{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:O344ASOPL2IB62QAJBAFGLRE3S","short_pith_number":"pith:O344ASOP","schema_version":"1.0","canonical_sha256":"76f9c049cf5e901f6a004840532e24dc92dc32ed80fe25dfe3161ffadeffa3be","source":{"kind":"arxiv","id":"2504.13028","version":1},"attestation_state":"computed","paper":{"title":"Profinite Iterated Monodromy Groups of Unicritical Polynomials","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Ophelia Adams, Trevor Hyde","submitted_at":"2025-04-17T15:39:16Z","abstract_excerpt":"Let $f(x) = ax^d + b \\in K[x]$ be a unicritical polynomial with degree $d \\geq 2$ which is coprime to $\\mathrm{char} K$. We provide an explicit presentation for the profinite iterated monodromy group of $f$, analyze the structure of this group, and use this analysis to determine the constant field extension in $K(f^{-\\infty}(t))/K(t)$."},"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":"2504.13028","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-04-17T15:39:16Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5cc225cc51f21441963c5b3692bbc5cac085b35b5da56e21c48fa1c09d6447a1","abstract_canon_sha256":"4950448544d2fff36b09231f0244b6b290170847bd2b7a6377ece38ae7fc7778"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:36.379703Z","signature_b64":"2FVrVUpCy7g5uJfHNhBpVOv+EcznkwmZMOqS7KRekklleRvJXfkm1ewbb9HYoajWpen0j2YlksUqX9IclUm2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76f9c049cf5e901f6a004840532e24dc92dc32ed80fe25dfe3161ffadeffa3be","last_reissued_at":"2026-07-05T10:50:36.379176Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:36.379176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Profinite Iterated Monodromy Groups of Unicritical Polynomials","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Ophelia Adams, Trevor Hyde","submitted_at":"2025-04-17T15:39:16Z","abstract_excerpt":"Let $f(x) = ax^d + b \\in K[x]$ be a unicritical polynomial with degree $d \\geq 2$ which is coprime to $\\mathrm{char} K$. We provide an explicit presentation for the profinite iterated monodromy group of $f$, analyze the structure of this group, and use this analysis to determine the constant field extension in $K(f^{-\\infty}(t))/K(t)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.13028","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.13028/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":"2504.13028","created_at":"2026-07-05T10:50:36.379244+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.13028v1","created_at":"2026-07-05T10:50:36.379244+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.13028","created_at":"2026-07-05T10:50:36.379244+00:00"},{"alias_kind":"pith_short_12","alias_value":"O344ASOPL2IB","created_at":"2026-07-05T10:50:36.379244+00:00"},{"alias_kind":"pith_short_16","alias_value":"O344ASOPL2IB62QA","created_at":"2026-07-05T10:50:36.379244+00:00"},{"alias_kind":"pith_short_8","alias_value":"O344ASOP","created_at":"2026-07-05T10:50:36.379244+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.04649","citing_title":"Local-global conjugacy questions for affine extensions","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04524","citing_title":"Settled Elements in Arboreal Galois Groups of Quadratic PCF Polynomials","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S","json":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S.json","graph_json":"https://pith.science/api/pith-number/O344ASOPL2IB62QAJBAFGLRE3S/graph.json","events_json":"https://pith.science/api/pith-number/O344ASOPL2IB62QAJBAFGLRE3S/events.json","paper":"https://pith.science/paper/O344ASOP"},"agent_actions":{"view_html":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S","download_json":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S.json","view_paper":"https://pith.science/paper/O344ASOP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.13028&json=true","fetch_graph":"https://pith.science/api/pith-number/O344ASOPL2IB62QAJBAFGLRE3S/graph.json","fetch_events":"https://pith.science/api/pith-number/O344ASOPL2IB62QAJBAFGLRE3S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S/action/storage_attestation","attest_author":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S/action/author_attestation","sign_citation":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S/action/citation_signature","submit_replication":"https://pith.science/pith/O344ASOPL2IB62QAJBAFGLRE3S/action/replication_record"}},"created_at":"2026-07-05T10:50:36.379244+00:00","updated_at":"2026-07-05T10:50:36.379244+00:00"}