{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FQBIETMIISR77E6L3RATIINJDS","short_pith_number":"pith:FQBIETMI","schema_version":"1.0","canonical_sha256":"2c02824d8844a3ff93cbdc413421a91cb7b65f2be876362d1bfc636c66342348","source":{"kind":"arxiv","id":"1205.2310","version":2},"attestation_state":"computed","paper":{"title":"A note on the factorization conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Clelia De Felice","submitted_at":"2012-05-10T16:58:27Z","abstract_excerpt":"We give partial results on the factorization conjecture on codes proposed by Schutzenberger. We consider finite maximal codes C over the alphabet A = {a, b} with C \\cap a^* = a^p, for a prime number p. Let P, S in Z <A>, with S = S_0 + S_1, supp(S_0) \\subset a^* and supp(S_1) \\subset a^*b supp(S_0). We prove that if (P,S) is a factorization for C then (P,S) is positive, that is P,S have coefficients 0,1, and we characterize the structure of these codes. As a consequence, we prove that if C is a finite maximal code such that each word in C has at most 4 occurrences of b's and a^p is in C, then "},"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":"1205.2310","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-05-10T16:58:27Z","cross_cats_sorted":[],"title_canon_sha256":"f3ab06be0b0ef9cd784726173f8df9e7e996f7339da903df25609e6a9f33fe69","abstract_canon_sha256":"1495ab0523afb91c72333929e49d5b84f613f456bf6eabb61c01c21bba264461"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:10.452975Z","signature_b64":"03skD6A2KZkHvWl5pPvSULk6RuOITbFD8UrFhluFBmcmWhpBoP7Ygv0cVm7kbSr3uC0eQcWj9hNze3s8R/fFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c02824d8844a3ff93cbdc413421a91cb7b65f2be876362d1bfc636c66342348","last_reissued_at":"2026-05-18T02:21:10.452417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:10.452417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the factorization conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Clelia De Felice","submitted_at":"2012-05-10T16:58:27Z","abstract_excerpt":"We give partial results on the factorization conjecture on codes proposed by Schutzenberger. We consider finite maximal codes C over the alphabet A = {a, b} with C \\cap a^* = a^p, for a prime number p. Let P, S in Z <A>, with S = S_0 + S_1, supp(S_0) \\subset a^* and supp(S_1) \\subset a^*b supp(S_0). We prove that if (P,S) is a factorization for C then (P,S) is positive, that is P,S have coefficients 0,1, and we characterize the structure of these codes. As a consequence, we prove that if C is a finite maximal code such that each word in C has at most 4 occurrences of b's and a^p is in C, then "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2310","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":"1205.2310","created_at":"2026-05-18T02:21:10.452511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.2310v2","created_at":"2026-05-18T02:21:10.452511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2310","created_at":"2026-05-18T02:21:10.452511+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQBIETMIISR7","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQBIETMIISR77E6L","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQBIETMI","created_at":"2026-05-18T12:27:06.952714+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/FQBIETMIISR77E6L3RATIINJDS","json":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS.json","graph_json":"https://pith.science/api/pith-number/FQBIETMIISR77E6L3RATIINJDS/graph.json","events_json":"https://pith.science/api/pith-number/FQBIETMIISR77E6L3RATIINJDS/events.json","paper":"https://pith.science/paper/FQBIETMI"},"agent_actions":{"view_html":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS","download_json":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS.json","view_paper":"https://pith.science/paper/FQBIETMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.2310&json=true","fetch_graph":"https://pith.science/api/pith-number/FQBIETMIISR77E6L3RATIINJDS/graph.json","fetch_events":"https://pith.science/api/pith-number/FQBIETMIISR77E6L3RATIINJDS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS/action/storage_attestation","attest_author":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS/action/author_attestation","sign_citation":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS/action/citation_signature","submit_replication":"https://pith.science/pith/FQBIETMIISR77E6L3RATIINJDS/action/replication_record"}},"created_at":"2026-05-18T02:21:10.452511+00:00","updated_at":"2026-05-18T02:21:10.452511+00:00"}