{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5AQNGWCMS7QTOJ7V2YHLQU6GNM","short_pith_number":"pith:5AQNGWCM","schema_version":"1.0","canonical_sha256":"e820d3584c97e13727f5d60eb853c66b2b6ef62f1bb75fe44e8e1308851874a4","source":{"kind":"arxiv","id":"1703.02114","version":3},"attestation_state":"computed","paper":{"title":"The Ohm-Rush content function II. Noetherian rings, valuation domains, and base change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jay Shapiro, Neil Epstein","submitted_at":"2017-03-06T21:26:01Z","abstract_excerpt":"The notion of an Ohm-Rush algebra, and its associated content map, has connections with prime characteristic algebra, polynomial extensions, and the Ananyan-Hochster proof of Stillman's conjecture. As further restrictions are placed (creating the increasingly more specialized notions of weak content, semicontent, content, and Gaussian algebras), the construction becomes more powerful. Here we settle the question in the affirmative over a Noetherian ring from our previous article of whether a faithfully flat weak content algebra is semicontent (and over an Artinian ring of whether such an algeb"},"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":"1703.02114","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-03-06T21:26:01Z","cross_cats_sorted":[],"title_canon_sha256":"54a82368721b289c6e8d861a21aa21fbf1a31572ed7c7e931f5c42fc390d6f56","abstract_canon_sha256":"42ec569efd87d6960bb38cb388a8b7e05895a2021a892e743a77688e757258dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:19.562286Z","signature_b64":"DgNPGm7U0beZ5yiZSdWXU/hO/etSxqXLWSsSGqgQQYyAvHxEVZFpp06K8GTu+TE51pVELIiefQGdMiIsC+yaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e820d3584c97e13727f5d60eb853c66b2b6ef62f1bb75fe44e8e1308851874a4","last_reissued_at":"2026-05-18T00:16:19.561870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:19.561870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Ohm-Rush content function II. Noetherian rings, valuation domains, and base change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jay Shapiro, Neil Epstein","submitted_at":"2017-03-06T21:26:01Z","abstract_excerpt":"The notion of an Ohm-Rush algebra, and its associated content map, has connections with prime characteristic algebra, polynomial extensions, and the Ananyan-Hochster proof of Stillman's conjecture. As further restrictions are placed (creating the increasingly more specialized notions of weak content, semicontent, content, and Gaussian algebras), the construction becomes more powerful. Here we settle the question in the affirmative over a Noetherian ring from our previous article of whether a faithfully flat weak content algebra is semicontent (and over an Artinian ring of whether such an algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02114","kind":"arxiv","version":3},"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":"1703.02114","created_at":"2026-05-18T00:16:19.561939+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02114v3","created_at":"2026-05-18T00:16:19.561939+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02114","created_at":"2026-05-18T00:16:19.561939+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AQNGWCMS7QT","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AQNGWCMS7QTOJ7V","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AQNGWCM","created_at":"2026-05-18T12:31:00.734936+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/5AQNGWCMS7QTOJ7V2YHLQU6GNM","json":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM.json","graph_json":"https://pith.science/api/pith-number/5AQNGWCMS7QTOJ7V2YHLQU6GNM/graph.json","events_json":"https://pith.science/api/pith-number/5AQNGWCMS7QTOJ7V2YHLQU6GNM/events.json","paper":"https://pith.science/paper/5AQNGWCM"},"agent_actions":{"view_html":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM","download_json":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM.json","view_paper":"https://pith.science/paper/5AQNGWCM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02114&json=true","fetch_graph":"https://pith.science/api/pith-number/5AQNGWCMS7QTOJ7V2YHLQU6GNM/graph.json","fetch_events":"https://pith.science/api/pith-number/5AQNGWCMS7QTOJ7V2YHLQU6GNM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM/action/storage_attestation","attest_author":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM/action/author_attestation","sign_citation":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM/action/citation_signature","submit_replication":"https://pith.science/pith/5AQNGWCMS7QTOJ7V2YHLQU6GNM/action/replication_record"}},"created_at":"2026-05-18T00:16:19.561939+00:00","updated_at":"2026-05-18T00:16:19.561939+00:00"}