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If $Y\\subset F_s(X)$ is a regular center and $X\\leftarrow X_1$ is the blow up at $Y$, then the highest multiplicity of $X_1$ is less than or equal to $s$. A sequence of blow ups at regular centers $Y_i \\subset F_s(X_i)$, say $X \\leftarrow X_1 \\leftarrow \\dotsb \\leftarrow X_n$, is said to be a {\\em simplification} of the multiplicity if the maximum multiplicity of $X_n$ is strictly lower than that of $"},"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":"1710.01805","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-04T21:00:39Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"637177aadd2cbb75fa18113d98dc4e166c7cbd6944be129a841a031a6369b5cc","abstract_canon_sha256":"f9b04dd43c136035f7aa0924a0253fa8c8886cdcc5ebc90bede26829da96b7f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.306874Z","signature_b64":"4xNSoSsCdwPWeX+fkOY+dRqMTvKagjXJ5HJAs4uCUc2Os5Tab+njRBzKiXxM0ILQT5+PLmE4bpNujjUHfYe0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"546f5cabc80160684ccff58be8d6c00716b6dedbc6c2bc73150d005e84aabe35","last_reissued_at":"2026-05-18T00:01:15.306444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.306444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite morphisms and simultaneous reduction of the multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Ana Bravo, Carlos Abad, Orlando E. 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A sequence of blow ups at regular centers $Y_i \\subset F_s(X_i)$, say $X \\leftarrow X_1 \\leftarrow \\dotsb \\leftarrow X_n$, is said to be a {\\em simplification} of the multiplicity if the maximum multiplicity of $X_n$ is strictly lower than that of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01805","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":"1710.01805","created_at":"2026-05-18T00:01:15.306509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.01805v2","created_at":"2026-05-18T00:01:15.306509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01805","created_at":"2026-05-18T00:01:15.306509+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRXVZK6IAFQG","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRXVZK6IAFQGQTGP","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRXVZK6I","created_at":"2026-05-18T12:31:28.150371+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/KRXVZK6IAFQGQTGP6WF6RVWAA4","json":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4.json","graph_json":"https://pith.science/api/pith-number/KRXVZK6IAFQGQTGP6WF6RVWAA4/graph.json","events_json":"https://pith.science/api/pith-number/KRXVZK6IAFQGQTGP6WF6RVWAA4/events.json","paper":"https://pith.science/paper/KRXVZK6I"},"agent_actions":{"view_html":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4","download_json":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4.json","view_paper":"https://pith.science/paper/KRXVZK6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.01805&json=true","fetch_graph":"https://pith.science/api/pith-number/KRXVZK6IAFQGQTGP6WF6RVWAA4/graph.json","fetch_events":"https://pith.science/api/pith-number/KRXVZK6IAFQGQTGP6WF6RVWAA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4/action/storage_attestation","attest_author":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4/action/author_attestation","sign_citation":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4/action/citation_signature","submit_replication":"https://pith.science/pith/KRXVZK6IAFQGQTGP6WF6RVWAA4/action/replication_record"}},"created_at":"2026-05-18T00:01:15.306509+00:00","updated_at":"2026-05-18T00:01:15.306509+00:00"}