{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Y2D3ZQIS3T4CA7ABPQIX52PFGR","short_pith_number":"pith:Y2D3ZQIS","schema_version":"1.0","canonical_sha256":"c687bcc112dcf8207c017c117ee9e5347144994d35f3562ab49a68faeb8369c1","source":{"kind":"arxiv","id":"1511.00194","version":2},"attestation_state":"computed","paper":{"title":"Finite ramification for preimage fields of postcritically finite morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alon Levy, Andrew Bridy, Jamie Juul, Joseph H. Silverman, Michelle Manes, Patrick Ingram, Rafe Jones, Simon Rubinstein-Salzedo","submitted_at":"2015-11-01T00:51:31Z","abstract_excerpt":"Given a finite endomorphism $\\varphi$ of a variety $X$ defined over the field of fractions $K$ of a Dedekind domain, we study the extension $K(\\varphi^{-\\infty}(\\alpha)) : = \\bigcup_{n \\geq 1} K(\\varphi^{-n}(\\alpha))$ generated by the preimages of $\\alpha$ under all iterates of $\\varphi$. In particular when $\\varphi$ is post-critically finite, i.e., there exists a non-empty, Zariski-open $W \\subseteq X$ such that $\\varphi^{-1}(W) \\subseteq W$ and $\\varphi : W \\to X$ is \\'etale, we prove that $K(\\varphi^{-\\infty}(\\alpha))$ is ramified over only finitely many primes of $K$. This provides a large"},"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":"1511.00194","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-01T00:51:31Z","cross_cats_sorted":[],"title_canon_sha256":"9bdf19f5c03d178eb7fc2a285f74e1634ba0b373e81e3aef8557fe24e0157677","abstract_canon_sha256":"5ff3069946c52785e3fa758186f9961588b7c2e051987f2e69c24b3ee0eae368"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:26.027834Z","signature_b64":"mltYn016N+myGrWEnWvuBK21dG3lSi1b00nNFZ9fCK2sMxLmdm++TXAMyDXUyZOYi4V4yHf4pnlI9VGm62ISCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c687bcc112dcf8207c017c117ee9e5347144994d35f3562ab49a68faeb8369c1","last_reissued_at":"2026-05-18T01:25:26.027394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:26.027394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite ramification for preimage fields of postcritically finite morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alon Levy, Andrew Bridy, Jamie Juul, Joseph H. Silverman, Michelle Manes, Patrick Ingram, Rafe Jones, Simon Rubinstein-Salzedo","submitted_at":"2015-11-01T00:51:31Z","abstract_excerpt":"Given a finite endomorphism $\\varphi$ of a variety $X$ defined over the field of fractions $K$ of a Dedekind domain, we study the extension $K(\\varphi^{-\\infty}(\\alpha)) : = \\bigcup_{n \\geq 1} K(\\varphi^{-n}(\\alpha))$ generated by the preimages of $\\alpha$ under all iterates of $\\varphi$. In particular when $\\varphi$ is post-critically finite, i.e., there exists a non-empty, Zariski-open $W \\subseteq X$ such that $\\varphi^{-1}(W) \\subseteq W$ and $\\varphi : W \\to X$ is \\'etale, we prove that $K(\\varphi^{-\\infty}(\\alpha))$ is ramified over only finitely many primes of $K$. This provides a large"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00194","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":""},"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":"1511.00194","created_at":"2026-05-18T01:25:26.027460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.00194v2","created_at":"2026-05-18T01:25:26.027460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00194","created_at":"2026-05-18T01:25:26.027460+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2D3ZQIS3T4C","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2D3ZQIS3T4CA7AB","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2D3ZQIS","created_at":"2026-05-18T12:29:50.041715+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/Y2D3ZQIS3T4CA7ABPQIX52PFGR","json":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR.json","graph_json":"https://pith.science/api/pith-number/Y2D3ZQIS3T4CA7ABPQIX52PFGR/graph.json","events_json":"https://pith.science/api/pith-number/Y2D3ZQIS3T4CA7ABPQIX52PFGR/events.json","paper":"https://pith.science/paper/Y2D3ZQIS"},"agent_actions":{"view_html":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR","download_json":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR.json","view_paper":"https://pith.science/paper/Y2D3ZQIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.00194&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2D3ZQIS3T4CA7ABPQIX52PFGR/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2D3ZQIS3T4CA7ABPQIX52PFGR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR/action/storage_attestation","attest_author":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR/action/author_attestation","sign_citation":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR/action/citation_signature","submit_replication":"https://pith.science/pith/Y2D3ZQIS3T4CA7ABPQIX52PFGR/action/replication_record"}},"created_at":"2026-05-18T01:25:26.027460+00:00","updated_at":"2026-05-18T01:25:26.027460+00:00"}