{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:W6E6OMEXORTSMSBGCKGGQUYYDC","short_pith_number":"pith:W6E6OMEX","canonical_record":{"source":{"id":"1706.03185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T05:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"d89f0ef30cfb01ff22e19cd925bbde4889a818aa2e7c927aa0821235babd0a39","abstract_canon_sha256":"c60ecfbde804a4ad89c2d7b25cbe241b98c2c10150ee38e4f1a646fa2663839f"},"schema_version":"1.0"},"canonical_sha256":"b789e730977467264826128c68531818ad25182760c3758b21d5ff4e275858bb","source":{"kind":"arxiv","id":"1706.03185","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03185","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03185v1","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03185","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"W6E6OMEXORTS","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"W6E6OMEXORTSMSBG","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"W6E6OMEX","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:W6E6OMEXORTSMSBGCKGGQUYYDC","target":"record","payload":{"canonical_record":{"source":{"id":"1706.03185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T05:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"d89f0ef30cfb01ff22e19cd925bbde4889a818aa2e7c927aa0821235babd0a39","abstract_canon_sha256":"c60ecfbde804a4ad89c2d7b25cbe241b98c2c10150ee38e4f1a646fa2663839f"},"schema_version":"1.0"},"canonical_sha256":"b789e730977467264826128c68531818ad25182760c3758b21d5ff4e275858bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:38.241710Z","signature_b64":"PXMzqSWehVFV/GZ8kZU9jAmvghqsa0mLAQ+rgKC2TbEqwLLqBgWKymAugy9SxI45sKU1D9ZbZxtC6+8BO0uADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b789e730977467264826128c68531818ad25182760c3758b21d5ff4e275858bb","last_reissued_at":"2026-05-18T00:42:38.241247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:38.241247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.03185","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":"2026-05-18T00:42:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkdtKZ/g/gRGTqoY38I9Kd8ZZ5n1ziiZCPlze/VKqoL0ztyh31Q5zsqf5IcazSEGVoRtG5cyG5EUtGsGqTZ0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:36:23.572753Z"},"content_sha256":"e45babbda4f1350d04a793d1a1fdc286935db0f4c38ee74157e99e155ab70efd","schema_version":"1.0","event_id":"sha256:e45babbda4f1350d04a793d1a1fdc286935db0f4c38ee74157e99e155ab70efd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:W6E6OMEXORTSMSBGCKGGQUYYDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the Diophantine equations $x^{2}\\pm5^{\\alpha}\\cdot p^{n}=y^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"G\\\"okhan Soydan","submitted_at":"2017-06-10T05:58:45Z","abstract_excerpt":"Suppose that $x$ is odd, $n\\geq7$ and $p\\notin\\{2,5\\}$ are primes. In this paper, we prove that the Diophantine equations $x^{2}\\pm5^{\\alpha}p^{n}=y^{n}$ have no solutions in positive integers $\\alpha,x,y$ with $gcd(x,y)=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03185","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":"2026-05-18T00:42:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EK04sY9tMzfwzGziF4xcZAMh0SLhTkp+E623iScSbJBA0bdzjLGhVnx5aR8vqIhoimFhAdwGwl7GE1LvL6DCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:36:23.573365Z"},"content_sha256":"774d122a84d8d1598672225e4cc61aed1374b7ff3eb5b099b110ffa8ef506c9e","schema_version":"1.0","event_id":"sha256:774d122a84d8d1598672225e4cc61aed1374b7ff3eb5b099b110ffa8ef506c9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6E6OMEXORTSMSBGCKGGQUYYDC/bundle.json","state_url":"https://pith.science/pith/W6E6OMEXORTSMSBGCKGGQUYYDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6E6OMEXORTSMSBGCKGGQUYYDC/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":"2026-06-07T10:36:23Z","links":{"resolver":"https://pith.science/pith/W6E6OMEXORTSMSBGCKGGQUYYDC","bundle":"https://pith.science/pith/W6E6OMEXORTSMSBGCKGGQUYYDC/bundle.json","state":"https://pith.science/pith/W6E6OMEXORTSMSBGCKGGQUYYDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6E6OMEXORTSMSBGCKGGQUYYDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W6E6OMEXORTSMSBGCKGGQUYYDC","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":"c60ecfbde804a4ad89c2d7b25cbe241b98c2c10150ee38e4f1a646fa2663839f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T05:58:45Z","title_canon_sha256":"d89f0ef30cfb01ff22e19cd925bbde4889a818aa2e7c927aa0821235babd0a39"},"schema_version":"1.0","source":{"id":"1706.03185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03185","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03185v1","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03185","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"W6E6OMEXORTS","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"W6E6OMEXORTSMSBG","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"W6E6OMEX","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:774d122a84d8d1598672225e4cc61aed1374b7ff3eb5b099b110ffa8ef506c9e","target":"graph","created_at":"2026-05-18T00:42:38Z","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":"Suppose that $x$ is odd, $n\\geq7$ and $p\\notin\\{2,5\\}$ are primes. In this paper, we prove that the Diophantine equations $x^{2}\\pm5^{\\alpha}p^{n}=y^{n}$ have no solutions in positive integers $\\alpha,x,y$ with $gcd(x,y)=1$.","authors_text":"G\\\"okhan Soydan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T05:58:45Z","title":"A note on the Diophantine equations $x^{2}\\pm5^{\\alpha}\\cdot p^{n}=y^{n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03185","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:e45babbda4f1350d04a793d1a1fdc286935db0f4c38ee74157e99e155ab70efd","target":"record","created_at":"2026-05-18T00:42:38Z","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":"c60ecfbde804a4ad89c2d7b25cbe241b98c2c10150ee38e4f1a646fa2663839f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T05:58:45Z","title_canon_sha256":"d89f0ef30cfb01ff22e19cd925bbde4889a818aa2e7c927aa0821235babd0a39"},"schema_version":"1.0","source":{"id":"1706.03185","kind":"arxiv","version":1}},"canonical_sha256":"b789e730977467264826128c68531818ad25182760c3758b21d5ff4e275858bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b789e730977467264826128c68531818ad25182760c3758b21d5ff4e275858bb","first_computed_at":"2026-05-18T00:42:38.241247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:38.241247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PXMzqSWehVFV/GZ8kZU9jAmvghqsa0mLAQ+rgKC2TbEqwLLqBgWKymAugy9SxI45sKU1D9ZbZxtC6+8BO0uADg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:38.241710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e45babbda4f1350d04a793d1a1fdc286935db0f4c38ee74157e99e155ab70efd","sha256:774d122a84d8d1598672225e4cc61aed1374b7ff3eb5b099b110ffa8ef506c9e"],"state_sha256":"ed832159db60f2fa77467769daee609d2b3dd0521cff7cf8537b0146546d14c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uv55F4U0IEGD7L7rgpduQ0qhom6/l/FrmDnpq4fXNMMglIbTBRlNpULC/6JNIXy9MFxcw1DvYAVXeEYbkA6SCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:36:23.575702Z","bundle_sha256":"e3a3bf1b1f07ba5a3c898cbe798854b24d1fb75af75afd6e596f29ee2906a58d"}}