_at":"2026-05-18T02:58:33.780783+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.4590v1","created_at":"2026-05-18T02:58:33.780783+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4590","created_at":"2026-05-18T02:58:33.780783+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KBW6L76SGIS","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KBW6L76SGISWF7Q","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KBW6L76","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO","json":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO.json","graph_json":"https://pith.science/api/pith-number/2KBW6L76SGISWF7QXBGILJKWZO/graph.json","events_json":"https://pith.science/api/pith-number/2KBW6L76SGISWF7QXBGILJKWZO/events.json","paper":"https://pith.science/paper/2KBW6L76"},"agent_actions":{"view_html":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO","download_json":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO.json","view_paper":"https://pith.science/paper/2KBW6L76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.4590&json=true","fetch_graph":"https://pith.science/api/pith-number/2KBW6L76SGISWF7QXBGILJKWZO/graph.json","fetch_events":"https://pith.science/api/pith-number/2KBW6L76SGISWF7QXBGILJKWZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO/action/storage_attestation","attest_author":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO/action/author_attestation","sign_citation":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO/action/citation_signature","submit_replication":"https://pith.science/pith/2KBW6L76SGISWF7QXBGILJKWZO/action/replication_record"}},"created_at":"2026-05-18T02:58:33.780783+00:00","updated_at":"2026-05-18T02:58:33.780783+00:00"}