{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WC6RT43LR3FO4KX4PXTB3FCK36","short_pith_number":"pith:WC6RT43L","schema_version":"1.0","canonical_sha256":"b0bd19f36b8ecaee2afc7de61d944adf925f911ab02b9bbac552223177af1975","source":{"kind":"arxiv","id":"1507.03361","version":3},"attestation_state":"computed","paper":{"title":"Hypertranscendence of solutions of Mahler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Charlotte Hardouin, Julien Roques, Thomas Dreyfus","submitted_at":"2015-07-13T08:58:23Z","abstract_excerpt":"The last years have seen a growing interest from mathematicians in Mahler functions. This class of functions includes the generating series of the automatic sequences. The present paper is concerned with the following problem, which is omnipresent in combinatorics: a set of Mahler functions $u_{1},...,u_{n}$ being given, are $u_{1},...,u_{n}$ and their successive derivatives algebraically independent? In this paper, we give general criteria ensuring an affirmative answer to this question. We apply our main results to the generating series attached to the so-called Baum-Sweet and Rudin-Shapiro "},"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":"1507.03361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-13T08:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"92ad733a7cc107887e758e700d382c9301f6f7c2dd43f97d907e509a7aac213a","abstract_canon_sha256":"2c8b68827eb13e3113b62cf81581f4ec95c39801753b3ac06a3cce925e2f6aad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:56.491204Z","signature_b64":"YaEeRMtJZe2OmlqNW9v6I/Zuj5CYlTPByRzJ32v9tKAIW8efjqfu1EGtQnBMi8+VrwwXvBkBZAd7Q90VeAsbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0bd19f36b8ecaee2afc7de61d944adf925f911ab02b9bbac552223177af1975","last_reissued_at":"2026-05-17T23:52:56.490471Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:56.490471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypertranscendence of solutions of Mahler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Charlotte Hardouin, Julien Roques, Thomas Dreyfus","submitted_at":"2015-07-13T08:58:23Z","abstract_excerpt":"The last years have seen a growing interest from mathematicians in Mahler functions. This class of functions includes the generating series of the automatic sequences. The present paper is concerned with the following problem, which is omnipresent in combinatorics: a set of Mahler functions $u_{1},...,u_{n}$ being given, are $u_{1},...,u_{n}$ and their successive derivatives algebraically independent? In this paper, we give general criteria ensuring an affirmative answer to this question. We apply our main results to the generating series attached to the so-called Baum-Sweet and Rudin-Shapiro "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03361","kind":"arxiv","version":3},"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":"1507.03361","created_at":"2026-05-17T23:52:56.490597+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.03361v3","created_at":"2026-05-17T23:52:56.490597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03361","created_at":"2026-05-17T23:52:56.490597+00:00"},{"alias_kind":"pith_short_12","alias_value":"WC6RT43LR3FO","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WC6RT43LR3FO4KX4","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WC6RT43L","created_at":"2026-05-18T12:29:47.479230+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/WC6RT43LR3FO4KX4PXTB3FCK36","json":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36.json","graph_json":"https://pith.science/api/pith-number/WC6RT43LR3FO4KX4PXTB3FCK36/graph.json","events_json":"https://pith.science/api/pith-number/WC6RT43LR3FO4KX4PXTB3FCK36/events.json","paper":"https://pith.science/paper/WC6RT43L"},"agent_actions":{"view_html":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36","download_json":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36.json","view_paper":"https://pith.science/paper/WC6RT43L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.03361&json=true","fetch_graph":"https://pith.science/api/pith-number/WC6RT43LR3FO4KX4PXTB3FCK36/graph.json","fetch_events":"https://pith.science/api/pith-number/WC6RT43LR3FO4KX4PXTB3FCK36/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36/action/storage_attestation","attest_author":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36/action/author_attestation","sign_citation":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36/action/citation_signature","submit_replication":"https://pith.science/pith/WC6RT43LR3FO4KX4PXTB3FCK36/action/replication_record"}},"created_at":"2026-05-17T23:52:56.490597+00:00","updated_at":"2026-05-17T23:52:56.490597+00:00"}