{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MLHYNHCUM3PJINP65HCP7Z466Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"306e117b7c4515151cfab490b66b6b42b1b70421487c62847c921ffdaae0c8b8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-01T16:53:29Z","title_canon_sha256":"11ab345ff8350229862a858a36fa51aeef438157feb36f35a8894d75667acd36"},"schema_version":"1.0","source":{"id":"1202.0211","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0211","created_at":"2026-05-18T02:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0211v3","created_at":"2026-05-18T02:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0211","created_at":"2026-05-18T02:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"MLHYNHCUM3PJ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MLHYNHCUM3PJINP6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MLHYNHCU","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:1368c870f0d092e1d675188b8ad78167d67016797d99a0d70353ca8f60b4523b","target":"graph","created_at":"2026-05-18T02:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $F(X) = \\sum_{n \\geq 0} (-1)^{\\varepsilon_n} X^{-\\lambda_n}$ be a real lacunary formal power series, where $\\varepsilon_n = 0, 1$ and $\\lambda_{n+1}/\\lambda_n > 2$. It is known that the denominators $Q_n(X)$ of the convergents of its continued fraction expansion are polynomials with coefficients $0, \\pm 1$, and that the number of nonzero terms in $Q_n(X)$ is the $n$th term of the Stern-Brocot sequence. We show that replacing the index $n$ by any 2-adic integer $\\omega$ makes sense. We prove that $Q_{\\omega}(X)$ is a polynomial if and only if $\\omega \\in {\\mathbb Z}$. In all the other cases","authors_text":"Jean-Paul Allouche, Michel Mend\\`es France","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-01T16:53:29Z","title":"Lacunary formal power series and the Stern-Brocot sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0211","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7aff46f1c077496e444dc4e70e8a286a49e03b9528e572e622320b97bbf0d104","target":"record","created_at":"2026-05-18T02:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"306e117b7c4515151cfab490b66b6b42b1b70421487c62847c921ffdaae0c8b8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-01T16:53:29Z","title_canon_sha256":"11ab345ff8350229862a858a36fa51aeef438157feb36f35a8894d75667acd36"},"schema_version":"1.0","source":{"id":"1202.0211","kind":"arxiv","version":3}},"canonical_sha256":"62cf869c5466de9435fee9c4ffe79ef43ce9ac38e824031bf4d01d581b2f5fa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62cf869c5466de9435fee9c4ffe79ef43ce9ac38e824031bf4d01d581b2f5fa4","first_computed_at":"2026-05-18T02:53:15.685687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:15.685687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yoCDr6oo8BU9qkuIeh2qGT18B7uX9jWVq/g/41eFSCHBxu2Oa6SZC4FxD9fs6TrODkDWaJkgUX2xaHXBjCTZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:15.686351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0211","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aff46f1c077496e444dc4e70e8a286a49e03b9528e572e622320b97bbf0d104","sha256:1368c870f0d092e1d675188b8ad78167d67016797d99a0d70353ca8f60b4523b"],"state_sha256":"213362bed6d3219c5e1ba3b64d53ed45423b2c2d69b184da9e711e96f1590ef7"}