{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RR2MMKB3NPTEYTBDKPIOMTT7XJ","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":"e1198c55e04b1588edea0e465ef618211921cb99ccb322ec0da6c1be433b4a1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-30T20:06:45Z","title_canon_sha256":"718ce4b6470a8dfc400dfba63b7c99b35616e7c042a77b198524ac4fa54d9516"},"schema_version":"1.0","source":{"id":"1611.10337","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.10337","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1611.10337v3","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.10337","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"RR2MMKB3NPTE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RR2MMKB3NPTEYTBD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RR2MMKB3","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:b53b170854beedf4f2646d299a2d6bbf92c613a6037bd2d7c6399f5946c84884","target":"graph","created_at":"2026-05-17T23:53:34Z","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":"Let $p\\equiv 1\\bmod 4$ be a prime number. We use a number field variant of Vinogradov's method to prove density results about the following four arithmetic invariants: (i) $16$-rank of the class group $\\mathrm{Cl}(-4p)$ of the imaginary quadratic number field $\\mathbb{Q}(\\sqrt{-4p})$; (ii) $8$-rank of the ordinary class group $\\mathrm{Cl}(8p)$ of the real quadratic field $\\mathbb{Q}(\\sqrt{8p})$; (iii) the solvability of the negative Pell equation $x^2 - 2py^2 = -1$ over the integers; (iv) $2$-part of the Tate-\\v{S}afarevi\\v{c} group of the congruent number elliptic curve $E_p: y^2 = x^3-p^2x$.","authors_text":"Djordjo Milovic, Peter Koymans","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-30T20:06:45Z","title":"Spins of prime ideals and the negative Pell equation $x^2 - 2py^2 = -1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10337","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":"sha256:3f7d76098b4b7b27dc6c5d5817019b0d9577f822de23743aa3b20e2206f0e5a0","target":"record","created_at":"2026-05-17T23:53:34Z","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":"e1198c55e04b1588edea0e465ef618211921cb99ccb322ec0da6c1be433b4a1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-30T20:06:45Z","title_canon_sha256":"718ce4b6470a8dfc400dfba63b7c99b35616e7c042a77b198524ac4fa54d9516"},"schema_version":"1.0","source":{"id":"1611.10337","kind":"arxiv","version":3}},"canonical_sha256":"8c74c6283b6be64c4c2353d0e64e7fba5060b3ba8aa7ff4562e791abddfe309e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c74c6283b6be64c4c2353d0e64e7fba5060b3ba8aa7ff4562e791abddfe309e","first_computed_at":"2026-05-17T23:53:34.070412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:34.070412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"knON0WYOCEm706bq/pH1G5O/ITwJ3dxUHqCetlZTrhAWnH4rLIf4WB/hWDREh925gqkzj9UXSUBzseH6p+vUDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:34.071066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.10337","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f7d76098b4b7b27dc6c5d5817019b0d9577f822de23743aa3b20e2206f0e5a0","sha256:b53b170854beedf4f2646d299a2d6bbf92c613a6037bd2d7c6399f5946c84884"],"state_sha256":"83e1ef2eb99c13af5d0e566d8747efeaaee61f4c59d8e9cca41cf3908e9687e5"}