{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ORG6FZJO7HXTW6AWAEH65RXZKA","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":"de5008a3ce84f8a8f26fa7fc28d674d8d1bcfabff4a7dcd90dc78c7be3d40b26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-12T23:44:11Z","title_canon_sha256":"3af015228f88139e29a7bfecd43f682efffde2728237014c7aacd34d0e63d664"},"schema_version":"1.0","source":{"id":"1405.3000","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3000","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3000v2","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3000","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"ORG6FZJO7HXT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"ORG6FZJO7HXTW6AW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"ORG6FZJO","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:0fc8a96d7d3b7a14dcf1d16440f775b317ec8abd7ffc092856bf268b14e55345","target":"graph","created_at":"2026-05-18T01:24:38Z","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"},"paper":{"abstract_excerpt":"The content of a polynomial over a ring $R$ is a well understood notion. Ohm and Rush generalized this concept of a content map to an arbitrary ring extension of $R$, although it can behave quite badly. We examine five properties an algebra may have with respect to this function -- content algebra, weak content algebra, semicontent algebra (our own definition), Gaussian algebra, and Ohm-Rush algebra. We show that the Gaussian, weak content, and semicontent algebra properties are all transitive. However, transitivity is unknown for the content algebra property. We then compare the Ohm-Rush noti","authors_text":"Jay Shapiro, Neil Epstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-12T23:44:11Z","title":"The Ohm-Rush content function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3000","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":"sha256:9d97e2e6aa31a967e3d85e64302253bf6fff2415a216fc648e61c8a66d887e0f","target":"record","created_at":"2026-05-18T01:24:38Z","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":"de5008a3ce84f8a8f26fa7fc28d674d8d1bcfabff4a7dcd90dc78c7be3d40b26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-12T23:44:11Z","title_canon_sha256":"3af015228f88139e29a7bfecd43f682efffde2728237014c7aacd34d0e63d664"},"schema_version":"1.0","source":{"id":"1405.3000","kind":"arxiv","version":2}},"canonical_sha256":"744de2e52ef9ef3b7816010feec6f9502b680c8f8fe1572222a2f139dbbce9be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"744de2e52ef9ef3b7816010feec6f9502b680c8f8fe1572222a2f139dbbce9be","first_computed_at":"2026-05-18T01:24:38.683880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:38.683880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mcyqnFC8asC8X7rdLoFeSJGdLQ21yUHs8qrOBJIDkKl5j4aRR0bjdZ/zSN4YLzfwFSvLzGU/SgF6LB96wY0tDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:38.684375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3000","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d97e2e6aa31a967e3d85e64302253bf6fff2415a216fc648e61c8a66d887e0f","sha256:0fc8a96d7d3b7a14dcf1d16440f775b317ec8abd7ffc092856bf268b14e55345"],"state_sha256":"c6648afd99f8ea8e432746f2f33474bb7fceaad6d062c8e893ead3b7b15e6b38"}