{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4SB3PXM7DHRQU5WIMSQANAJBBZ","short_pith_number":"pith:4SB3PXM7","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"},"canonical_sha256":"e483b7dd9f19e30a76c864a00681210e596dd9ece3a1fbd527ce77253295a549","source":{"kind":"arxiv","id":"2511.20282","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.20282","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"2511.20282v2","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.20282","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"4SB3PXM7DHRQ","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"pith_short_16","alias_value":"4SB3PXM7DHRQU5WI","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"pith_short_8","alias_value":"4SB3PXM7","created_at":"2026-05-28T01:04:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4SB3PXM7DHRQU5WIMSQANAJBBZ","target":"record","payload":{"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"},"canonical_sha256":"e483b7dd9f19e30a76c864a00681210e596dd9ece3a1fbd527ce77253295a549","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"},"source_kind":"arxiv","source_id":"2511.20282","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T01:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIU9lCvr4Zf34sMP9xZunEgDS/l2c0snz/+6A+5YMf5XG18w80KKUBNzjD1a3v6WUxops6ihK9o6HfB5QdZPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:23:17.296890Z"},"content_sha256":"e9b9fdceee851c2b5b43a7b59d4d9fe35e6f24a53eb034483db8847e375222af","schema_version":"1.0","event_id":"sha256:e9b9fdceee851c2b5b43a7b59d4d9fe35e6f24a53eb034483db8847e375222af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4SB3PXM7DHRQU5WIMSQANAJBBZ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T01:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ru4aikRtduuOCgqktUA1T5nYakURLPpkkGEjEGAcn5NcPn6ZOCwJ1K4d6L+97NjadwAWxRo3a0RDQDKVHtNHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:23:17.297740Z"},"content_sha256":"0e0f2be70ad75e26d4ac6203a52b13d05c98c13e1ac3ce30827d585d062f35e9","schema_version":"1.0","event_id":"sha256:0e0f2be70ad75e26d4ac6203a52b13d05c98c13e1ac3ce30827d585d062f35e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/bundle.json","state_url":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T21:23:17Z","links":{"resolver":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ","bundle":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/bundle.json","state":"https://pith.science/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SB3PXM7DHRQU5WIMSQANAJBBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4SB3PXM7DHRQU5WIMSQANAJBBZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b008085d9176db3519977120d9f91674859d7401ec864bdd5adabb8447ec57ac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-11-25T13:10:37Z","title_canon_sha256":"9149f2c6aa03187c1afb50adc4665335994afe5b58a1fa1b5e4e0649079d079f"},"schema_version":"1.0","source":{"id":"2511.20282","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.20282","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"2511.20282v2","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.20282","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"4SB3PXM7DHRQ","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"pith_short_16","alias_value":"4SB3PXM7DHRQU5WI","created_at":"2026-05-28T01:04:33Z"},{"alias_kind":"pith_short_8","alias_value":"4SB3PXM7","created_at":"2026-05-28T01:04:33Z"}],"graph_snapshots":[{"event_id":"sha256:0e0f2be70ad75e26d4ac6203a52b13d05c98c13e1ac3ce30827d585d062f35e9","target":"graph","created_at":"2026-05-28T01:04:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2511.20282/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Mathieu Da Silva","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-11-25T13:10:37Z","title":"Solubility of a family of conics with polynomial coefficients in many variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.20282","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e9b9fdceee851c2b5b43a7b59d4d9fe35e6f24a53eb034483db8847e375222af","target":"record","created_at":"2026-05-28T01:04:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b008085d9176db3519977120d9f91674859d7401ec864bdd5adabb8447ec57ac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-11-25T13:10:37Z","title_canon_sha256":"9149f2c6aa03187c1afb50adc4665335994afe5b58a1fa1b5e4e0649079d079f"},"schema_version":"1.0","source":{"id":"2511.20282","kind":"arxiv","version":2}},"canonical_sha256":"e483b7dd9f19e30a76c864a00681210e596dd9ece3a1fbd527ce77253295a549","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e483b7dd9f19e30a76c864a00681210e596dd9ece3a1fbd527ce77253295a549","first_computed_at":"2026-05-28T01:04:33.502984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:33.502984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bRenN4KhdyfyDOelcdcE5uKvy4gxI/6qBcpOO79BBfYzhmnbQoo0uQqGrsjYJP9CY4vEqVMpLZafdGpU49YdCA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:33.503514Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.20282","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9b9fdceee851c2b5b43a7b59d4d9fe35e6f24a53eb034483db8847e375222af","sha256:0e0f2be70ad75e26d4ac6203a52b13d05c98c13e1ac3ce30827d585d062f35e9"],"state_sha256":"7c29360eae7ca88069bbfa647dcf8e5854a8be4a989d43a449c3aa808fa608ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q7IBbeOU7+hdA5wcqCr2smPIdtyrcWEEqsuRra74B7ihmXUTrRnQ5IJLG2ZAxupflHGVxZGH17/i6umlkNGaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:23:17.301836Z","bundle_sha256":"ff4e4633d50482f066bbfb057381bca741bfef63623daafd670505008673e02e"}}