{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DFEL7SBWHAQJZNFRLSYUE5S7BC","short_pith_number":"pith:DFEL7SBW","schema_version":"1.0","canonical_sha256":"1948bfc83638209cb4b15cb142765f08a39ac551342283c8570365251626c90f","source":{"kind":"arxiv","id":"2501.19049","version":1},"attestation_state":"computed","paper":{"title":"The finite basis problem for additively idempotent semirings that relate to S_7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Marcel Jackson, Miaomiao Ren, Xianzhong Zhao, Zidong Gao","submitted_at":"2025-01-31T11:21:21Z","abstract_excerpt":"The $3$-element additively idempotent semiring $S_7$ is a nonnitely based algebra of the smallest possible order. In this paper we study the nite basis problem for some additively idempotent semirings that relate to $S_7$. We present a su cient condition under which an additively idempotent semiring variety is nonnitely based and as applications, show that some additively idempotent semiring varieties that contain $S_7$ are also nonnitely based. We then consider the subdirectly irreducible members of the variety $\\mathsf{V}(S_7)$ generated by $S_7$. We show that $\\mathsf{V}(S_7)$ contains exac"},"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":"2501.19049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-01-31T11:21:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"063bfb760f0ed9c6c6876b3222122414b9ba053a66bd0deb1dc3ffcf69296a56","abstract_canon_sha256":"934113a957d1ae031c0edcec77cba2759f0e4c8d62491abfada9376b7459a5f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:55.460079Z","signature_b64":"UKdJlP5wJ+18/scIGHx/uB5+oVxAAoQyeuCEEmBrjaFoATa1soSINjmB+ujIL2u40J7hFNsR2mgdkyC79Rq3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1948bfc83638209cb4b15cb142765f08a39ac551342283c8570365251626c90f","last_reissued_at":"2026-07-05T10:07:55.459662Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:55.459662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The finite basis problem for additively idempotent semirings that relate to S_7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Marcel Jackson, Miaomiao Ren, Xianzhong Zhao, Zidong Gao","submitted_at":"2025-01-31T11:21:21Z","abstract_excerpt":"The $3$-element additively idempotent semiring $S_7$ is a nonnitely based algebra of the smallest possible order. In this paper we study the nite basis problem for some additively idempotent semirings that relate to $S_7$. We present a su cient condition under which an additively idempotent semiring variety is nonnitely based and as applications, show that some additively idempotent semiring varieties that contain $S_7$ are also nonnitely based. We then consider the subdirectly irreducible members of the variety $\\mathsf{V}(S_7)$ generated by $S_7$. We show that $\\mathsf{V}(S_7)$ contains exac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19049","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.19049/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2501.19049","created_at":"2026-07-05T10:07:55.459716+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.19049v1","created_at":"2026-07-05T10:07:55.459716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.19049","created_at":"2026-07-05T10:07:55.459716+00:00"},{"alias_kind":"pith_short_12","alias_value":"DFEL7SBWHAQJ","created_at":"2026-07-05T10:07:55.459716+00:00"},{"alias_kind":"pith_short_16","alias_value":"DFEL7SBWHAQJZNFR","created_at":"2026-07-05T10:07:55.459716+00:00"},{"alias_kind":"pith_short_8","alias_value":"DFEL7SBW","created_at":"2026-07-05T10:07:55.459716+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.15493","citing_title":"A nonfinitely based additively idempotent semiring of order four","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18588","citing_title":"A new limit variety of additively idempotent semirings","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC","json":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC.json","graph_json":"https://pith.science/api/pith-number/DFEL7SBWHAQJZNFRLSYUE5S7BC/graph.json","events_json":"https://pith.science/api/pith-number/DFEL7SBWHAQJZNFRLSYUE5S7BC/events.json","paper":"https://pith.science/paper/DFEL7SBW"},"agent_actions":{"view_html":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC","download_json":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC.json","view_paper":"https://pith.science/paper/DFEL7SBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.19049&json=true","fetch_graph":"https://pith.science/api/pith-number/DFEL7SBWHAQJZNFRLSYUE5S7BC/graph.json","fetch_events":"https://pith.science/api/pith-number/DFEL7SBWHAQJZNFRLSYUE5S7BC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC/action/storage_attestation","attest_author":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC/action/author_attestation","sign_citation":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC/action/citation_signature","submit_replication":"https://pith.science/pith/DFEL7SBWHAQJZNFRLSYUE5S7BC/action/replication_record"}},"created_at":"2026-07-05T10:07:55.459716+00:00","updated_at":"2026-07-05T10:07:55.459716+00:00"}