{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LKDO2LENLNVCG3F4RLJHRDG6XQ","short_pith_number":"pith:LKDO2LEN","schema_version":"1.0","canonical_sha256":"5a86ed2c8d5b6a236cbc8ad2788cdebc0c7b971c255fcd7b3a4699b50f10d155","source":{"kind":"arxiv","id":"1706.03233","version":2},"attestation_state":"computed","paper":{"title":"On some interesting ternary formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Matthieu Rosenfeld, Pascal Ochem","submitted_at":"2017-06-10T13:21:29Z","abstract_excerpt":"We obtain the following results about the avoidance of ternary formulas. Up to renaming of the letters, the only infinite ternary words avoiding the formula $ABCAB.ABCBA.ACB.BAC$ (resp. $ABCA.BCAB.BCB.CBA$) have the same set of recurrent factors as the fixed point of $\\texttt{0}\\mapsto\\texttt{012}$, $\\texttt{1}\\mapsto\\texttt{02}$, $\\texttt{2}\\mapsto\\texttt{1}$. The formula $ABAC.BACA.ABCA$ is avoided by polynomially many binary words and there exist arbitrarily many infinite binary words with different sets of recurrent factors that avoid it. If every variable of a ternary formula appears at l"},"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":"1706.03233","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-10T13:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"3c76f5befee7cc5c7bf3d11329fb0da4c0ea2aaa6563165cbe40b4847707424a","abstract_canon_sha256":"fdef38b362b8f3e3f6ef64f62e68e33f14ef5ac3d7c8f9b3a7152af88469c520"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:00.573746Z","signature_b64":"iHMQQEUV/X8s4Bkfh7EADHH5YxeTZkNXrZfoPBE5Hn6B8/QcNsWjDAmp21JiklBq7mYBE5it5wltdsvnwSPrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a86ed2c8d5b6a236cbc8ad2788cdebc0c7b971c255fcd7b3a4699b50f10d155","last_reissued_at":"2026-05-18T00:05:00.573309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:00.573309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some interesting ternary formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Matthieu Rosenfeld, Pascal Ochem","submitted_at":"2017-06-10T13:21:29Z","abstract_excerpt":"We obtain the following results about the avoidance of ternary formulas. Up to renaming of the letters, the only infinite ternary words avoiding the formula $ABCAB.ABCBA.ACB.BAC$ (resp. $ABCA.BCAB.BCB.CBA$) have the same set of recurrent factors as the fixed point of $\\texttt{0}\\mapsto\\texttt{012}$, $\\texttt{1}\\mapsto\\texttt{02}$, $\\texttt{2}\\mapsto\\texttt{1}$. The formula $ABAC.BACA.ABCA$ is avoided by polynomially many binary words and there exist arbitrarily many infinite binary words with different sets of recurrent factors that avoid it. If every variable of a ternary formula appears at l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03233","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":"1706.03233","created_at":"2026-05-18T00:05:00.573385+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.03233v2","created_at":"2026-05-18T00:05:00.573385+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03233","created_at":"2026-05-18T00:05:00.573385+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKDO2LENLNVC","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKDO2LENLNVCG3F4","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKDO2LEN","created_at":"2026-05-18T12:31:28.150371+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/LKDO2LENLNVCG3F4RLJHRDG6XQ","json":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ.json","graph_json":"https://pith.science/api/pith-number/LKDO2LENLNVCG3F4RLJHRDG6XQ/graph.json","events_json":"https://pith.science/api/pith-number/LKDO2LENLNVCG3F4RLJHRDG6XQ/events.json","paper":"https://pith.science/paper/LKDO2LEN"},"agent_actions":{"view_html":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ","download_json":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ.json","view_paper":"https://pith.science/paper/LKDO2LEN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.03233&json=true","fetch_graph":"https://pith.science/api/pith-number/LKDO2LENLNVCG3F4RLJHRDG6XQ/graph.json","fetch_events":"https://pith.science/api/pith-number/LKDO2LENLNVCG3F4RLJHRDG6XQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ/action/storage_attestation","attest_author":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ/action/author_attestation","sign_citation":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ/action/citation_signature","submit_replication":"https://pith.science/pith/LKDO2LENLNVCG3F4RLJHRDG6XQ/action/replication_record"}},"created_at":"2026-05-18T00:05:00.573385+00:00","updated_at":"2026-05-18T00:05:00.573385+00:00"}