{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KUOQZO2JAXMOHRPZXPW6VAMQPB","short_pith_number":"pith:KUOQZO2J","schema_version":"1.0","canonical_sha256":"551d0cbb4905d8e3c5f9bbedea8190785932c457e410090359781672eb509c46","source":{"kind":"arxiv","id":"1510.02993","version":2},"attestation_state":"computed","paper":{"title":"Rational Singularities and Uniform Symbolic Topologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Robert M. Walker","submitted_at":"2015-10-10T23:58:35Z","abstract_excerpt":"Take $(R, \\mathfrak{m})$ any normal Noetherian domain, either local or $\\mathbb{N}$-graded over a field. We study the question of when $R$ satisfies the uniform symbolic topology property (USTP) of Huneke, Katz, and Validashti: namely, that there exists an integer $D>0$ such that for all prime ideals $P \\subseteq R$, the symbolic power $P^{(Da)} \\subseteq P^a$ for all $a >0$. Reinterpreting results of Lipman, we deduce that when $R$ is a two-dimensional rational singularity, then it satisfies the USTP. Emphasizing the non-regular setting, we produce explicit, effective multipliers $D$, working"},"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":"1510.02993","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-10T23:58:35Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d1f74e0d650c172cf14670c02e690c1e72dee756c50d922d07e68460acd62f16","abstract_canon_sha256":"57d777ae4cfb5884e9ede6ec2d71858d7e9c03d02b4d0a4c33310a8f6cd188cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:53.495920Z","signature_b64":"7is7BfzJAI0EebTeAvdJi1au6xU0kCVyNAUkY3ALK/KEefeZ2W5PCI2I7ek9yv7omwvKuekd8ebnefw5wiJPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"551d0cbb4905d8e3c5f9bbedea8190785932c457e410090359781672eb509c46","last_reissued_at":"2026-05-18T00:33:53.495401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:53.495401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational Singularities and Uniform Symbolic Topologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Robert M. Walker","submitted_at":"2015-10-10T23:58:35Z","abstract_excerpt":"Take $(R, \\mathfrak{m})$ any normal Noetherian domain, either local or $\\mathbb{N}$-graded over a field. We study the question of when $R$ satisfies the uniform symbolic topology property (USTP) of Huneke, Katz, and Validashti: namely, that there exists an integer $D>0$ such that for all prime ideals $P \\subseteq R$, the symbolic power $P^{(Da)} \\subseteq P^a$ for all $a >0$. Reinterpreting results of Lipman, we deduce that when $R$ is a two-dimensional rational singularity, then it satisfies the USTP. Emphasizing the non-regular setting, we produce explicit, effective multipliers $D$, working"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02993","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":"1510.02993","created_at":"2026-05-18T00:33:53.495496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02993v2","created_at":"2026-05-18T00:33:53.495496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02993","created_at":"2026-05-18T00:33:53.495496+00:00"},{"alias_kind":"pith_short_12","alias_value":"KUOQZO2JAXMO","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KUOQZO2JAXMOHRPZ","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KUOQZO2J","created_at":"2026-05-18T12:29:29.992203+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/KUOQZO2JAXMOHRPZXPW6VAMQPB","json":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB.json","graph_json":"https://pith.science/api/pith-number/KUOQZO2JAXMOHRPZXPW6VAMQPB/graph.json","events_json":"https://pith.science/api/pith-number/KUOQZO2JAXMOHRPZXPW6VAMQPB/events.json","paper":"https://pith.science/paper/KUOQZO2J"},"agent_actions":{"view_html":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB","download_json":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB.json","view_paper":"https://pith.science/paper/KUOQZO2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02993&json=true","fetch_graph":"https://pith.science/api/pith-number/KUOQZO2JAXMOHRPZXPW6VAMQPB/graph.json","fetch_events":"https://pith.science/api/pith-number/KUOQZO2JAXMOHRPZXPW6VAMQPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB/action/storage_attestation","attest_author":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB/action/author_attestation","sign_citation":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB/action/citation_signature","submit_replication":"https://pith.science/pith/KUOQZO2JAXMOHRPZXPW6VAMQPB/action/replication_record"}},"created_at":"2026-05-18T00:33:53.495496+00:00","updated_at":"2026-05-18T00:33:53.495496+00:00"}