{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7RXTOQB25AGRDB27OJAFWCSZX6","short_pith_number":"pith:7RXTOQB2","canonical_record":{"source":{"id":"1805.02756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-07T21:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"d7585e18d4abe978148b2887de53395290cd2b1f0c98eae8b64770255eb7cbcd","abstract_canon_sha256":"7e26d8b0cfa39429e67bfb885db399e499332776d43f74a24af675e5069cda60"},"schema_version":"1.0"},"canonical_sha256":"fc6f37403ae80d11875f72405b0a59bf9de6da9f5c19428fe2412fda363b0878","source":{"kind":"arxiv","id":"1805.02756","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02756","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02756v2","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02756","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"7RXTOQB25AGR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7RXTOQB25AGRDB27","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7RXTOQB2","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7RXTOQB25AGRDB27OJAFWCSZX6","target":"record","payload":{"canonical_record":{"source":{"id":"1805.02756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-07T21:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"d7585e18d4abe978148b2887de53395290cd2b1f0c98eae8b64770255eb7cbcd","abstract_canon_sha256":"7e26d8b0cfa39429e67bfb885db399e499332776d43f74a24af675e5069cda60"},"schema_version":"1.0"},"canonical_sha256":"fc6f37403ae80d11875f72405b0a59bf9de6da9f5c19428fe2412fda363b0878","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:59.571581Z","signature_b64":"Gpd2a4FAoG8pCXPPr0Egm0P5NveuYfkMmf5R+vsW5fggAkSBASzMFTx1nRqp7R4N/ZSLhN5g/dhx0zLswKmyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc6f37403ae80d11875f72405b0a59bf9de6da9f5c19428fe2412fda363b0878","last_reissued_at":"2026-05-17T23:44:59.570932Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:59.570932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.02756","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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aimxokHSKHsfwZbyqdlDbDut2mZIPPz+lTL4wL7iAI33o6AHPVp5e91GE5/RrL+lTO27ui8nwGMQ4bCILBz0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:27:45.043504Z"},"content_sha256":"640fd407933224896da5203cb8fbf831e1c386d4ba6c7aab27e06ca41a0fe567","schema_version":"1.0","event_id":"sha256:640fd407933224896da5203cb8fbf831e1c386d4ba6c7aab27e06ca41a0fe567"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7RXTOQB25AGRDB27OJAFWCSZX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The power-saving Manin-Peyre's conjectures for a senary cubic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kevin Destagnol, Sandro Bettin","submitted_at":"2018-05-07T21:39:12Z","abstract_excerpt":"Using recent work of the first author~\\cite{Bet}, we prove a strong version of the Manin-Peyre's conjectures with a full asymptotic and a power-saving error term for the two varieties respectively in $\\mathbb{P}^2 \\times \\mathbb{P}^2$ with bihomogeneous coordinates $[x_1:x_2:x_3],[y_1:y_2,y_3]$ and in $\\mathbb{P}^1\\times \\mathbb{P}^1 \\times \\mathbb{P}^1$ with multihomogeneous coordinates $[x_1:y_1],[x_2:y_2],[x_3:y_3]$ defined by the same equation $x_1y_2y_3+x_2y_1y_3+x_3y_1y_2=0$. We thus improve on recent work of Blomer, Br\\\"udern and Salberger \\cite{BBS} and provide a different proof based "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02756","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":""},"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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JjS9qnqAMRHdwsouH04xUojyAEAaRvZGCDvk684fJqyFejkL0tpRT4pPe8yDvsSl0bKrM/WQqD7uRQdin22+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:27:45.043849Z"},"content_sha256":"8f5daf40ae7a7a1fdbe60df26528b6503d89782f041ba6d49e2eab1010aa9186","schema_version":"1.0","event_id":"sha256:8f5daf40ae7a7a1fdbe60df26528b6503d89782f041ba6d49e2eab1010aa9186"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RXTOQB25AGRDB27OJAFWCSZX6/bundle.json","state