{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:4QJGUUKJB7NTM4SUUEL7XZBNPM","short_pith_number":"pith:4QJGUUKJ","canonical_record":{"source":{"id":"0810.0225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-01T16:58:08Z","cross_cats_sorted":[],"title_canon_sha256":"11c42dc66bd3dd45e9427869c8c68f3eb0d4b6640594ccdfa29869129dc52fae","abstract_canon_sha256":"7a55d1962eaaee2f22e76cd32c401a75dabf63e38e79121013d15a5717aa4afb"},"schema_version":"1.0"},"canonical_sha256":"e4126a51490fdb367254a117fbe42d7b319a49cf544d31c96206fc7aea2a4745","source":{"kind":"arxiv","id":"0810.0225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0225","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0225v1","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0225","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"4QJGUUKJB7NT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4QJGUUKJB7NTM4SU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4QJGUUKJ","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:4QJGUUKJB7NTM4SUUEL7XZBNPM","target":"record","payload":{"canonical_record":{"source":{"id":"0810.0225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-01T16:58:08Z","cross_cats_sorted":[],"title_canon_sha256":"11c42dc66bd3dd45e9427869c8c68f3eb0d4b6640594ccdfa29869129dc52fae","abstract_canon_sha256":"7a55d1962eaaee2f22e76cd32c401a75dabf63e38e79121013d15a5717aa4afb"},"schema_version":"1.0"},"canonical_sha256":"e4126a51490fdb367254a117fbe42d7b319a49cf544d31c96206fc7aea2a4745","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:33.168242Z","signature_b64":"aMLuCfqMBi2E1h9L58+CIsfSomSuA/qMxlbwyVQq5juZCoYkoXBl+/YUKDrzZcJ0z9OMDlw2QXsq4p5YXFFVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4126a51490fdb367254a117fbe42d7b319a49cf544d31c96206fc7aea2a4745","last_reissued_at":"2026-05-18T02:15:33.167479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:33.167479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.0225","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":"2026-05-18T02:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1wlXxXzZJRJVP3J0ueMSxJmXa3Enuue1ncUMUXBkVpN5HPpCdmpn+pwn9OTr/0vjTwna0TGNGvlepHZ27sVFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:02:36.478821Z"},"content_sha256":"cb251a123fc209868c69ebc42e1b33dddfc1975c7b2b7729cac417d890a6170e","schema_version":"1.0","event_id":"sha256:cb251a123fc209868c69ebc42e1b33dddfc1975c7b2b7729cac417d890a6170e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:4QJGUUKJB7NTM4SUUEL7XZBNPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational points on certain quintic hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maciej Ulas","submitted_at":"2008-10-01T16:58:08Z","abstract_excerpt":"Let $f(x)=x^5+ax^3+bx^2+cx \\in \\Z[x]$ and consider the hypersurface of degree five given by the equation \\cal{V}_{f}: f(p)+f(q)=f(r)+f(s). Under the assumption $b\\neq 0$ we show that there exists $\\Q$-unirational elliptic surface contained in $\\cal{V}_{f}$. If $b=0, a<0$ and $-a\\not\\equiv 2,18,34 \\pmod {48}$ then there exists $\\Q$-rational surface contained in $\\cal{V}_{f}$. Moreover, we prove that for each $f$ of degree five there exists $\\Q(i)$-rational surface contained in $\\cal{V}_{f}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0225","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":"2026-05-18T02:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XyXT2Ik7kS8H+Gq3AlejtRM4daqZUzvn9EttC8T/xYeNK+GnGKvR5xEDMeQIGfP+qlhGwgLnfVKJBXxRhKgtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:02:36.479170Z"},"content_sha256":"12501443a707a464c4c7bad51b72fc1c27e943514f4f2c339d2cea0762d4a263","schema_version":"1.0","event_id":"sha256:12501443a707a464c4c7bad51b72fc1c27e943514f4f2c339d2cea0762d4a263"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4QJGUUKJB7NTM4SUUEL7XZBNPM/bundle.json","state_url":"https://pith.