{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4X2Q3NIGSICPXPPVPH6UA5XM5C","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cecb94100fb61b4df58918a3bc988a954cfaa413b5b9a6cdacdf74fdf4a8d543","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-19T07:52:33Z","title_canon_sha256":"fd77294d4e96e59be2231f97669bf6026135e4e7e1c2efdcfc249257ee625377"},"schema_version":"1.0","source":{"id":"2605.19502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19502","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19502v1","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19502","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"4X2Q3NIGSICP","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"4X2Q3NIGSICPXPPV","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"4X2Q3NIG","created_at":"2026-05-20T01:05:48Z"}],"graph_snapshots":[{"event_id":"sha256:a2156334bfbdd79b8dc60197e00c9b470c68b002a62311a58759e5ee7dc98f78","target":"graph","created_at":"2026-05-20T01:05:48Z","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/2605.19502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sun proposed a collection of congruence and quadratic-residue conjectures for determinants and permanents over residue classes modulo a prime. This article proves Conjectures 4.6, 4.7, 4.8(ii), 4.9, 4.10(ii), 4.11 and 4.12 from Sun's list. The determinant part is strengthened to a root-quotient criterion for irreducible binary quadratic forms over the quadratic extension of the prime field; the criterion gives the stated result for the determinant associated with the remaining binary quadratic form. The Cauchy-kernel part gives both derangement congruences modulo the square of the prime and a ","authors_text":"Yaoran Yang, Yutong Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-19T07:52:33Z","title":"Sun-type determinant and permanent congruences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19502","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":"sha256:5480fe40dfabdef88386f8ed6ac0250003726acc9ab53deccf5d3c9d0dfc0212","target":"record","created_at":"2026-05-20T01:05:48Z","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":"cecb94100fb61b4df58918a3bc988a954cfaa413b5b9a6cdacdf74fdf4a8d543","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-19T07:52:33Z","title_canon_sha256":"fd77294d4e96e59be2231f97669bf6026135e4e7e1c2efdcfc249257ee625377"},"schema_version":"1.0","source":{"id":"2605.19502","kind":"arxiv","version":1}},"canonical_sha256":"e5f50db5069204fbbdf579fd4076ece88eb376e28cee1e7d4352499166a62145","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5f50db5069204fbbdf579fd4076ece88eb376e28cee1e7d4352499166a62145","first_computed_at":"2026-05-20T01:05:48.900203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:48.900203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NKMY4YPqFHMPgaGAAJl2ZDuRAnp6F8L9T5S0KUEDx0Kk/qv+2UWilPlDzG7vUQIgjh6nmgGbdvaYQUpnvZGrCg==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:48.900919Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5480fe40dfabdef88386f8ed6ac0250003726acc9ab53deccf5d3c9d0dfc0212","sha256:a2156334bfbdd79b8dc60197e00c9b470c68b002a62311a58759e5ee7dc98f78","sha256:0ac1dee746a9a86844f6c2000bbf1362d96eefc3d864954b721f68c0d68dbfa5"],"state_sha256":"795c145e1393cc4056709454efbd12d8748406cf846c22253f154d153cc9ba58"}