_url":"https://pith.science/pith/7RXTOQB25AGRDB27OJAFWCSZX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RXTOQB25AGRDB27OJAFWCSZX6/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":"2026-06-02T00:27:45Z","links":{"resolver":"https://pith.science/pith/7RXTOQB25AGRDB27OJAFWCSZX6","bundle":"https://pith.science/pith/7RXTOQB25AGRDB27OJAFWCSZX6/bundle.json","state":"https://pith.science/pith/7RXTOQB25AGRDB27OJAFWCSZX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RXTOQB25AGRDB27OJAFWCSZX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7RXTOQB25AGRDB27OJAFWCSZX6","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":"7e26d8b0cfa39429e67bfb885db399e499332776d43f74a24af675e5069cda60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-07T21:39:12Z","title_canon_sha256":"d7585e18d4abe978148b2887de53395290cd2b1f0c98eae8b64770255eb7cbcd"},"schema_version":"1.0","source":{"id":"1805.02756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02756","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02756v2","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02756","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"7RXTOQB25AGR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7RXTOQB25AGRDB27","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7RXTOQB2","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:8f5daf40ae7a7a1fdbe60df26528b6503d89782f041ba6d49e2eab1010aa9186","target":"graph","created_at":"2026-05-17T23:44:59Z","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"},"paper":{"abstract_excerpt":"Using recent work of the first author~\\cite{Bet}, we prove a strong version of the Manin-Peyre's conjectures with a full asymptotic and a power-saving error term for the two varieties respectively in $\\mathbb{P}^2 \\times \\mathbb{P}^2$ with bihomogeneous coordinates $[x_1:x_2:x_3],[y_1:y_2,y_3]$ and in $\\mathbb{P}^1\\times \\mathbb{P}^1 \\times \\mathbb{P}^1$ with multihomogeneous coordinates $[x_1:y_1],[x_2:y_2],[x_3:y_3]$ defined by the same equation $x_1y_2y_3+x_2y_1y_3+x_3y_1y_2=0$. We thus improve on recent work of Blomer, Br\\\"udern and Salberger \\cite{BBS} and provide a different proof based ","authors_text":"Kevin Destagnol, Sandro Bettin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-07T21:39:12Z","title":"The power-saving Manin-Peyre's conjectures for a senary cubic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02756","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":"sha256:640fd407933224896da5203cb8fbf831e1c386d4ba6c7aab27e06ca41a0fe567","target":"record","created_at":"2026-05-17T23:44:59Z","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":"7e26d8b0cfa39429e67bfb885db399e499332776d43f74a24af675e5069cda60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-07T21:39:12Z","title_canon_sha256":"d7585e18d4abe978148b2887de53395290cd2b1f0c98eae8b64770255eb7cbcd"},"schema_version":"1.0","source":{"id":"1805.02756","kind":"arxiv","version":2}},"canonical_sha256":"fc6f37403ae80d11875f72405b0a59bf9de6da9f5c19428fe2412fda363b0878","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc6f37403ae80d11875f72405b0a59bf9de6da9f5c19428fe2412fda363b0878","first_computed_at":"2026-05-17T23:44:59.570932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:59.570932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gpd2a4FAoG8pCXPPr0Egm0P5NveuYfkMmf5R+vsW5fggAkSBASzMFTx1nRqp7R4N/ZSLhN5g/dhx0zLswKmyDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:59.571581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:640fd407933224896da5203cb8fbf831e1c386d4ba6c7aab27e06ca41a0fe567","sha256:8f5daf40ae7a7a1fdbe60df26528b6503d89782f041ba6d49e2eab1010aa9186"],"state_sha256":"a5b81f05ef6d8b4dd663697c9adb9a3388f2fe01b64d48a6e004d2ed4a79e7cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlAFHfc/IFke3gc1Eh5F2rRPRhuIUBGXRhm0VJL1MtVRrW90jF9vindw+a+/Low/0rU+R7iHeI7HvDTNi29mAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:27:45.045730Z","bundle_sha256":"013e0aac8579453b62f3c188d2e7b877a3e7ac5e6830ccd43435a1ee0df07d47"}}