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We provide an asymptotic formula for the number of $\\mathbf{y}$ of bounded height such that the corresponding conic $(\\mathcal{C}_{\\mathbf{F}, \\mathbf{y}})$ has a ratio"},"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":"2511.20282","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-11-25T13:10:37Z","cross_cats_sorted":[],"title_canon_sha256":"9149f2c6aa03187c1afb50adc4665335994afe5b58a1fa1b5e4e0649079d079f","abstract_canon_sha256":"b008085d9176db3519977120d9f91674859d7401ec864bdd5adabb8447ec57ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:33.503514Z","signature_b64":"bRenN4KhdyfyDOelcdcE5uKvy4gxI/6qBcpOO79BBfYzhmnbQoo0uQqGrsjYJP9CY4vEqVMpLZafdGpU49YdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e483b7dd9f19e30a76c864a00681210e596dd9ece3a1fbd527ce77253295a549","last_reissued_at":"2026-05-28T01:04:33.502984Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:33.502984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solubility of a family of conics with polynomial coefficients in many variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mathieu Da Silva","submitted_at":"2025-11-25T13:10:37Z","abstract_excerpt":"We study the proportion of conics given by $(\\mathcal{C}_{\\mathbf{F}, \\mathbf{y}}) : F_0(\\mathbf{y})x_0^2 + F_1(\\mathbf{y})x_1^2 = F_2( \\mathbf{y})x_2^2 $ which have a rational point $\\mathbf{x} = (x_0 :x_1:x_2) \\in \\mathbb{P}^2(\\mathbb{Q})$, where $\\mathbf{y} = (y_0 : \\dots : y_n)\\in \\mathbb{P}^n(\\mathbb{Q})$ and $F_0,F_1,F_2 \\in \\mathbb{Z}[X_0,\\ldots, X_n]$ are homogeneous polynomials in many variables of the same degree $d$. We provide an asymptotic formula for the number of $\\mathbf{y}$ of bounded height such that the corresponding conic $(\\mathcal{C}_{\\mathbf{F}, \\mathbf{y}})$ has a ratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.20282","kind":"arxiv","version":2},"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/2511.20282/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":"2511.20282","created_at":"2026-05-28T01:04:33.503056+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.20282v2","created_at":"2026-05-28T01:04:33.503056+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.20282","created_at":"2026-05-28T01:04:33.503056+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SB3PXM7DHRQ","created_at":"2026-05-28T01:04:33.503056+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SB3PXM7DHRQU5WI","created_at":"2026-05-28T01:04:33.503056+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SB3PXM7","created_at":"2026-05-28T01:04:33.503056+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/4SB3PXM7DHRQU5WIMSQANAJBBZ","json":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ.json","graph_json":"https://pith.science/api/pith-number/4SB3PXM7DHRQU5WIMSQANAJBBZ/graph.json","events_json":"https://pith.science/api/pith-number/4SB3PXM7DHRQU5WIMSQANAJBBZ/events.json","paper":"https://pith.science/paper/4SB3PXM7"},"agent_actions":{"view_html":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ","download_json":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ.json","view_paper":"https://pith.science/paper/4SB3PXM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.20282&json=true","fetch_graph":"https://pith.science/api/pith-number/4SB3PXM7DHRQU5WIMSQANAJBBZ/graph.json","fetch_events":"https://pith.science/api/pith-number/4SB3PXM7DHRQU5WIMSQANAJBBZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/action/storage_attestation","attest_author":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/action/author_attestation","sign_citation":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/action/citation_signature","submit_replication":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/action/replication_record"}},"created_at":"2026-05-28T01:04:33.503056+00:00","updated_at":"2026-05-28T01:04:33.503056+00:00"}