{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UCBUEHFLEFGHYCPBJBNXB4CMHV","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":"616ec6d23b5bacc334d7c31848b90f13a46f699d17cf14b573c83f681a3ae30b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-08-20T15:45:11Z","title_canon_sha256":"6f044f37c40049627eb4ec23af73e4155214d0b22940314cc0c81df0a61016d6"},"schema_version":"1.0","source":{"id":"2508.14793","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.14793","created_at":"2026-05-28T01:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"2508.14793v3","created_at":"2026-05-28T01:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.14793","created_at":"2026-05-28T01:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"UCBUEHFLEFGH","created_at":"2026-05-28T01:04:29Z"},{"alias_kind":"pith_short_16","alias_value":"UCBUEHFLEFGHYCPB","created_at":"2026-05-28T01:04:29Z"},{"alias_kind":"pith_short_8","alias_value":"UCBUEHFL","created_at":"2026-05-28T01:04:29Z"}],"graph_snapshots":[{"event_id":"sha256:caa4277187782c706b6f81056bd9f958c29f75829eb2a3b42adf1541a4eefe9d","target":"graph","created_at":"2026-05-28T01:04:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.14793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form $xy-zw=r$, where $r$ is a non-zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables $x, y, z, w$ as well as of $r$. We also establish an asymptotic formula for counting integer solutions with smooth weights to the congruence $xy-zw \\equiv 1 (\\text{mod }p)$, where $p$ is a large prime, with a strong bound on the error term.","authors_text":"Rachita Guria, Satadal Ganguly","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-08-20T15:45:11Z","title":"Distribution of integer points on determinant surfaces and a $\\text{mod-}p$ analogue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14793","kind":"arxiv","version":3},"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":"sha256:6cad0be892ea599077d1f12a987d3e53cdbb5f6b5b244fc6d46574f1a3917111","target":"record","created_at":"2026-05-28T01:04:29Z","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":"616ec6d23b5bacc334d7c31848b90f13a46f699d17cf14b573c83f681a3ae30b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-08-20T15:45:11Z","title_canon_sha256":"6f044f37c40049627eb4ec23af73e4155214d0b22940314cc0c81df0a61016d6"},"schema_version":"1.0","source":{"id":"2508.14793","kind":"arxiv","version":3}},"canonical_sha256":"a083421cab214c7c09e1485b70f04c3d58002be06648f235c71b20e121b3ed93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a083421cab214c7c09e1485b70f04c3d58002be06648f235c71b20e121b3ed93","first_computed_at":"2026-05-28T01:04:29.693576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:29.693576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FY8soNUNBu6lhu6pEJHP5JphvdPw/Q/i/T30H6RfUe8DpPSAkIkUJE5Q4MAPIAZ8rcFdYewDC8TmLh0weRXFCA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:29.694374Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.14793","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cad0be892ea599077d1f12a987d3e53cdbb5f6b5b244fc6d46574f1a3917111","sha256:caa4277187782c706b6f81056bd9f958c29f75829eb2a3b42adf1541a4eefe9d"],"state_sha256":"2987ad338bd9d031d7bee4776ba1a32087717211ff3cdf938961091012e3f482"}