{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GIMTSSGWNXRTMR3OCREUHYKP2V","short_pith_number":"pith:GIMTSSGW","canonical_record":{"source":{"id":"1211.4215","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-18T12:25:06Z","cross_cats_sorted":[],"title_canon_sha256":"2ecaf5ccbb115d7fd2a0c82f03d6ccd2e6fd4efbbb0ab498761e4e748d165260","abstract_canon_sha256":"8dabd5b35c7363c0286be6ec853004f66cf8afb0e0908b4ea62c9d0d8abf9f04"},"schema_version":"1.0"},"canonical_sha256":"32193948d66de336476e144943e14fd57ec7d7ade20a7f75a7e79b9fd45278ad","source":{"kind":"arxiv","id":"1211.4215","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4215","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4215v3","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4215","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"pith_short_12","alias_value":"GIMTSSGWNXRT","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GIMTSSGWNXRTMR3O","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GIMTSSGW","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GIMTSSGWNXRTMR3OCREUHYKP2V","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4215","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-18T12:25:06Z","cross_cats_sorted":[],"title_canon_sha256":"2ecaf5ccbb115d7fd2a0c82f03d6ccd2e6fd4efbbb0ab498761e4e748d165260","abstract_canon_sha256":"8dabd5b35c7363c0286be6ec853004f66cf8afb0e0908b4ea62c9d0d8abf9f04"},"schema_version":"1.0"},"canonical_sha256":"32193948d66de336476e144943e14fd57ec7d7ade20a7f75a7e79b9fd45278ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:56.251644Z","signature_b64":"YEp3O2iQAOmXenTDzditBaEw3Oqbf1oohQTDev851+X1MJHGTsljVm7Uw81Iddd17n7RmduNkl1zQzQ+mDKNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32193948d66de336476e144943e14fd57ec7d7ade20a7f75a7e79b9fd45278ad","last_reissued_at":"2026-05-18T03:36:56.250954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:56.250954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4215","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hoTddnFYLW5eXM/JFB2RPmufjkNhsFlWcliSqPgXQTNEyxQP5xvlh3GNWbd2nr2BID+WrXlJ+CM0hWtSPNsgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:30:13.022937Z"},"content_sha256":"3ccaab817bd5c560de85dd259206a491947dcfdcc8895e099c523f63085d008d","schema_version":"1.0","event_id":"sha256:3ccaab817bd5c560de85dd259206a491947dcfdcc8895e099c523f63085d008d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GIMTSSGWNXRTMR3OCREUHYKP2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational points on cubic hypersurfaces that split off two forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Boqing Xue, Haobo Dai","submitted_at":"2012-11-18T12:25:06Z","abstract_excerpt":"We show that if $X\\subseteq \\mathbb{P}^{n-1}$, defined over $\\mathbb{Q}$ by a cubic form that splits off two forms, with $n\\geq 11$, then $X(\\mathbb{Q})$ is non-empty. The same holds for an $(m_1,m_2)$-form with $m_1\\geq 4$ and $m_2\\geq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4215","kind":"arxiv","version":3},"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":"2026-05-18T03:36:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OOp9i7fXCqysNnhbde3eR7d8P34vq1fX3GmBJEgO54k0pguWyr5dLYDCIw1lSxzoyVT3U58II6RVB1HrMz+HDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:30:13.023279Z"},"content_sha256":"9a93671413bcbd87682f4eff39a6061484633a73d93270f9bab3b0d1640cc2b3","schema_version":"1.0","event_id":"sha256:9a93671413bcbd87682f4eff39a6061484633a73d93270f9bab3b0d1640cc2b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GIMTSSGWNXRTMR3OCREUHYKP2V/bundle.json","state_url":"https://pith.science/pith/GIMTSSGWNXRTMR3OCREUHYKP2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GIMTSSGWNXRTMR3OCREUHYKP2V/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":"2026-07-03T09:30:13Z","links":{"resolver":"https://pith.science/pith/GIMTSSGWNXRTMR3OCREUHYKP2V","bundle":"https://pith.science/pith/GIMTSSGWNXRTMR3OCREUHYKP2V/bundle.json","state":"https://pith.science/pith/GIMTSSGWNXRTMR3OCREUHYKP2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GIMTSSGWNXRTMR3OCREUHYKP2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GIMTSSGWNXRTMR3OCREUHYKP2V","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":"8dabd5b35c7363c0286be6ec853004f66cf8afb0e0908b4ea62c9d0d8abf9f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-18T12:25:06Z","title_canon_sha256":"2ecaf5ccbb115d7fd2a0c82f03d6ccd2e6fd4efbbb0ab498761e4e748d165260"},"schema_version":"1.0","source":{"id":"1211.4215","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4215","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4215v3","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4215","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"pith_short_12","alias_value":"GIMTSSGWNXRT","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GIMTSSGWNXRTMR3O","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GIMTSSGW","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:9a93671413bcbd87682f4eff39a6061484633a73d93270f9bab3b0d1640cc2b3","target":"graph","created_at":"2026-05-18T03:36:56Z","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":"We show that if $X\\subseteq \\mathbb{P}^{n-1}$, defined over $\\mathbb{Q}$ by a cubic form that splits off two forms, with $n\\geq 11$, then $X(\\mathbb{Q})$ is non-empty. The same holds for an $(m_1,m_2)$-form with $m_1\\geq 4$ and $m_2\\geq 5$.","authors_text":"Boqing Xue, Haobo Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-18T12:25:06Z","title":"Rational points on cubic hypersurfaces that split off two forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4215","kind":"arxiv","version":3},"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":"sha256:3ccaab817bd5c560de85dd259206a491947dcfdcc8895e099c523f63085d008d","target":"record","created_at":"2026-05-18T03:36:56Z","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":"8dabd5b35c7363c0286be6ec853004f66cf8afb0e0908b4ea62c9d0d8abf9f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-18T12:25:06Z","title_canon_sha256":"2ecaf5ccbb115d7fd2a0c82f03d6ccd2e6fd4efbbb0ab498761e4e748d165260"},"schema_version":"1.0","source":{"id":"1211.4215","kind":"arxiv","version":3}},"canonical_sha256":"32193948d66de336476e144943e14fd57ec7d7ade20a7f75a7e79b9fd45278ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32193948d66de336476e144943e14fd57ec7d7ade20a7f75a7e79b9fd45278ad","first_computed_at":"2026-05-18T03:36:56.250954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:56.250954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YEp3O2iQAOmXenTDzditBaEw3Oqbf1oohQTDev851+X1MJHGTsljVm7Uw81Iddd17n7RmduNkl1zQzQ+mDKNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:56.251644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4215","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ccaab817bd5c560de85dd259206a491947dcfdcc8895e099c523f63085d008d","sha256:9a93671413bcbd87682f4eff39a6061484633a73d93270f9bab3b0d1640cc2b3"],"state_sha256":"d5a367bb691d16e2b59530f9457665aa2943f13a40a6b2d4b4a889468a5e604c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"49qHC/YVJpvzlsp7cGmgNMH66Ys8YYAoX0NpS0Uq3uThXaW/UyW+/pO5uNK+gJFJb5hfBca+nawD9VL9aOp+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T09:30:13.025417Z","bundle_sha256":"cd1065972a42e4cba626025da90917f9f643e9f4e6d23cc1ab4f933a239fa4f8"}}