{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:S7KMWZF6TBLACZ3M6SOMAHE6FO","short_pith_number":"pith:S7KMWZF6","schema_version":"1.0","canonical_sha256":"97d4cb64be985601676cf49cc01c9e2b9463ec800eafc8ed4f6d935f7f2616a3","source":{"kind":"arxiv","id":"1208.6376","version":1},"attestation_state":"computed","paper":{"title":"Towards a statement of the S-adic conjecture through examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fabien Durand (LAMFA), Gw\\'ena\\\"el Richomme (LIRMM), Julien Leroy (LAMFA)","submitted_at":"2012-08-31T06:17:13Z","abstract_excerpt":"The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the factor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be \"a good Condition $C$\"."},"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":"1208.6376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-08-31T06:17:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"73f4c349783034728bd3993d201fd8157aeca2e96127dd5b3d6c40e57f0faf5e","abstract_canon_sha256":"2755b388fb08af6bc43756c753abef0d53bc6336c3e1d65e06a784e5532b7aee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:33.493221Z","signature_b64":"X0Wm11r5Og+alhPbJW6If+xpVpol8RjWz1RvH/U3vRLRAEDjdBYFYm7mG+qTT9dxDUmjLg09WbBisYNTlrjuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97d4cb64be985601676cf49cc01c9e2b9463ec800eafc8ed4f6d935f7f2616a3","last_reissued_at":"2026-05-18T03:46:33.492512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:33.492512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards a statement of the S-adic conjecture through examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fabien Durand (LAMFA), Gw\\'ena\\\"el Richomme (LIRMM), Julien Leroy (LAMFA)","submitted_at":"2012-08-31T06:17:13Z","abstract_excerpt":"The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the factor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be \"a good Condition $C$\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6376","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":"1208.6376","created_at":"2026-05-18T03:46:33.492623+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.6376v1","created_at":"2026-05-18T03:46:33.492623+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6376","created_at":"2026-05-18T03:46:33.492623+00:00"},{"alias_kind":"pith_short_12","alias_value":"S7KMWZF6TBLA","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"S7KMWZF6TBLACZ3M","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"S7KMWZF6","created_at":"2026-05-18T12:27:20.899486+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/S7KMWZF6TBLACZ3M6SOMAHE6FO","json":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO.json","graph_json":"https://pith.science/api/pith-number/S7KMWZF6TBLACZ3M6SOMAHE6FO/graph.json","events_json":"https://pith.science/api/pith-number/S7KMWZF6TBLACZ3M6SOMAHE6FO/events.json","paper":"https://pith.science/paper/S7KMWZF6"},"agent_actions":{"view_html":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO","download_json":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO.json","view_paper":"https://pith.science/paper/S7KMWZF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.6376&json=true","fetch_graph":"https://pith.science/api/pith-number/S7KMWZF6TBLACZ3M6SOMAHE6FO/graph.json","fetch_events":"https://pith.science/api/pith-number/S7KMWZF6TBLACZ3M6SOMAHE6FO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO/action/storage_attestation","attest_author":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO/action/author_attestation","sign_citation":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO/action/citation_signature","submit_replication":"https://pith.science/pith/S7KMWZF6TBLACZ3M6SOMAHE6FO/action/replication_record"}},"created_at":"2026-05-18T03:46:33.492623+00:00","updated_at":"2026-05-18T03:46:33.492623+00:00"}