{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:Q5N7KGFEO32NPR3ZHJGASSETUH","short_pith_number":"pith:Q5N7KGFE","schema_version":"1.0","canonical_sha256":"875bf518a476f4d7c7793a4c094893a1fbf3a400f2cfc8718991a1330f54129d","source":{"kind":"arxiv","id":"2206.08060","version":2},"attestation_state":"computed","paper":{"title":"On arc fibers of morphisms of schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christopher Chiu, Roi Docampo, Tommaso de Fernex","submitted_at":"2022-06-16T10:23:58Z","abstract_excerpt":"Given a morphism $f \\colon X \\to Y$ of schemes over a field, we prove several finiteness results about the fibers of the induced map on arc spaces $f_\\infty \\colon X_\\infty \\to Y_\\infty$. Assuming that $f$ is quasi-finite and $X$ is separated and quasi-compact, our theorem states that $f_\\infty$ has topologically finite fibers of bounded cardinality and its restriction to $X_\\infty \\setminus R_\\infty$, where $R$ is the ramification locus of $f$, has scheme-theoretically finite reduced fibers. We also provide an effective bound on the cardinality of the fibers of $f_\\infty$ when $f$ is a finite"},"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":"2206.08060","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-06-16T10:23:58Z","cross_cats_sorted":[],"title_canon_sha256":"6f0413ec25fd260696494fa26afdbf1f58e38c75c357a25986ef0963ee2d7ea5","abstract_canon_sha256":"ad5eec3f3e6a2f5b125044499721fe60c9eb3f6b21155da649306427d7673ffd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:02:24.103968Z","signature_b64":"Utq3yKkXo0sR1eac3Sv25ca9RpWi2OdZ+w14UGl6qspIiydiLizAycjrMkjqfbmVS/0irlLLZBsZTm6qD/hHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"875bf518a476f4d7c7793a4c094893a1fbf3a400f2cfc8718991a1330f54129d","last_reissued_at":"2026-05-26T01:02:24.103174Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:02:24.103174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On arc fibers of morphisms of schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christopher Chiu, Roi Docampo, Tommaso de Fernex","submitted_at":"2022-06-16T10:23:58Z","abstract_excerpt":"Given a morphism $f \\colon X \\to Y$ of schemes over a field, we prove several finiteness results about the fibers of the induced map on arc spaces $f_\\infty \\colon X_\\infty \\to Y_\\infty$. Assuming that $f$ is quasi-finite and $X$ is separated and quasi-compact, our theorem states that $f_\\infty$ has topologically finite fibers of bounded cardinality and its restriction to $X_\\infty \\setminus R_\\infty$, where $R$ is the ramification locus of $f$, has scheme-theoretically finite reduced fibers. We also provide an effective bound on the cardinality of the fibers of $f_\\infty$ when $f$ is a finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08060","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/2206.08060/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":"2206.08060","created_at":"2026-05-26T01:02:24.103300+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.08060v2","created_at":"2026-05-26T01:02:24.103300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08060","created_at":"2026-05-26T01:02:24.103300+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5N7KGFEO32N","created_at":"2026-05-26T01:02:24.103300+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5N7KGFEO32NPR3Z","created_at":"2026-05-26T01:02:24.103300+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5N7KGFE","created_at":"2026-05-26T01:02:24.103300+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/Q5N7KGFEO32NPR3ZHJGASSETUH","json":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH.json","graph_json":"https://pith.science/api/pith-number/Q5N7KGFEO32NPR3ZHJGASSETUH/graph.json","events_json":"https://pith.science/api/pith-number/Q5N7KGFEO32NPR3ZHJGASSETUH/events.json","paper":"https://pith.science/paper/Q5N7KGFE"},"agent_actions":{"view_html":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH","download_json":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH.json","view_paper":"https://pith.science/paper/Q5N7KGFE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.08060&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5N7KGFEO32NPR3ZHJGASSETUH/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5N7KGFEO32NPR3ZHJGASSETUH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH/action/storage_attestation","attest_author":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH/action/author_attestation","sign_citation":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH/action/citation_signature","submit_replication":"https://pith.science/pith/Q5N7KGFEO32NPR3ZHJGASSETUH/action/replication_record"}},"created_at":"2026-05-26T01:02:24.103300+00:00","updated_at":"2026-05-26T01:02:24.103300+00:00"}