{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LQ6ESIG2CH3IT2T7MLQSJPFXHP","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":"80230bd6a9a664c55025bb80f9837a3c88715b3511d9e1e616d08d9e87c2f852","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T12:53:50Z","title_canon_sha256":"2fe4d24c0f87988a07df60adcf5dcf8ec99617458a4e7569b1ab01f8617339c2"},"schema_version":"1.0","source":{"id":"1403.5937","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5937","created_at":"2026-05-18T02:28:11Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5937v2","created_at":"2026-05-18T02:28:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5937","created_at":"2026-05-18T02:28:11Z"},{"alias_kind":"pith_short_12","alias_value":"LQ6ESIG2CH3I","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LQ6ESIG2CH3IT2T7","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LQ6ESIG2","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:eddbd0f2ad27853d7b098f78d4d4afa4a306f56d60d62b4b423fc3ad4e2f3b31","target":"graph","created_at":"2026-05-18T02:28:11Z","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 generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral projective variety, provided only that its dimension is large enough in terms of its degree.","authors_text":"D.R. Heath-Brown, T.D. Browning","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T12:53:50Z","title":"Forms in many variables and differing degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5937","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":"sha256:669e71aad4fe16379ccfd4af79b12efd31ae52749c655dc9550b1c1de5269d6e","target":"record","created_at":"2026-05-18T02:28:11Z","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":"80230bd6a9a664c55025bb80f9837a3c88715b3511d9e1e616d08d9e87c2f852","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-24T12:53:50Z","title_canon_sha256":"2fe4d24c0f87988a07df60adcf5dcf8ec99617458a4e7569b1ab01f8617339c2"},"schema_version":"1.0","source":{"id":"1403.5937","kind":"arxiv","version":2}},"canonical_sha256":"5c3c4920da11f689ea7f62e124bcb73bfb38e059f4ccde890355202e129a58b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c3c4920da11f689ea7f62e124bcb73bfb38e059f4ccde890355202e129a58b3","first_computed_at":"2026-05-18T02:28:11.988977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:11.988977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JJCUSCwuJzeQU+mP/LYhVYFNlJLZ2WH64UWF/vyzxeX8ITtqxf0MEaEHb4OEIl2RFuiVtZuLTsq1eQ69Q2fFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:11.989680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5937","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:669e71aad4fe16379ccfd4af79b12efd31ae52749c655dc9550b1c1de5269d6e","sha256:eddbd0f2ad27853d7b098f78d4d4afa4a306f56d60d62b4b423fc3ad4e2f3b31"],"state_sha256":"6962e26d8d64bba061e24e222ed8b2a013e4b5511132e287d43353255ec439e3"}