{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:W3KU6N4SYKJXUXRCTO4BZ3A2KZ","short_pith_number":"pith:W3KU6N4S","schema_version":"1.0","canonical_sha256":"b6d54f3792c2937a5e229bb81cec1a56662e133620a54dbf1e0ee575ce55aeee","source":{"kind":"arxiv","id":"2411.14960","version":2},"attestation_state":"computed","paper":{"title":"First-order definitions of rings of integral functions over algebraic extensions of function fields and undecidability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.NT","authors_text":"Alexandra Shlapentokh, Caleb Springer","submitted_at":"2024-11-22T14:18:10Z","abstract_excerpt":"In this paper, we study questions of definability and decidability for infinite algebraic extensions ${\\bf K}$ of $\\mathbb{F}_p(t)$ and their subrings of $\\mathcal{S}$-integral functions. We focus on fields ${\\bf K}$ satisfying a local property which we call $q$-boundedness. This can be considered a function field analogue of prior work of the first author which considered algebraic extensions of $\\mathbb{Q}$. One simple consequence of our work states that if ${\\bf K}$ is a $q$-bounded Galois extension of $\\mathbb{F}_p(t)$, then for infinitely many non-constant $u$ the integral closure $\\mathc"},"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":"2411.14960","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-22T14:18:10Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"183073bf327d2cbf3054fc9f91a0220ed11db5347b9f3045a49ba9250757035e","abstract_canon_sha256":"f0531c3dcb1beefd8fabdb03219e1516fa9ba81710cc4850492d7ba7506caea0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:38.072947Z","signature_b64":"H8YFBUWp65vfGRk/SPD69f0sojHnl7eEVRgW/NAHVWF2VF62wXA+Pw2Vo5H1TAFoUQ4SQ+ifSuD3eSaL/5moDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6d54f3792c2937a5e229bb81cec1a56662e133620a54dbf1e0ee575ce55aeee","last_reissued_at":"2026-07-05T10:01:38.072545Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:38.072545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First-order definitions of rings of integral functions over algebraic extensions of function fields and undecidability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.NT","authors_text":"Alexandra Shlapentokh, Caleb Springer","submitted_at":"2024-11-22T14:18:10Z","abstract_excerpt":"In this paper, we study questions of definability and decidability for infinite algebraic extensions ${\\bf K}$ of $\\mathbb{F}_p(t)$ and their subrings of $\\mathcal{S}$-integral functions. We focus on fields ${\\bf K}$ satisfying a local property which we call $q$-boundedness. This can be considered a function field analogue of prior work of the first author which considered algebraic extensions of $\\mathbb{Q}$. One simple consequence of our work states that if ${\\bf K}$ is a $q$-bounded Galois extension of $\\mathbb{F}_p(t)$, then for infinitely many non-constant $u$ the integral closure $\\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14960","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14960/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.14960","created_at":"2026-07-05T10:01:38.072602+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.14960v2","created_at":"2026-07-05T10:01:38.072602+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14960","created_at":"2026-07-05T10:01:38.072602+00:00"},{"alias_kind":"pith_short_12","alias_value":"W3KU6N4SYKJX","created_at":"2026-07-05T10:01:38.072602+00:00"},{"alias_kind":"pith_short_16","alias_value":"W3KU6N4SYKJXUXRC","created_at":"2026-07-05T10:01:38.072602+00:00"},{"alias_kind":"pith_short_8","alias_value":"W3KU6N4S","created_at":"2026-07-05T10:01:38.072602+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/W3KU6N4SYKJXUXRCTO4BZ3A2KZ","json":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ.json","graph_json":"https://pith.science/api/pith-number/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/graph.json","events_json":"https://pith.science/api/pith-number/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/events.json","paper":"https://pith.science/paper/W3KU6N4S"},"agent_actions":{"view_html":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ","download_json":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ.json","view_paper":"https://pith.science/paper/W3KU6N4S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.14960&json=true","fetch_graph":"https://pith.science/api/pith-number/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/graph.json","fetch_events":"https://pith.science/api/pith-number/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/action/storage_attestation","attest_author":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/action/author_attestation","sign_citation":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/action/citation_signature","submit_replication":"https://pith.science/pith/W3KU6N4SYKJXUXRCTO4BZ3A2KZ/action/replication_record"}},"created_at":"2026-07-05T10:01:38.072602+00:00","updated_at":"2026-07-05T10:01:38.072602+00:00"}