{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZB2UYKJQRW6UC2ZJ2QWKISI2I5","short_pith_number":"pith:ZB2UYKJQ","canonical_record":{"source":{"id":"1108.5348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-26T16:31:00Z","cross_cats_sorted":[],"title_canon_sha256":"de894f2d43e269a4b99dd285dd8f80397f9dc20c83a92cd810e02cfbedec0c30","abstract_canon_sha256":"8ae0e9626fb441a619ed925c53e466d241077a5543c5454a162d682a10203564"},"schema_version":"1.0"},"canonical_sha256":"c8754c29308dbd416b29d42ca4491a4777016602a74715cce261f0a0b03a6b8d","source":{"kind":"arxiv","id":"1108.5348","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZB2UYKJQRW6UC2ZJ2QWKISI2I5","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-26T16:31:00Z","cross_cats_sorted":[],"title_canon_sha256":"de894f2d43e269a4b99dd285dd8f80397f9dc20c83a92cd810e02cfbedec0c30","abstract_canon_sha256":"8ae0e9626fb441a619ed925c53e466d241077a5543c5454a162d682a10203564"},"schema_version":"1.0"},"canonical_sha256":"c8754c29308dbd416b29d42ca4491a4777016602a74715cce261f0a0b03a6b8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:40.559042Z","signature_b64":"Y4NiK+KhcP6DrkIvLttSpQEuNqxbH02dS7A2Ho+fdBCLLtxpUKJguT0rKuJpN2H9tK0FDimdx+xC5NBzj4LAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8754c29308dbd416b29d42ca4491a4777016602a74715cce261f0a0b03a6b8d","last_reissued_at":"2026-05-18T03:57:40.558309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:40.558309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5348","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sp1bge6de0q9iHlJxwMOX5DjLrWPkSRZ7hJkhKwTAzXL/hTM8FP0nRHphuefCoBiQ0qCv0a53L4lmxSbFQ6xCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:47:48.786500Z"},"content_sha256":"05078458d84e6ab6fe048c20787621ddf4981df62a3a8805dde8ae3d091da9e7","schema_version":"1.0","event_id":"sha256:05078458d84e6ab6fe048c20787621ddf4981df62a3a8805dde8ae3d091da9e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZB2UYKJQRW6UC2ZJ2QWKISI2I5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfect cuboids and irreducible polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ruslan Sharipov","submitted_at":"2011-08-26T16:31:00Z","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 $u$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5348","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYYH2ODZtrcfqLootR7Ip2VqlFtNT1OwwMU4GRq2TGXTbsuqkehC8czLh74XQPv4yJzx98eHwQIbJCcVa4ktAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:47:48.787175Z"},"content_sha256":"7406709b14e94dfb67340d3a97abd6397ea1d35a2ae9694adb0252baae958aa4","schema_version":"1.0","event_id":"sha256:7406709b14e94dfb67340d3a97abd6397ea1d35a2ae9694adb0252baae958aa4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZB2UYKJQRW6UC2ZJ2QWKISI2I5/bundle.json","state_url":"https://pith.science/pith/ZB2UYKJQRW6UC2ZJ2QWKISI2I5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZB2UYKJQRW6UC2ZJ2QWKISI2I5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T11:47:48Z","links":{"resolver":"https://pith.science/pith/ZB2UYKJQRW6UC2ZJ2QWKISI2I5","bundle":"https://pith.science/pith/ZB2UYKJQRW6UC2ZJ2QWKISI2I5/bundle.json","state":"https://pith.science/pith/ZB2UYKJQRW6UC2ZJ2QWKISI2I5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZB2UYKJQRW6UC2ZJ2QWKISI2I5/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"StlaOOds1aqBUNjzk/Wx/6IWjd3qtqtVNTj2OrI7q4xGJ/zNRCeJcx8RU8+JPrqFw1NKOavobh1m2iWTgyGWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:47:48.791683Z","bundle_sha256":"6768c507fd5ea4d12bd32bf6817a7876bae59d4446b31ee7be97c56e07bdfdcb"}}