{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:Q5N7KGFEO32NPR3ZHJGASSETUH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ad5eec3f3e6a2f5b125044499721fe60c9eb3f6b21155da649306427d7673ffd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-06-16T10:23:58Z","title_canon_sha256":"6f0413ec25fd260696494fa26afdbf1f58e38c75c357a25986ef0963ee2d7ea5"},"schema_version":"1.0","source":{"id":"2206.08060","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08060","created_at":"2026-05-26T01:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08060v2","created_at":"2026-05-26T01:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08060","created_at":"2026-05-26T01:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"Q5N7KGFEO32N","created_at":"2026-05-26T01:02:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q5N7KGFEO32NPR3Z","created_at":"2026-05-26T01:02:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q5N7KGFE","created_at":"2026-05-26T01:02:24Z"}],"graph_snapshots":[{"event_id":"sha256:27632a8318dd98ac9c29d173664ff6730ff19705f4ec0b1e1743744b007666c3","target":"graph","created_at":"2026-05-26T01:02:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.08060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Christopher Chiu, Roi Docampo, Tommaso de Fernex","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-06-16T10:23:58Z","title":"On arc fibers of morphisms of schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08060","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:273efca3ba654b000adc20f771d4682a0f1b70958c445594e219b7b34d89a188","target":"record","created_at":"2026-05-26T01:02:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ad5eec3f3e6a2f5b125044499721fe60c9eb3f6b21155da649306427d7673ffd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-06-16T10:23:58Z","title_canon_sha256":"6f0413ec25fd260696494fa26afdbf1f58e38c75c357a25986ef0963ee2d7ea5"},"schema_version":"1.0","source":{"id":"2206.08060","kind":"arxiv","version":2}},"canonical_sha256":"875bf518a476f4d7c7793a4c094893a1fbf3a400f2cfc8718991a1330f54129d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"875bf518a476f4d7c7793a4c094893a1fbf3a400f2cfc8718991a1330f54129d","first_computed_at":"2026-05-26T01:02:24.103174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:02:24.103174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Utq3yKkXo0sR1eac3Sv25ca9RpWi2OdZ+w14UGl6qspIiydiLizAycjrMkjqfbmVS/0irlLLZBsZTm6qD/hHDA==","signature_status":"signed_v1","signed_at":"2026-05-26T01:02:24.103968Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.08060","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:273efca3ba654b000adc20f771d4682a0f1b70958c445594e219b7b34d89a188","sha256:27632a8318dd98ac9c29d173664ff6730ff19705f4ec0b1e1743744b007666c3"],"state_sha256":"fabed98786f985a56a4d7a16940dcbbf53583c2f7e43adfbf660f7dbbe87315d"}