science/pith/4QJGUUKJB7NTM4SUUEL7XZBNPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4QJGUUKJB7NTM4SUUEL7XZBNPM/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":"2026-06-09T05:02:36Z","links":{"resolver":"https://pith.science/pith/4QJGUUKJB7NTM4SUUEL7XZBNPM","bundle":"https://pith.science/pith/4QJGUUKJB7NTM4SUUEL7XZBNPM/bundle.json","state":"https://pith.science/pith/4QJGUUKJB7NTM4SUUEL7XZBNPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4QJGUUKJB7NTM4SUUEL7XZBNPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4QJGUUKJB7NTM4SUUEL7XZBNPM","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":"7a55d1962eaaee2f22e76cd32c401a75dabf63e38e79121013d15a5717aa4afb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-01T16:58:08Z","title_canon_sha256":"11c42dc66bd3dd45e9427869c8c68f3eb0d4b6640594ccdfa29869129dc52fae"},"schema_version":"1.0","source":{"id":"0810.0225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0225","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0225v1","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0225","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"4QJGUUKJB7NT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4QJGUUKJB7NTM4SU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4QJGUUKJ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:12501443a707a464c4c7bad51b72fc1c27e943514f4f2c339d2cea0762d4a263","target":"graph","created_at":"2026-05-18T02:15:33Z","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 $f(x)=x^5+ax^3+bx^2+cx \\in \\Z[x]$ and consider the hypersurface of degree five given by the equation \\cal{V}_{f}: f(p)+f(q)=f(r)+f(s). Under the assumption $b\\neq 0$ we show that there exists $\\Q$-unirational elliptic surface contained in $\\cal{V}_{f}$. If $b=0, a<0$ and $-a\\not\\equiv 2,18,34 \\pmod {48}$ then there exists $\\Q$-rational surface contained in $\\cal{V}_{f}$. Moreover, we prove that for each $f$ of degree five there exists $\\Q(i)$-rational surface contained in $\\cal{V}_{f}$.","authors_text":"Maciej Ulas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-01T16:58:08Z","title":"Rational points on certain quintic hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0225","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:cb251a123fc209868c69ebc42e1b33dddfc1975c7b2b7729cac417d890a6170e","target":"record","created_at":"2026-05-18T02:15:33Z","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":"7a55d1962eaaee2f22e76cd32c401a75dabf63e38e79121013d15a5717aa4afb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-01T16:58:08Z","title_canon_sha256":"11c42dc66bd3dd45e9427869c8c68f3eb0d4b6640594ccdfa29869129dc52fae"},"schema_version":"1.0","source":{"id":"0810.0225","kind":"arxiv","version":1}},"canonical_sha256":"e4126a51490fdb367254a117fbe42d7b319a49cf544d31c96206fc7aea2a4745","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4126a51490fdb367254a117fbe42d7b319a49cf544d31c96206fc7aea2a4745","first_computed_at":"2026-05-18T02:15:33.167479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:33.167479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMLuCfqMBi2E1h9L58+CIsfSomSuA/qMxlbwyVQq5juZCoYkoXBl+/YUKDrzZcJ0z9OMDlw2QXsq4p5YXFFVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:33.168242Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.0225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb251a123fc209868c69ebc42e1b33dddfc1975c7b2b7729cac417d890a6170e","sha256:12501443a707a464c4c7bad51b72fc1c27e943514f4f2c339d2cea0762d4a263"],"state_sha256":"e255dcddae7c6098114347c6f05c2af43f69573c75a093bbc5591386098cc845"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cuOtbPAz3+KemmDuQ8J5TvTXcnS7VxnfsS8ht0mGEJ5gUnxIAYsu7NdbCdGs/ClHIjcyWc5MOpMG4NboU/u8Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:02:36.481555Z","bundle_sha256":"08d7db8d825a666144e59782331ebb942295a50dc41c1be9c22faad0798d04b7"}}