{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VJBLLXK44Y7MAKL22U7V5ZXGND","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":"4f318ec30e70d7cd420b6c9dab069cd1996965b6dcb5027ea1c111014b0e208c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-26T12:10:58Z","title_canon_sha256":"2cb724c97d9c348a7d6031f07718c0723b0dcf806fd142a73d3fa66903f5d049"},"schema_version":"1.0","source":{"id":"1712.09355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09355","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09355v1","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09355","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"VJBLLXK44Y7M","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VJBLLXK44Y7MAKL2","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VJBLLXK4","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:45c98f0ae4667eccd7003a76b1c1c3a235f314d17c6ce94dc9c6ae69368616c5","target":"graph","created_at":"2026-05-18T00:27:08Z","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 a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.","authors_text":"Aleksei S. Volostnov","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-26T12:10:58Z","title":"On some double sums with multiplicative characters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09355","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":"sha256:33b43b2c9cbd4a16b08e1710c7dc96bb800cec8fc98679ae200394c35499bdb5","target":"record","created_at":"2026-05-18T00:27:08Z","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":"4f318ec30e70d7cd420b6c9dab069cd1996965b6dcb5027ea1c111014b0e208c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-26T12:10:58Z","title_canon_sha256":"2cb724c97d9c348a7d6031f07718c0723b0dcf806fd142a73d3fa66903f5d049"},"schema_version":"1.0","source":{"id":"1712.09355","kind":"arxiv","version":1}},"canonical_sha256":"aa42b5dd5ce63ec0297ad53f5ee6e668d080b9b56db99b0ac578658bb10dcfed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa42b5dd5ce63ec0297ad53f5ee6e668d080b9b56db99b0ac578658bb10dcfed","first_computed_at":"2026-05-18T00:27:08.648655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:08.648655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QheliZ9VPOOq+DaMC6STnU/NWeLQ628qGyYGcbSHP9/cHhNMF75/rXt3G7cRBiMfJXKwLOboB7Te0YZEKD8kDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:08.649283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33b43b2c9cbd4a16b08e1710c7dc96bb800cec8fc98679ae200394c35499bdb5","sha256:45c98f0ae4667eccd7003a76b1c1c3a235f314d17c6ce94dc9c6ae69368616c5"],"state_sha256":"44a2984e0172a0e9a52fcad470ee36c87e294f64283b80fc2e37034e61da4878"}