{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZB2UYKJQRW6UC2ZJ2QWKISI2I5","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":"8ae0e9626fb441a619ed925c53e466d241077a5543c5454a162d682a10203564","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-26T16:31:00Z","title_canon_sha256":"de894f2d43e269a4b99dd285dd8f80397f9dc20c83a92cd810e02cfbedec0c30"},"schema_version":"1.0","source":{"id":"1108.5348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5348","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5348v1","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5348","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZB2UYKJQRW6U","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZB2UYKJQRW6UC2ZJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZB2UYKJQ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:7406709b14e94dfb67340d3a97abd6397ea1d35a2ae9694adb0252baae958aa4","target":"graph","created_at":"2026-05-18T03:57:40Z","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":"The problem of constructing a perfect cuboid is related to a certain class of univariate polynomials with three integer parameters $a$, $b$, and $u$. Their irreducibility over the ring of integers under certain restrictions for $a$, $b$, and $u$ would mean the non-existence of perfect cuboids. This irreducibility is conjectured and then verified numerically for approximately 10000 instances of $a$, $b$, and $u$.","authors_text":"Ruslan Sharipov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-26T16:31:00Z","title":"Perfect cuboids and irreducible polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5348","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":"sha256:05078458d84e6ab6fe048c20787621ddf4981df62a3a8805dde8ae3d091da9e7","target":"record","created_at":"2026-05-18T03:57:40Z","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":"8ae0e9626fb441a619ed925c53e466d241077a5543c5454a162d682a10203564","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-26T16:31:00Z","title_canon_sha256":"de894f2d43e269a4b99dd285dd8f80397f9dc20c83a92cd810e02cfbedec0c30"},"schema_version":"1.0","source":{"id":"1108.5348","kind":"arxiv","version":1}},"canonical_sha256":"c8754c29308dbd416b29d42ca4491a4777016602a74715cce261f0a0b03a6b8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8754c29308dbd416b29d42ca4491a4777016602a74715cce261f0a0b03a6b8d","first_computed_at":"2026-05-18T03:57:40.558309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:40.558309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y4NiK+KhcP6DrkIvLttSpQEuNqxbH02dS7A2Ho+fdBCLLtxpUKJguT0rKuJpN2H9tK0FDimdx+xC5NBzj4LAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:40.559042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05078458d84e6ab6fe048c20787621ddf4981df62a3a8805dde8ae3d091da9e7","sha256:7406709b14e94dfb67340d3a97abd6397ea1d35a2ae9694adb0252baae958aa4"],"state_sha256":"546a1d0207d3b265a667f09adfae5e2e64ad71d06a6952d7efb34a377d1dd0a6"}