{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:27SMJ426PIHTXC2HQ5STLSHSBP","short_pith_number":"pith:27SMJ426","schema_version":"1.0","canonical_sha256":"d7e4c4f35e7a0f3b8b47876535c8f20bd2af4394a1f0bfd44fa0d7fa0aa19586","source":{"kind":"arxiv","id":"1305.0434","version":1},"attestation_state":"computed","paper":{"title":"An $S$-adic characterization of minimal subshifts with first difference of complexity $1 \\leq p(n+1) - p(n) \\leq 2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Julien Leroy","submitted_at":"2013-05-02T13:53:28Z","abstract_excerpt":"In [Ergodic Theory Dynam. System, 16 (1996) 663--682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is $S$-adic with $\\card S \\leq 3^{27}$. In this paper, we improve this result by giving an $S$-adic charaterization of these subshifts with a set $S$ of 5 morphisms, solving by this way the $S$-adic conjecture for this particular case."},"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":"1305.0434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-05-02T13:53:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"348a40226561c06188537198cffb97132f7fd2ee29f1f3fead43b945fe36111d","abstract_canon_sha256":"d463a7d0ba5735141b41e6e76d945fedcc1d64aa16c1cc4b1d9c72c5fc42a3f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:40.319806Z","signature_b64":"nevgNG9x+HaEhuGQcBfUzU6Nbo5lATduCw05yuxy0c1mFwuyFae/CLn1DKns8wdN+Mhmyebq4h1LNHRhXT9ACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7e4c4f35e7a0f3b8b47876535c8f20bd2af4394a1f0bfd44fa0d7fa0aa19586","last_reissued_at":"2026-05-18T03:26:40.319261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:40.319261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An $S$-adic characterization of minimal subshifts with first difference of complexity $1 \\leq p(n+1) - p(n) \\leq 2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Julien Leroy","submitted_at":"2013-05-02T13:53:28Z","abstract_excerpt":"In [Ergodic Theory Dynam. System, 16 (1996) 663--682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is $S$-adic with $\\card S \\leq 3^{27}$. In this paper, we improve this result by giving an $S$-adic charaterization of these subshifts with a set $S$ of 5 morphisms, solving by this way the $S$-adic conjecture for this particular case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0434","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":"1305.0434","created_at":"2026-05-18T03:26:40.319357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0434v1","created_at":"2026-05-18T03:26:40.319357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0434","created_at":"2026-05-18T03:26:40.319357+00:00"},{"alias_kind":"pith_short_12","alias_value":"27SMJ426PIHT","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"27SMJ426PIHTXC2H","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"27SMJ426","created_at":"2026-05-18T12:27:30.460161+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/27SMJ426PIHTXC2HQ5STLSHSBP","json":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP.json","graph_json":"https://pith.science/api/pith-number/27SMJ426PIHTXC2HQ5STLSHSBP/graph.json","events_json":"https://pith.science/api/pith-number/27SMJ426PIHTXC2HQ5STLSHSBP/events.json","paper":"https://pith.science/paper/27SMJ426"},"agent_actions":{"view_html":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP","download_json":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP.json","view_paper":"https://pith.science/paper/27SMJ426","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0434&json=true","fetch_graph":"https://pith.science/api/pith-number/27SMJ426PIHTXC2HQ5STLSHSBP/graph.json","fetch_events":"https://pith.science/api/pith-number/27SMJ426PIHTXC2HQ5STLSHSBP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP/action/storage_attestation","attest_author":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP/action/author_attestation","sign_citation":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP/action/citation_signature","submit_replication":"https://pith.science/pith/27SMJ426PIHTXC2HQ5STLSHSBP/action/replication_record"}},"created_at":"2026-05-18T03:26:40.319357+00:00","updated_at":"2026-05-18T03:26:40.319357+00:00"}