{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QCGAHUHAM3CVPFMUYAF3N6FVKQ","short_pith_number":"pith:QCGAHUHA","schema_version":"1.0","canonical_sha256":"808c03d0e066c5579594c00bb6f8b5543d2a9d977ee423460d00150415a7c1d9","source":{"kind":"arxiv","id":"2507.09679","version":1},"attestation_state":"computed","paper":{"title":"Borel subgroups of the automorphism groups of affine toric surfaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Arzhantsev, Mikhail Zaidenberg","submitted_at":"2025-07-13T15:30:54Z","abstract_excerpt":"In [I. Arzhantsev and M. Zaidenberg, Acyclic curves and group actions on affine toric surfaces. Affine Algebraic Geometry, 1--41. World Scientific Publishing Co. 2013] we described the automorphism groups of the cyclic quotients of the affine plane. In this article, we study the Borel subgroups and, more generally, the maximal solvable subgroups of these ind-groups. We show that the cyclic quotients of the affine plane are divided into two species. In one of them, the Borel subgroups form a single conjugacy class, while in the other, there are two conjugacy classes of Borel subgroups. The proo"},"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":"2507.09679","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-13T15:30:54Z","cross_cats_sorted":[],"title_canon_sha256":"5287413eb01d4b0fac962ba9bbabd7619761ffbaa3569d0c76c3e1a0e07ef67e","abstract_canon_sha256":"3e08a8426e9d0d56e1dfe73882602251801ccfe2c3c8417924d1aa84172dd953"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:37.982962Z","signature_b64":"VHpWNE8eUzQfyGLiKy8lh96CmzHKEELKPFCaLyORrX2KE+uKuu117X7Kd04xPI02JJaty1brF96OHed5YI8xDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"808c03d0e066c5579594c00bb6f8b5543d2a9d977ee423460d00150415a7c1d9","last_reissued_at":"2026-07-05T11:36:37.982445Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:37.982445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Borel subgroups of the automorphism groups of affine toric surfaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Arzhantsev, Mikhail Zaidenberg","submitted_at":"2025-07-13T15:30:54Z","abstract_excerpt":"In [I. Arzhantsev and M. Zaidenberg, Acyclic curves and group actions on affine toric surfaces. Affine Algebraic Geometry, 1--41. World Scientific Publishing Co. 2013] we described the automorphism groups of the cyclic quotients of the affine plane. In this article, we study the Borel subgroups and, more generally, the maximal solvable subgroups of these ind-groups. We show that the cyclic quotients of the affine plane are divided into two species. In one of them, the Borel subgroups form a single conjugacy class, while in the other, there are two conjugacy classes of Borel subgroups. The proo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09679","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/2507.09679/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":"2507.09679","created_at":"2026-07-05T11:36:37.982509+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.09679v1","created_at":"2026-07-05T11:36:37.982509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09679","created_at":"2026-07-05T11:36:37.982509+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCGAHUHAM3CV","created_at":"2026-07-05T11:36:37.982509+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCGAHUHAM3CVPFMU","created_at":"2026-07-05T11:36:37.982509+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCGAHUHA","created_at":"2026-07-05T11:36:37.982509+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2510.17223","citing_title":"Borel subalgebras of Lie algebras of vector fields","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2604.02864","citing_title":"Locally finite solvable Lie algebras of derivations","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ","json":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ.json","graph_json":"https://pith.science/api/pith-number/QCGAHUHAM3CVPFMUYAF3N6FVKQ/graph.json","events_json":"https://pith.science/api/pith-number/QCGAHUHAM3CVPFMUYAF3N6FVKQ/events.json","paper":"https://pith.science/paper/QCGAHUHA"},"agent_actions":{"view_html":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ","download_json":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ.json","view_paper":"https://pith.science/paper/QCGAHUHA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.09679&json=true","fetch_graph":"https://pith.science/api/pith-number/QCGAHUHAM3CVPFMUYAF3N6FVKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/QCGAHUHAM3CVPFMUYAF3N6FVKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ/action/storage_attestation","attest_author":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ/action/author_attestation","sign_citation":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ/action/citation_signature","submit_replication":"https://pith.science/pith/QCGAHUHAM3CVPFMUYAF3N6FVKQ/action/replication_record"}},"created_at":"2026-07-05T11:36:37.982509+00:00","updated_at":"2026-07-05T11:36:37.982509+00:00"}