{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ZKZFPNSXUCBT3EB5VZBJ3O5HF3","short_pith_number":"pith:ZKZFPNSX","schema_version":"1.0","canonical_sha256":"cab257b657a0833d903dae429dbba72ee5df0bf0c31efe7f1bb78894ebc3085b","source":{"kind":"arxiv","id":"2505.04562","version":1},"attestation_state":"computed","paper":{"title":"Manin's Conjecture for Equivariant compactifications of forms of $\\mathbb{G}_a^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Abdulmuhsin Alfaraj","submitted_at":"2025-05-07T16:52:53Z","abstract_excerpt":"We prove the Batyrev-Manin conjecture for smooth equivariant compactifications of forms of $\\mathbb{G}_a^n$ over a global function field $F$, assuming some conditions on the boundary divisor. To verify that the leading constant agrees with Peyre's predicition we also show that a commutative unipotent group admitting a smooth equivariant compactification satisfies the Hasse principle for algebraic groups and weak approximation. We study in detail the case of $\\mathbb{P}^{p-1}$, where $p$ is the characteristic of $F$, viewed as a compactification of appropriate $F$-wound groups to illustrate new"},"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":"2505.04562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-07T16:52:53Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e5c9b1ba32a7c6db18de8c92970f09010b2f5167ef633b161d2121ee681b9951","abstract_canon_sha256":"6a8a0fdf2aedc9b613c28c2cbee060a600d20186fd57b33df1d31aa53922e4d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:53.784866Z","signature_b64":"Jzpch6x2F8LFtDbBAiGAZH5BCGcAbdYGLHIhOOD/J7S7mo5rv7y1iQ/xqNyd+x5gC4PnMn1jFVPCv5oph1MNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cab257b657a0833d903dae429dbba72ee5df0bf0c31efe7f1bb78894ebc3085b","last_reissued_at":"2026-07-05T10:59:53.784429Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:53.784429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Manin's Conjecture for Equivariant compactifications of forms of $\\mathbb{G}_a^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Abdulmuhsin Alfaraj","submitted_at":"2025-05-07T16:52:53Z","abstract_excerpt":"We prove the Batyrev-Manin conjecture for smooth equivariant compactifications of forms of $\\mathbb{G}_a^n$ over a global function field $F$, assuming some conditions on the boundary divisor. To verify that the leading constant agrees with Peyre's predicition we also show that a commutative unipotent group admitting a smooth equivariant compactification satisfies the Hasse principle for algebraic groups and weak approximation. We study in detail the case of $\\mathbb{P}^{p-1}$, where $p$ is the characteristic of $F$, viewed as a compactification of appropriate $F$-wound groups to illustrate new"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04562","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/2505.04562/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":"2505.04562","created_at":"2026-07-05T10:59:53.784485+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.04562v1","created_at":"2026-07-05T10:59:53.784485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04562","created_at":"2026-07-05T10:59:53.784485+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKZFPNSXUCBT","created_at":"2026-07-05T10:59:53.784485+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKZFPNSXUCBT3EB5","created_at":"2026-07-05T10:59:53.784485+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKZFPNSX","created_at":"2026-07-05T10:59:53.784485+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/ZKZFPNSXUCBT3EB5VZBJ3O5HF3","json":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3.json","graph_json":"https://pith.science/api/pith-number/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/graph.json","events_json":"https://pith.science/api/pith-number/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/events.json","paper":"https://pith.science/paper/ZKZFPNSX"},"agent_actions":{"view_html":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3","download_json":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3.json","view_paper":"https://pith.science/paper/ZKZFPNSX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.04562&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/action/storage_attestation","attest_author":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/action/author_attestation","sign_citation":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/action/citation_signature","submit_replication":"https://pith.science/pith/ZKZFPNSXUCBT3EB5VZBJ3O5HF3/action/replication_record"}},"created_at":"2026-07-05T10:59:53.784485+00:00","updated_at":"2026-07-05T10:59:53.784485+00:00"}