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Examples of $t$-super potent domains include domains each of whose maximal $t$-ideals is $t$-invertible (e.g., Krull domains). We show that if the domain $R$ is $\\star$-super potent for some finite-type star operation $\\star$, then $R$ is $t$-super potent, we study $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.06725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-19T00:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"a4d90be6bf3f1a31c58aa666063bf5e43add5ffeed97868919cb20aec377b209","abstract_canon_sha256":"1ea4cc0bf7a5c3dc57d44d172a7b1dd7c9cff0039ec375a0271421ebf8c058fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:40.597952Z","signature_b64":"7ZTDXD5gQrsQ+dlPvk6IFjc06cZmlm7R0ywN6IusBB1GOtBP7iMvJOY8XdP/hky0tGmHSq+d/zkA4fJszmPLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1795db89d2df132376fcb1dc2c82ea1c5dba2f7b691629ccb2eca32c7d1c167a","last_reissued_at":"2026-05-18T00:27:40.597174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:40.597174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\star $-super potent domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Evan Houston, Muhammad Zafrullah","submitted_at":"2017-12-19T00:28:14Z","abstract_excerpt":"For a finite-type star operation $\\star$ on a domain $R$, we say that $R$ is $\\star$-super potent if each maximal $\\star$-ideal of $R$ contains a finitely generated ideal $I$ such that (1) $I$ is contained in no other maximal $\\star$-ideal of $R$ and (2) $J$ is $\\star$-invertible for every finitely generated ideal $J \\supseteq I$. Examples of $t$-super potent domains include domains each of whose maximal $t$-ideals is $t$-invertible (e.g., Krull domains). We show that if the domain $R$ is $\\star$-super potent for some finite-type star operation $\\star$, then $R$ is $t$-super potent, we study $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06725","kind":"arxiv","version":1},"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":"1712.06725","created_at":"2026-05-18T00:27:40.597297+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.06725v1","created_at":"2026-05-18T00:27:40.597297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06725","created_at":"2026-05-18T00:27:40.597297+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6K5XCOS34JS","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6K5XCOS34JSG5X4","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6K5XCOS","created_at":"2026-05-18T12:31:08.081275+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/C6K5XCOS34JSG5X4WHOCZAXKDR","json":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR.json","graph_json":"https://pith.science/api/pith-number/C6K5XCOS34JSG5X4WHOCZAXKDR/graph.json","events_json":"https://pith.science/api/pith-number/C6K5XCOS34JSG5X4WHOCZAXKDR/events.json","paper":"https://pith.science/paper/C6K5XCOS"},"agent_actions":{"view_html":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR","download_json":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR.json","view_paper":"https://pith.science/paper/C6K5XCOS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.06725&json=true","fetch_graph":"https://pith.science/api/pith-number/C6K5XCOS34JSG5X4WHOCZAXKDR/graph.json","fetch_events":"https://pith.science/api/pith-number/C6K5XCOS34JSG5X4WHOCZAXKDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR/action/storage_attestation","attest_author":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR/action/author_attestation","sign_citation":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR/action/citation_signature","submit_replication":"https://pith.science/pith/C6K5XCOS34JSG5X4WHOCZAXKDR/action/replication_record"}},"created_at":"2026-05-18T00:27:40.597297+00:00","updated_at":"2026-05-18T00:27:40.597297+00:00"}