{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VTIX3HFEKORDG3UYTQUCJILTYN","short_pith_number":"pith:VTIX3HFE","canonical_record":{"source":{"id":"1209.5706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-25T18:05:06Z","cross_cats_sorted":[],"title_canon_sha256":"130803af586bf60ee489fa5b5467cce173583870a23326f821a69982fc66e126","abstract_canon_sha256":"b1fb7bc36c734f6bf4b65be0e4c381b079796845891a5d744d02a30082328496"},"schema_version":"1.0"},"canonical_sha256":"acd17d9ca453a2336e989c2824a173c366473d84761052de6b57e23b41080cb2","source":{"kind":"arxiv","id":"1209.5706","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5706","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5706v1","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5706","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"VTIX3HFEKORD","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VTIX3HFEKORDG3UY","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VTIX3HFE","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VTIX3HFEKORDG3UYTQUCJILTYN","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-25T18:05:06Z","cross_cats_sorted":[],"title_canon_sha256":"130803af586bf60ee489fa5b5467cce173583870a23326f821a69982fc66e126","abstract_canon_sha256":"b1fb7bc36c734f6bf4b65be0e4c381b079796845891a5d744d02a30082328496"},"schema_version":"1.0"},"canonical_sha256":"acd17d9ca453a2336e989c2824a173c366473d84761052de6b57e23b41080cb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:47.752342Z","signature_b64":"gUVP/WTAdNsJX2f8F3K1adthP+Hdav7xTCuUec8xhhPg/ytZTSMrckZn7RKOtOjX5581ukQxxQAsJpQDgDjFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acd17d9ca453a2336e989c2824a173c366473d84761052de6b57e23b41080cb2","last_reissued_at":"2026-05-18T03:44:47.751655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:47.751655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5706","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":"2026-05-18T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1JnL1XvGlkwqkUnlTEj2jhFB21oQnoNjxalEdSrvlr5gIXmT4T3OdXzLCM3cXzw5GXTxPn57Jqfb2r1Ku+/rCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:20:55.166445Z"},"content_sha256":"69352e192139695523915cde958f63c15afbcc44dee75d7f0ca3d1400890ca84","schema_version":"1.0","event_id":"sha256:69352e192139695523915cde958f63c15afbcc44dee75d7f0ca3d1400890ca84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VTIX3HFEKORDG3UYTQUCJILTYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on rational and elliptic curves associated with the cuboid factor equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ruslan Sharipov","submitted_at":"2012-09-25T18:05:06Z","abstract_excerpt":"A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. It is described by a system of four equations with respect to six variables. The cuboid factor equations were derived from these four equations by symmetrization procedure. They constitute a system of eight polynomial equations, which has been solved parametrically. In the present paper its parametric solution is expressed through intersections or rational and elliptic curves arranged into parametric families."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5706","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":"2026-05-18T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nASb3kpkwcxUNIBflEHgrxxoNmCp4aYBb+tmnugSrLqDAJIF955DAr4YJE1vG0nkiKoVl/u9R7y6EmoSY/GZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:20:55.166996Z"},"content_sha256":"7bdfd9f69e1d825924a7ea1d781d7c7961f2284d0a3dd973b7c7f954c4045e3c","schema_version":"1.0","event_id":"sha256:7bdfd9f69e1d825924a7ea1d781d7c7961f2284d0a3dd973b7c7f954c4045e3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTIX3HFEKORDG3UYTQUCJILTYN/bundle.json","state_url":"https://pith.science/pith/VTIX3HFEKORDG3UYTQUCJILTYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTIX3HFEKORDG3UYTQUCJILTYN/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":"2026-06-09T22:20:55Z","links":{"resolver":"https://pith.science/pith/VTIX3HFEKORDG3UYTQUCJILTYN","bundle":"https://pith.science/pith/VTIX3HFEKORDG3UYTQUCJILTYN/bundle.json","state":"https://pith.science/pith/VTIX3HFEKORDG3UYTQUCJILTYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTIX3HFEKORDG3UYTQUCJILTYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VTIX3HFEKORDG3UYTQUCJILTYN","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":"b1fb7bc36c734f6bf4b65be0e4c381b079796845891a5d744d02a30082328496","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-25T18:05:06Z","title_canon_sha256":"130803af586bf60ee489fa5b5467cce173583870a23326f821a69982fc66e126"},"schema_version":"1.0","source":{"id":"1209.5706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5706","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5706v1","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5706","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"VTIX3HFEKORD","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VTIX3HFEKORDG3UY","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VTIX3HFE","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:7bdfd9f69e1d825924a7ea1d781d7c7961f2284d0a3dd973b7c7f954c4045e3c","target":"graph","created_at":"2026-05-18T03:44:47Z","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":"A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. It is described by a system of four equations with respect to six variables. The cuboid factor equations were derived from these four equations by symmetrization procedure. They constitute a system of eight polynomial equations, which has been solved parametrically. In the present paper its parametric solution is expressed through intersections or rational and elliptic curves arranged into parametric families.","authors_text":"Ruslan Sharipov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-25T18:05:06Z","title":"A note on rational and elliptic curves associated with the cuboid factor equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5706","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":"sha256:69352e192139695523915cde958f63c15afbcc44dee75d7f0ca3d1400890ca84","target":"record","created_at":"2026-05-18T03:44:47Z","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":"b1fb7bc36c734f6bf4b65be0e4c381b079796845891a5d744d02a30082328496","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-25T18:05:06Z","title_canon_sha256":"130803af586bf60ee489fa5b5467cce173583870a23326f821a69982fc66e126"},"schema_version":"1.0","source":{"id":"1209.5706","kind":"arxiv","version":1}},"canonical_sha256":"acd17d9ca453a2336e989c2824a173c366473d84761052de6b57e23b41080cb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acd17d9ca453a2336e989c2824a173c366473d84761052de6b57e23b41080cb2","first_computed_at":"2026-05-18T03:44:47.751655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:47.751655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gUVP/WTAdNsJX2f8F3K1adthP+Hdav7xTCuUec8xhhPg/ytZTSMrckZn7RKOtOjX5581ukQxxQAsJpQDgDjFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:47.752342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69352e192139695523915cde958f63c15afbcc44dee75d7f0ca3d1400890ca84","sha256:7bdfd9f69e1d825924a7ea1d781d7c7961f2284d0a3dd973b7c7f954c4045e3c"],"state_sha256":"accb66406729e4939619f4df62cebf087da713c2377f8b11e51d11bfeb0fc085"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RPdO9Wg42jGVel2nC6XMgUxBkErV35D4QaPHnqm5FNEvaoz0Wbn5DxEG/M1qXdQKUPWrnusUUf+XZaoLAZx3BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T22:20:55.170099Z","bundle_sha256":"10b5e8e166dd76177ed2be8ec1f888c384b1ab87a57f1c2e47b14f29c03b6f4e"}}