{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GRZSR3HSBW4ACNIBP4WALC7FHC","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":"052e903f8b9a3db8f62d7889c33d249be8ababb51e3a10886fcb4ed0fa4444bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-03T16:46:20Z","title_canon_sha256":"99a2514c23e132f42a8cb8b11a813a901df36349c20463d417b3cce3bf3baca7"},"schema_version":"1.0","source":{"id":"1512.01152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01152","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01152v1","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01152","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"GRZSR3HSBW4A","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GRZSR3HSBW4ACNIB","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GRZSR3HS","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:8ce6921eec69ecbb45540e70eae8f31f8fc5f94e4158b5fbd29311e990ab29d2","target":"graph","created_at":"2026-05-18T01:25:18Z","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 prove best-possible bounds for bilinear forms in Kloosterman sums for GL(3) associated with the long Weyl element. As an application we derive a best-possible spectral large sieve inequality on GL(3).","authors_text":"Jack Buttcane, Valentin Blomer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-03T16:46:20Z","title":"Global decomposition of GL(3) Kloosterman sums and the spectral large sieve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01152","kind":"arxiv","version":1},"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:ec9795e7ae499fb6c56fefa7ede025487ccad0e93b80e02df29e14ae0afe94c6","target":"record","created_at":"2026-05-18T01:25:18Z","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":"052e903f8b9a3db8f62d7889c33d249be8ababb51e3a10886fcb4ed0fa4444bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-03T16:46:20Z","title_canon_sha256":"99a2514c23e132f42a8cb8b11a813a901df36349c20463d417b3cce3bf3baca7"},"schema_version":"1.0","source":{"id":"1512.01152","kind":"arxiv","version":1}},"canonical_sha256":"347328ecf20db80135017f2c058be538b20cf77ff33b9a68c9f19bbb2b75cbc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"347328ecf20db80135017f2c058be538b20cf77ff33b9a68c9f19bbb2b75cbc9","first_computed_at":"2026-05-18T01:25:18.812857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:18.812857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"liiaKybyHRNfzZUZ760WMW+GJZiZep1UirvbLIhM3m1cxRdNVWUhN3JJTN6WmhgRcU0WBHxVoNoxvlhW7fliAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:18.813468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec9795e7ae499fb6c56fefa7ede025487ccad0e93b80e02df29e14ae0afe94c6","sha256:8ce6921eec69ecbb45540e70eae8f31f8fc5f94e4158b5fbd29311e990ab29d2"],"state_sha256":"f6e487013b502498762afc131cce6843290e74fe15feee62c2381c6bef1f173e"}