{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AW623WGQ6L377MZZDISNXJTNRF","short_pith_number":"pith:AW623WGQ","schema_version":"1.0","canonical_sha256":"05bdadd8d0f2f7ffb3391a24dba66d8966199bfca69e2ae46f39940c3814c79f","source":{"kind":"arxiv","id":"1502.01381","version":4},"attestation_state":"computed","paper":{"title":"Behavior of canonical divisors under purely inseparable base changes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hiromu Tanaka","submitted_at":"2015-02-04T22:24:48Z","abstract_excerpt":"Let $k$ be an imperfect field. Let $X$ be a regular variety over $k$ and set $Y$ to be the normalization of $(X \\times_k k^{1/p^{\\infty}})_{{\\rm red}}$. In this paper, we show that $K_Y+C=f^*K_X$ for some effective divisor $C$ on $Y$. We obtain the following three applications. First, we show that a $K_X$-trivial fiber space with non-normal fibers is uniruled. Second, we prove that general fibers of Mori fiber spaces are rationally chain connected. Third, we obtain a weakening of the cone theorem for surfaces and threefolds defined over an imperfect field."},"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":"1502.01381","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-04T22:24:48Z","cross_cats_sorted":[],"title_canon_sha256":"5cd1b951af4a53ebd3381437c876cb4b00ffe2e4f18c326385b99b3de0d52bf8","abstract_canon_sha256":"480ab03237028f5eb49834a4d6485a7d9fcc81d26286a90cfdd7e086a5f0b692"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:25.328902Z","signature_b64":"vL8eZulRRShPXsZEXOEGXyEpK5lOWbbE8Rq4riP+70MAOxXXEm1vLoO8pezTx6rx9bOJ861A1TJ4r84c+BGLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05bdadd8d0f2f7ffb3391a24dba66d8966199bfca69e2ae46f39940c3814c79f","last_reissued_at":"2026-05-18T01:12:25.328578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:25.328578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Behavior of canonical divisors under purely inseparable base changes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hiromu Tanaka","submitted_at":"2015-02-04T22:24:48Z","abstract_excerpt":"Let $k$ be an imperfect field. Let $X$ be a regular variety over $k$ and set $Y$ to be the normalization of $(X \\times_k k^{1/p^{\\infty}})_{{\\rm red}}$. In this paper, we show that $K_Y+C=f^*K_X$ for some effective divisor $C$ on $Y$. We obtain the following three applications. First, we show that a $K_X$-trivial fiber space with non-normal fibers is uniruled. Second, we prove that general fibers of Mori fiber spaces are rationally chain connected. Third, we obtain a weakening of the cone theorem for surfaces and threefolds defined over an imperfect field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01381","kind":"arxiv","version":4},"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":"1502.01381","created_at":"2026-05-18T01:12:25.328627+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.01381v4","created_at":"2026-05-18T01:12:25.328627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01381","created_at":"2026-05-18T01:12:25.328627+00:00"},{"alias_kind":"pith_short_12","alias_value":"AW623WGQ6L37","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AW623WGQ6L377MZZ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AW623WGQ","created_at":"2026-05-18T12:29:10.953037+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/AW623WGQ6L377MZZDISNXJTNRF","json":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF.json","graph_json":"https://pith.science/api/pith-number/AW623WGQ6L377MZZDISNXJTNRF/graph.json","events_json":"https://pith.science/api/pith-number/AW623WGQ6L377MZZDISNXJTNRF/events.json","paper":"https://pith.science/paper/AW623WGQ"},"agent_actions":{"view_html":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF","download_json":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF.json","view_paper":"https://pith.science/paper/AW623WGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.01381&json=true","fetch_graph":"https://pith.science/api/pith-number/AW623WGQ6L377MZZDISNXJTNRF/graph.json","fetch_events":"https://pith.science/api/pith-number/AW623WGQ6L377MZZDISNXJTNRF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF/action/storage_attestation","attest_author":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF/action/author_attestation","sign_citation":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF/action/citation_signature","submit_replication":"https://pith.science/pith/AW623WGQ6L377MZZDISNXJTNRF/action/replication_record"}},"created_at":"2026-05-18T01:12:25.328627+00:00","updated_at":"2026-05-18T01:12:25.328627+00:00"}