{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QXR6KFYV3VOAP2NMARHAXNZK45","short_pith_number":"pith:QXR6KFYV","schema_version":"1.0","canonical_sha256":"85e3e51715dd5c07e9ac044e0bb72ae742c8fa384996af225c9175b8c02b6b6b","source":{"kind":"arxiv","id":"1807.11899","version":1},"attestation_state":"computed","paper":{"title":"The Formal Inverse of the Period-Doubling Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"Manon Stipulanti, Narad Rampersad","submitted_at":"2018-07-31T16:22:08Z","abstract_excerpt":"If $p$ is a prime number, consider a $p$-automatic sequence $(u_n)_{n\\ge 0}$, and let $U(X) = \\sum_{n\\ge 0} u_n X^n \\in \\mathbb{F}_p[[X]]$ be its generating function. Assume that there exists a formal power series $V(X) = \\sum_{n\\ge 0} v_n X^n \\in \\mathbb{F}_p[[X]]$ which is the compositional inverse of $U$, i.e., $U(V(X))=X=V(U(X))$. The problem investigated in this paper is to study the properties of the sequence $(v_n)_{n\\ge 0}$. The work was first initiated for the Thue-Morse sequence, and more recently the case of two variations of the Baum-Sweet sequence has been treated. In this paper, "},"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":"1807.11899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-31T16:22:08Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"9571ad9775fb7c70ba62515fa153aa806e49e5689888409b21be84356d44d694","abstract_canon_sha256":"2cd472b12c8d21a802e93c63d99a1294c4c0d3ca2c29f7b78c746bc469724b6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:20.795468Z","signature_b64":"gKTl2q6etw+eRhmhBEAOk3LCXeQ0s/CUyfKvIMXDaRnk5wI2gBlTWMJVJo2EfxT/SH/S5Q8a/vRkvC0ubd1WBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85e3e51715dd5c07e9ac044e0bb72ae742c8fa384996af225c9175b8c02b6b6b","last_reissued_at":"2026-05-18T00:09:20.794855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:20.794855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Formal Inverse of the Period-Doubling Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"Manon Stipulanti, Narad Rampersad","submitted_at":"2018-07-31T16:22:08Z","abstract_excerpt":"If $p$ is a prime number, consider a $p$-automatic sequence $(u_n)_{n\\ge 0}$, and let $U(X) = \\sum_{n\\ge 0} u_n X^n \\in \\mathbb{F}_p[[X]]$ be its generating function. Assume that there exists a formal power series $V(X) = \\sum_{n\\ge 0} v_n X^n \\in \\mathbb{F}_p[[X]]$ which is the compositional inverse of $U$, i.e., $U(V(X))=X=V(U(X))$. The problem investigated in this paper is to study the properties of the sequence $(v_n)_{n\\ge 0}$. The work was first initiated for the Thue-Morse sequence, and more recently the case of two variations of the Baum-Sweet sequence has been treated. In this paper, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11899","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":"1807.11899","created_at":"2026-05-18T00:09:20.794955+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11899v1","created_at":"2026-05-18T00:09:20.794955+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11899","created_at":"2026-05-18T00:09:20.794955+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXR6KFYV3VOA","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXR6KFYV3VOAP2NM","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXR6KFYV","created_at":"2026-05-18T12:32:50.500415+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/QXR6KFYV3VOAP2NMARHAXNZK45","json":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45.json","graph_json":"https://pith.science/api/pith-number/QXR6KFYV3VOAP2NMARHAXNZK45/graph.json","events_json":"https://pith.science/api/pith-number/QXR6KFYV3VOAP2NMARHAXNZK45/events.json","paper":"https://pith.science/paper/QXR6KFYV"},"agent_actions":{"view_html":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45","download_json":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45.json","view_paper":"https://pith.science/paper/QXR6KFYV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11899&json=true","fetch_graph":"https://pith.science/api/pith-number/QXR6KFYV3VOAP2NMARHAXNZK45/graph.json","fetch_events":"https://pith.science/api/pith-number/QXR6KFYV3VOAP2NMARHAXNZK45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45/action/storage_attestation","attest_author":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45/action/author_attestation","sign_citation":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45/action/citation_signature","submit_replication":"https://pith.science/pith/QXR6KFYV3VOAP2NMARHAXNZK45/action/replication_record"}},"created_at":"2026-05-18T00:09:20.794955+00:00","updated_at":"2026-05-18T00:09:20.794955+00:00"}