{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PSVFGMIUUMTB2W65U3LXMEOTC6","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":"982ca9eab2fe79e4b2090d313a9da6bdc3c26cfa150391e597e6f5d555cc451a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T19:18:47Z","title_canon_sha256":"8323094a6d50bdc3028455b931987395a3806a11b5e4fbc6256ea1b004b0b273"},"schema_version":"1.0","source":{"id":"1111.4977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4977","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4977v1","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4977","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"pith_short_12","alias_value":"PSVFGMIUUMTB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PSVFGMIUUMTB2W65","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PSVFGMIU","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:25f31c92a81d0ce2c9e27f85a6a171bd91305d490a49cbf5499478b26d01b4bc","target":"graph","created_at":"2026-05-18T04:07:54Z","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":"New lower bounds involving sum, difference, product, and ratio sets for $A\\subset \\C$ are given.","authors_text":"Misha Rudnev","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T19:18:47Z","title":"On new sum-product type estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4977","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:bf110be0be39de78c6ab08c94c58134fece9498779ba0fd2606a4728f516ee0e","target":"record","created_at":"2026-05-18T04:07:54Z","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":"982ca9eab2fe79e4b2090d313a9da6bdc3c26cfa150391e597e6f5d555cc451a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T19:18:47Z","title_canon_sha256":"8323094a6d50bdc3028455b931987395a3806a11b5e4fbc6256ea1b004b0b273"},"schema_version":"1.0","source":{"id":"1111.4977","kind":"arxiv","version":1}},"canonical_sha256":"7caa533114a3261d5bdda6d77611d317bbe28ea5ec86abfee2caf40b1dd8bb5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7caa533114a3261d5bdda6d77611d317bbe28ea5ec86abfee2caf40b1dd8bb5e","first_computed_at":"2026-05-18T04:07:54.604294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:54.604294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zA26JS4iVi1TbzOibagoHbueAJDO975mA5uXV/+di66QWTTNhg6lYO+ja6AuH7NHAhZXQKfHwSdGMo+aebK6AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:54.604958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf110be0be39de78c6ab08c94c58134fece9498779ba0fd2606a4728f516ee0e","sha256:25f31c92a81d0ce2c9e27f85a6a171bd91305d490a49cbf5499478b26d01b4bc"],"state_sha256":"55d88137f31ba98cc9c88959e21b8aa7a30e787fc9e95669f8456e1cb25afb90"}