{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:S77X7642XUT74DFTMIGVBA4TWK","short_pith_number":"pith:S77X7642","schema_version":"1.0","canonical_sha256":"97ff7ffb9abd27fe0cb3620d508393b28a247d927111daec46ebde320dbf3162","source":{"kind":"arxiv","id":"2601.16619","version":3},"attestation_state":"computed","paper":{"title":"Varieties of initial dialgebras and some of their Koszul dual operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For any variety of algebras, a universal algorithm constructs the subvariety of initial dialgebras from which the original algebras can be recovered.","cross_cats":[],"primary_cat":"math.RA","authors_text":"Abdenacer Makhlouf, Aigerim Dauletiyarova, Bauyrzhan Sartayev","submitted_at":"2026-01-23T10:18:05Z","abstract_excerpt":"In this paper, for a given variety $\\Var$, we present a universal algorithm for constructing a subvariety of $\\Var$-dialgebras from which one can recover an algebra belonging to $\\Var$. Such a subvariety is called the variety of initial $\\Var$-dialgebras. In addition, we construct a basis of the free initial Lie and associative dialgebras."},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2601.16619","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-01-23T10:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"8cb2cab3b85a510e3c9ff0750e72704511acdc529f7dad0236b00796e52551a6","abstract_canon_sha256":"ccfc6e079168a815f8318c05760d59169b5db50f6674c7ab90c8cbce0e7e87db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T14:03:24.530462Z","signature_b64":"KXUi94d+ray4R3OsoR+gdu9xpyHGMu7QRVHWPfSju07YS3XIA/+EBkdD9G78NSzs/auRDccQ1pEJRxi7U8bcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97ff7ffb9abd27fe0cb3620d508393b28a247d927111daec46ebde320dbf3162","last_reissued_at":"2026-05-20T14:03:24.529931Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T14:03:24.529931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Varieties of initial dialgebras and some of their Koszul dual operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For any variety of algebras, a universal algorithm constructs the subvariety of initial dialgebras from which the original algebras can be recovered.","cross_cats":[],"primary_cat":"math.RA","authors_text":"Abdenacer Makhlouf, Aigerim Dauletiyarova, Bauyrzhan Sartayev","submitted_at":"2026-01-23T10:18:05Z","abstract_excerpt":"In this paper, for a given variety $\\Var$, we present a universal algorithm for constructing a subvariety of $\\Var$-dialgebras from which one can recover an algebra belonging to $\\Var$. Such a subvariety is called the variety of initial $\\Var$-dialgebras. In addition, we construct a basis of the free initial Lie and associative dialgebras."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For a given variety Var, we present a universal algorithm for constructing a subvariety of Var-dialgebras from which one can recover an algebra belonging to Var. Such a subvariety is called the variety of initial Var-dialgebras.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a universal algorithm exists which, for arbitrary Var, produces a subvariety of dialgebras allowing recovery of an algebra in Var, without additional restrictions on the identities defining Var.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A universal algorithm constructs the variety of initial dialgebras for any given variety Var, with bases provided for the free initial Lie and associative dialgebras.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For any variety of algebras, a universal algorithm constructs the subvariety of initial dialgebras from which the original algebras can be recovered.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"732b9d2bacdd2714455ab9f1b735b7dc08cb499e426b71c171ce5a2e44e9e2ca"},"source":{"id":"2601.16619","kind":"arxiv","version":3},"verdict":{"id":"0491bcf5-e058-4f5a-9571-c57e4bb4b866","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T12:04:56.463832Z","strongest_claim":"For a given variety Var, we present a universal algorithm for constructing a subvariety of Var-dialgebras from which one can recover an algebra belonging to Var. Such a subvariety is called the variety of initial Var-dialgebras.","one_line_summary":"A universal algorithm constructs the variety of initial dialgebras for any given variety Var, with bases provided for the free initial Lie and associative dialgebras.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a universal algorithm exists which, for arbitrary Var, produces a subvariety of dialgebras allowing recovery of an algebra in Var, without additional restrictions on the identities defining Var.","pith_extraction_headline":"For any variety of algebras, a universal algorithm constructs the subvariety of initial dialgebras from which the original algebras can be recovered."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.16619/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":15,"sample":[{"doi":"","year":null,"title":"Albert version 4.0M6; https://web.osu.cz/∼Zusmanovich/soft/albert/","work_id":"8a319ee0-4945-4762-b004-91ff2c5565b8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"A. Dauletiyarova, B. K. Sartayev, Basis of the free noncommutative Novikov algebra, Journal of Algebra and Its Applications, 2025, 24(12), 2550292","work_id":"7536b992-4dad-47db-9522-5c914e919f4e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"V. Dotsenko, B. Zhakhayev, Distributive lattices of varieties of Novikov algebras, Manuscripta Mathematica, 2025, 176(2), 29","work_id":"b6474d55-ec92-4391-9727-72e8f0085322","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"V. Dotsenko, W. Heijltjes. Gr¨ obner bases for operads, http://irma.math.unistra.fr/dotsenko/operads.html, 2019","work_id":"e239cb05-1b30-483e-8bdd-38cccc903311","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"X. Gao, L. Guo, Z. Han, Y. Zhang, Rota-Baxter operators, differential operators, pre- and Novikov structures on groups and Lie algebras, Journal of Algebra, 684 (2025), 109–148","work_id":"2899a93a-b52a-4386-900f-1b487db5d9d8","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":15,"snapshot_sha256":"a5f9cfe3ca538bdaafcb9f8cb9b6fef306d5c064712e683a836ca993ba2253fc","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"05061ba60c67db768aa079ccc71a5da568e848dae992ad231d0a5ecda1685393"},"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":"2601.16619","created_at":"2026-05-20T14:03:24.529987+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.16619v3","created_at":"2026-05-20T14:03:24.529987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.16619","created_at":"2026-05-20T14:03:24.529987+00:00"},{"alias_kind":"pith_short_12","alias_value":"S77X7642XUT7","created_at":"2026-05-20T14:03:24.529987+00:00"},{"alias_kind":"pith_short_16","alias_value":"S77X7642XUT74DFT","created_at":"2026-05-20T14:03:24.529987+00:00"},{"alias_kind":"pith_short_8","alias_value":"S77X7642","created_at":"2026-05-20T14:03:24.529987+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":1,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK","json":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK.json","graph_json":"https://pith.science/api/pith-number/S77X7642XUT74DFTMIGVBA4TWK/graph.json","events_json":"https://pith.science/api/pith-number/S77X7642XUT74DFTMIGVBA4TWK/events.json","paper":"https://pith.science/paper/S77X7642"},"agent_actions":{"view_html":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK","download_json":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK.json","view_paper":"https://pith.science/paper/S77X7642","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.16619&json=true","fetch_graph":"https://pith.science/api/pith-number/S77X7642XUT74DFTMIGVBA4TWK/graph.json","fetch_events":"https://pith.science/api/pith-number/S77X7642XUT74DFTMIGVBA4TWK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK/action/storage_attestation","attest_author":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK/action/author_attestation","sign_citation":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK/action/citation_signature","submit_replication":"https://pith.science/pith/S77X7642XUT74DFTMIGVBA4TWK/action/replication_record"}},"created_at":"2026-05-20T14:03:24.529987+00:00","updated_at":"2026-05-20T14:03:24.529987+00:00"}