{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4AZEANNR5UDV5FD6J2YN5MNZRV","short_pith_number":"pith:4AZEANNR","schema_version":"1.0","canonical_sha256":"e0324035b1ed075e947e4eb0deb1b98d470d6224baab2652454b42e2f052cc96","source":{"kind":"arxiv","id":"1301.7345","version":2},"attestation_state":"computed","paper":{"title":"Codes on Lattices for Random SAF Routing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anirban Ghatak","submitted_at":"2013-01-30T20:10:25Z","abstract_excerpt":"In this paper, a construction of constant weight codes based on the unique decomposition of elements in lattices is presented. The conditions for unique primary decomposition and unique irreducible decomposition in lattices are discussed and connections with the decomposition of ideals in Noetherian commutative rings established. In this context it is shown, drawing on the definitive works of Dilworth, Ward and others, that, as opposed to Noetherian commutative rings, the existence of unique irreducible decomposition in lattices does not guarantee unique primary decomposition. The source alpha"},"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":"1301.7345","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-30T20:10:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"dfb5f2696e102e2970c3a0b2905aed210279f4dcac358ae3e6dc04da5f8a96c3","abstract_canon_sha256":"0b2bff7b49d23120ea9467a51782b7e662baed007c6d7735c9a17c406518c087"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:01.061658Z","signature_b64":"a0wF2KaQL9HrbNz2/PMhLqb+Uoqgpjg79JoLcSTqkyLKgoXrsURpBmjssFn2bYIaLp4CR9jaXjHWJ240vKQXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0324035b1ed075e947e4eb0deb1b98d470d6224baab2652454b42e2f052cc96","last_reissued_at":"2026-05-18T03:27:01.061069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:01.061069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Codes on Lattices for Random SAF Routing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anirban Ghatak","submitted_at":"2013-01-30T20:10:25Z","abstract_excerpt":"In this paper, a construction of constant weight codes based on the unique decomposition of elements in lattices is presented. The conditions for unique primary decomposition and unique irreducible decomposition in lattices are discussed and connections with the decomposition of ideals in Noetherian commutative rings established. In this context it is shown, drawing on the definitive works of Dilworth, Ward and others, that, as opposed to Noetherian commutative rings, the existence of unique irreducible decomposition in lattices does not guarantee unique primary decomposition. The source alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7345","kind":"arxiv","version":2},"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":"1301.7345","created_at":"2026-05-18T03:27:01.061154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.7345v2","created_at":"2026-05-18T03:27:01.061154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7345","created_at":"2026-05-18T03:27:01.061154+00:00"},{"alias_kind":"pith_short_12","alias_value":"4AZEANNR5UDV","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"4AZEANNR5UDV5FD6","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"4AZEANNR","created_at":"2026-05-18T12:27:32.513160+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/4AZEANNR5UDV5FD6J2YN5MNZRV","json":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV.json","graph_json":"https://pith.science/api/pith-number/4AZEANNR5UDV5FD6J2YN5MNZRV/graph.json","events_json":"https://pith.science/api/pith-number/4AZEANNR5UDV5FD6J2YN5MNZRV/events.json","paper":"https://pith.science/paper/4AZEANNR"},"agent_actions":{"view_html":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV","download_json":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV.json","view_paper":"https://pith.science/paper/4AZEANNR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.7345&json=true","fetch_graph":"https://pith.science/api/pith-number/4AZEANNR5UDV5FD6J2YN5MNZRV/graph.json","fetch_events":"https://pith.science/api/pith-number/4AZEANNR5UDV5FD6J2YN5MNZRV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV/action/storage_attestation","attest_author":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV/action/author_attestation","sign_citation":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV/action/citation_signature","submit_replication":"https://pith.science/pith/4AZEANNR5UDV5FD6J2YN5MNZRV/action/replication_record"}},"created_at":"2026-05-18T03:27:01.061154+00:00","updated_at":"2026-05-18T03:27:01.061154+00:00"}