{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PVLCRMG7P5S7RVFLBYQTFNY7TK","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":"743bf9a2d99e10d79123eb4be883ada8f7851cc17bf3dfd3798c1492648a1be3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-21T02:31:35Z","title_canon_sha256":"8525effe0b2538a5112363dfdc05d0be21ad1027fcf09fa4082cea86a036b3b2"},"schema_version":"1.0","source":{"id":"1611.06635","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06635","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06635v2","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06635","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"pith_short_12","alias_value":"PVLCRMG7P5S7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PVLCRMG7P5S7RVFL","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PVLCRMG7","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:df5a17e3d00b255c32e1379a58d1d0527d2907a0933ce83be055c02edcd2de17","target":"graph","created_at":"2026-05-18T00:56:37Z","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 obtain several estimates for bilinear form with exponential sums with binomials $mx^k + nx^\\ell$. In particular we show the existence of nontrivial cancellations between such sums when the coefficients $m$ and $n$ vary over rather sparse sets of general nature","authors_text":"Igor E. Shparlinski, Kui Liu, Tianping Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-21T02:31:35Z","title":"Bilinear Forms with Exponential Sums with Binomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06635","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:aa683c7b2a4eb5306661d4521da0a4dd2cf6cc30a2f99f899c363436b3401a25","target":"record","created_at":"2026-05-18T00:56:37Z","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":"743bf9a2d99e10d79123eb4be883ada8f7851cc17bf3dfd3798c1492648a1be3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-21T02:31:35Z","title_canon_sha256":"8525effe0b2538a5112363dfdc05d0be21ad1027fcf09fa4082cea86a036b3b2"},"schema_version":"1.0","source":{"id":"1611.06635","kind":"arxiv","version":2}},"canonical_sha256":"7d5628b0df7f65f8d4ab0e2132b71f9a92ab019dae85e33bcaddd2bfd784f1d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d5628b0df7f65f8d4ab0e2132b71f9a92ab019dae85e33bcaddd2bfd784f1d7","first_computed_at":"2026-05-18T00:56:37.481701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:37.481701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e7Z6d/91XXBW0/6fj1p3KNeXcwt1ybGyqnK3ULVTRijDfvqFSU4bS1nJT6h5D3BadbUf8aYFn0e9agAuDolKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:37.482276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06635","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa683c7b2a4eb5306661d4521da0a4dd2cf6cc30a2f99f899c363436b3401a25","sha256:df5a17e3d00b255c32e1379a58d1d0527d2907a0933ce83be055c02edcd2de17"],"state_sha256":"9874561a2b8e6cef7bf0dea592ead2a9488adbf552a28bf32d63ac79514c220c"}