{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:D4OLDZJARYS73LFVOMG6PKSXIW","short_pith_number":"pith:D4OLDZJA","canonical_record":{"source":{"id":"1502.04346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-15T18:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"2a86ae5af676ca84a490e0f7ba2faf6e54e3d3c308c9d0901acb8b32345d9461","abstract_canon_sha256":"cd21515cafe6bf9a85c78cef46f2b543f34a7db0dd98f580b759c58c889c6177"},"schema_version":"1.0"},"canonical_sha256":"1f1cb1e5208e25fdacb5730de7aa57458c2add674658cd3f1278db481d466cc0","source":{"kind":"arxiv","id":"1502.04346","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04346","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04346v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04346","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"D4OLDZJARYS7","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D4OLDZJARYS73LFV","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D4OLDZJA","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:D4OLDZJARYS73LFVOMG6PKSXIW","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-15T18:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"2a86ae5af676ca84a490e0f7ba2faf6e54e3d3c308c9d0901acb8b32345d9461","abstract_canon_sha256":"cd21515cafe6bf9a85c78cef46f2b543f34a7db0dd98f580b759c58c889c6177"},"schema_version":"1.0"},"canonical_sha256":"1f1cb1e5208e25fdacb5730de7aa57458c2add674658cd3f1278db481d466cc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:59.924277Z","signature_b64":"lRsNmH7gBwTBFaf/zcYHtEoDYbUTVer5s3KTchRu3bNHKZpKsqfYmXLsbu6KeGj/vEUJMUtlVmrbm1NRBHPqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f1cb1e5208e25fdacb5730de7aa57458c2add674658cd3f1278db481d466cc0","last_reissued_at":"2026-05-18T02:26:59.923830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:59.923830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04346","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HMbvbpcXvvX1o66SmOVxh3XGZO0UHL4ax0+yWuF4upHuMSJb2iriDBIjhSHECXapq2bRlLoo/oFSeY9PwukhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:48:32.039266Z"},"content_sha256":"201c8a9472b71313c49fb77c9af4dd4b292e7a0d7a7e6592dbb1eaaf4cd375a5","schema_version":"1.0","event_id":"sha256:201c8a9472b71313c49fb77c9af4dd4b292e7a0d7a7e6592dbb1eaaf4cd375a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:D4OLDZJARYS73LFVOMG6PKSXIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic forms representing the $p$-th Fibonacci number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alberto Mendoza, Florian Luca, Pedro Berrizbeitia","submitted_at":"2015-02-15T18:47:08Z","abstract_excerpt":"In this paper, we show that if $p\\equiv 1\\pmod 4$ is prime, then $4F_p$ admits a representation of the form $u^2-pv^2$ for some integers $u$ and $v$, where $F_n$ is the $n$th Fibonacci number. We prove a similar result when $p\\equiv -1\\pmod 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04346","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttpM7mzS8qzWd5Kxez1+n4meN+k/tYIKYrAf72PngQHga0gRpKp2xMfbU82j8YIrkz3BqgZPNxu4FyWvqveSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:48:32.039963Z"},"content_sha256":"799076c0ff3bd55483a76a1f5b7be2e06be96627b9c7c75dab751d92633ed776","schema_version":"1.0","event_id":"sha256:799076c0ff3bd55483a76a1f5b7be2e06be96627b9c7c75dab751d92633ed776"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4OLDZJARYS73LFVOMG6PKSXIW/bundle.json","state_url":"https://pith.science/pith/D4OLDZJARYS73LFVOMG6PKSXIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4OLDZJARYS73LFVOMG6PKSXIW/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":"2026-05-25T09:48:32Z","links":{"resolver":"https://pith.science/pith/D4OLDZJARYS73LFVOMG6PKSXIW","bundle":"https://pith.science/pith/D4OLDZJARYS73LFVOMG6PKSXIW/bundle.json","state":"https://pith.science/pith/D4OLDZJARYS73LFVOMG6PKSXIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4OLDZJARYS73LFVOMG6PKSXIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D4OLDZJARYS73LFVOMG6PKSXIW","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":"cd21515cafe6bf9a85c78cef46f2b543f34a7db0dd98f580b759c58c889c6177","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-15T18:47:08Z","title_canon_sha256":"2a86ae5af676ca84a490e0f7ba2faf6e54e3d3c308c9d0901acb8b32345d9461"},"schema_version":"1.0","source":{"id":"1502.04346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04346","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04346v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04346","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"D4OLDZJARYS7","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D4OLDZJARYS73LFV","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D4OLDZJA","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:799076c0ff3bd55483a76a1f5b7be2e06be96627b9c7c75dab751d92633ed776","target":"graph","created_at":"2026-05-18T02:26:59Z","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":"In this paper, we show that if $p\\equiv 1\\pmod 4$ is prime, then $4F_p$ admits a representation of the form $u^2-pv^2$ for some integers $u$ and $v$, where $F_n$ is the $n$th Fibonacci number. We prove a similar result when $p\\equiv -1\\pmod 4$.","authors_text":"Alberto Mendoza, Florian Luca, Pedro Berrizbeitia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-15T18:47:08Z","title":"Quadratic forms representing the $p$-th Fibonacci number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04346","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":"sha256:201c8a9472b71313c49fb77c9af4dd4b292e7a0d7a7e6592dbb1eaaf4cd375a5","target":"record","created_at":"2026-05-18T02:26:59Z","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":"cd21515cafe6bf9a85c78cef46f2b543f34a7db0dd98f580b759c58c889c6177","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-15T18:47:08Z","title_canon_sha256":"2a86ae5af676ca84a490e0f7ba2faf6e54e3d3c308c9d0901acb8b32345d9461"},"schema_version":"1.0","source":{"id":"1502.04346","kind":"arxiv","version":1}},"canonical_sha256":"1f1cb1e5208e25fdacb5730de7aa57458c2add674658cd3f1278db481d466cc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f1cb1e5208e25fdacb5730de7aa57458c2add674658cd3f1278db481d466cc0","first_computed_at":"2026-05-18T02:26:59.923830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:59.923830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lRsNmH7gBwTBFaf/zcYHtEoDYbUTVer5s3KTchRu3bNHKZpKsqfYmXLsbu6KeGj/vEUJMUtlVmrbm1NRBHPqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:59.924277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:201c8a9472b71313c49fb77c9af4dd4b292e7a0d7a7e6592dbb1eaaf4cd375a5","sha256:799076c0ff3bd55483a76a1f5b7be2e06be96627b9c7c75dab751d92633ed776"],"state_sha256":"8389386c2813220c4a3e1a8b22aa7187fd6a160fa9cc645cd667324ca1d6ba2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X/pNKb/pmGSyHpwAD98ignXlvrliTsucbMHRF+vBasIRaxNc04mrWMSMl9d5ZPWve+YluSUtCPyZ03EW7GbRAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:48:32.043591Z","bundle_sha256":"728ecd1d86a56a0a9baa1dccc979cee2320ac5698c3cbb35b10227664771eee0"}}