{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AJPSF5DBX53J7WTCIBD57YQLSP","short_pith_number":"pith:AJPSF5DB","canonical_record":{"source":{"id":"1809.04591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-12T17:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"f439b583c3951029bcdddaa3d35511101d743b26964704d1adb4a30644a61815","abstract_canon_sha256":"b9fefbdfb9b9a4bb46fbe7c714761d55399d0e6296a0ac2802312b5ae7a9a450"},"schema_version":"1.0"},"canonical_sha256":"025f22f461bf769fda624047dfe20b93e2ec3cc71424ab01a825a574366971d3","source":{"kind":"arxiv","id":"1809.04591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04591","created_at":"2026-05-17T23:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04591v2","created_at":"2026-05-17T23:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04591","created_at":"2026-05-17T23:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"AJPSF5DBX53J","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AJPSF5DBX53J7WTC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AJPSF5DB","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AJPSF5DBX53J7WTCIBD57YQLSP","target":"record","payload":{"canonical_record":{"source":{"id":"1809.04591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-12T17:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"f439b583c3951029bcdddaa3d35511101d743b26964704d1adb4a30644a61815","abstract_canon_sha256":"b9fefbdfb9b9a4bb46fbe7c714761d55399d0e6296a0ac2802312b5ae7a9a450"},"schema_version":"1.0"},"canonical_sha256":"025f22f461bf769fda624047dfe20b93e2ec3cc71424ab01a825a574366971d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:58.281205Z","signature_b64":"1enWaVR46Ua2WAvnKh3Z+M3Ath/Zqk1cLFtk1duZ2OIjUM0HeJ3zhRFXLiqAQymzleW9V1w13ytJiV+zRoTpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"025f22f461bf769fda624047dfe20b93e2ec3cc71424ab01a825a574366971d3","last_reissued_at":"2026-05-17T23:56:58.280636Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:58.280636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.04591","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DSRspSPUH4y4ekJVmtvCbfXHTRQm9ydh+ozheuV6wn6vFMVjodXxVjxtb/x9Umg5LJQ22TH/NDq8BpqeszUnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:38:45.497145Z"},"content_sha256":"dd43df85001290bd2768fdc50bd5a6d26fcf423cf69276c55cc9812c2f34e84f","schema_version":"1.0","event_id":"sha256:dd43df85001290bd2768fdc50bd5a6d26fcf423cf69276c55cc9812c2f34e84f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AJPSF5DBX53J7WTCIBD57YQLSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Diophantine equation with five prime variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinjiang Li, Min Zhang","submitted_at":"2018-09-12T17:55:22Z","abstract_excerpt":"Let $[x]$ denote the integral part of the real number $x$, and $N$ be a sufficiently large integer. In this paper, it is proved that, for $1<c<\\frac{4109054}{1999527}, c\\not=2$, the Diophantine equation $N=[p_1^c]+[p_2^c]+[p_3^c]+[p_4^c]+[p_5^c]$ is solvable in prime variables $p_1,p_2,p_3,p_4,p_5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04591","kind":"arxiv","version":2},"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":"2026-05-17T23:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2j9xQnJ7CNu8fBHRqYAaUpu/hjP3Ol8zHhb/atoUFYX1O98zpPfUMock9AwwfcAKxC6SBt9OjreU1zX95dDXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:38:45.497505Z"},"content_sha256":"873fb89296f87fb64f2c855b13e4025a62d857ff3c6b1d3492914f68cf24999c","schema_version":"1.0","event_id":"sha256:873fb89296f87fb64f2c855b13e4025a62d857ff3c6b1d3492914f68cf24999c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJPSF5DBX53J7WTCIBD57YQLSP/bundle.json","state_url":"https://pith.science/pith/AJPSF5DBX53J7WTCIBD57YQLSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJPSF5DBX53J7WTCIBD57YQLSP/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":"2026-06-09T00:38:45Z","links":{"resolver":"https://pith.science/pith/AJPSF5DBX53J7WTCIBD57YQLSP","bundle":"https://pith.science/pith/AJPSF5DBX53J7WTCIBD57YQLSP/bundle.json","state":"https://pith.science/pith/AJPSF5DBX53J7WTCIBD57YQLSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJPSF5DBX53J7WTCIBD57YQLSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AJPSF5DBX53J7WTCIBD57YQLSP","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":"b9fefbdfb9b9a4bb46fbe7c714761d55399d0e6296a0ac2802312b5ae7a9a450","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-12T17:55:22Z","title_canon_sha256":"f439b583c3951029bcdddaa3d35511101d743b26964704d1adb4a30644a61815"},"schema_version":"1.0","source":{"id":"1809.04591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04591","created_at":"2026-05-17T23:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04591v2","created_at":"2026-05-17T23:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04591","created_at":"2026-05-17T23:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"AJPSF5DBX53J","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AJPSF5DBX53J7WTC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AJPSF5DB","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:873fb89296f87fb64f2c855b13e4025a62d857ff3c6b1d3492914f68cf24999c","target":"graph","created_at":"2026-05-17T23:56:58Z","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 $[x]$ denote the integral part of the real number $x$, and $N$ be a sufficiently large integer. In this paper, it is proved that, for $1<c<\\frac{4109054}{1999527}, c\\not=2$, the Diophantine equation $N=[p_1^c]+[p_2^c]+[p_3^c]+[p_4^c]+[p_5^c]$ is solvable in prime variables $p_1,p_2,p_3,p_4,p_5$.","authors_text":"Jinjiang Li, Min Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-12T17:55:22Z","title":"On a Diophantine equation with five prime variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04591","kind":"arxiv","version":2},"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:dd43df85001290bd2768fdc50bd5a6d26fcf423cf69276c55cc9812c2f34e84f","target":"record","created_at":"2026-05-17T23:56:58Z","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":"b9fefbdfb9b9a4bb46fbe7c714761d55399d0e6296a0ac2802312b5ae7a9a450","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-12T17:55:22Z","title_canon_sha256":"f439b583c3951029bcdddaa3d35511101d743b26964704d1adb4a30644a61815"},"schema_version":"1.0","source":{"id":"1809.04591","kind":"arxiv","version":2}},"canonical_sha256":"025f22f461bf769fda624047dfe20b93e2ec3cc71424ab01a825a574366971d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"025f22f461bf769fda624047dfe20b93e2ec3cc71424ab01a825a574366971d3","first_computed_at":"2026-05-17T23:56:58.280636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:58.280636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1enWaVR46Ua2WAvnKh3Z+M3Ath/Zqk1cLFtk1duZ2OIjUM0HeJ3zhRFXLiqAQymzleW9V1w13ytJiV+zRoTpCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:58.281205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd43df85001290bd2768fdc50bd5a6d26fcf423cf69276c55cc9812c2f34e84f","sha256:873fb89296f87fb64f2c855b13e4025a62d857ff3c6b1d3492914f68cf24999c"],"state_sha256":"eb75b52a4e5ad6762868c3027e6cb193e76f3c59f3fb065633f9ea0469fd7c84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVKdm/b4hbFUQDEsUj884zi8+gwFnHnqdKmyyg/nMwYfcJTPphQgfuzhu7OP04s7wyIerfF0AiNl7eBL4QMEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:38:45.499364Z","bundle_sha256":"3685f2b24458d5e48a8866072faf8fd4d9e602fbfa9a7f4760b26c7ea94a189b"}}