{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TJ6QMLOMPCULYIVN3HXFXCYTXM","short_pith_number":"pith:TJ6QMLOM","canonical_record":{"source":{"id":"1707.07229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-22T22:55:54Z","cross_cats_sorted":[],"title_canon_sha256":"39c6506be4eb9f9eed831367c754575dd306c8300e483afc6a1dcf917e86a0d2","abstract_canon_sha256":"90ded4b9b24ce0084924163d39991298043cd1b6db597f202e6a08098d41f075"},"schema_version":"1.0"},"canonical_sha256":"9a7d062dcc78a8bc22add9ee5b8b13bb20dd864d14ce3191072e8bd85ca91009","source":{"kind":"arxiv","id":"1707.07229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07229","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07229v1","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07229","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"TJ6QMLOMPCUL","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TJ6QMLOMPCULYIVN","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TJ6QMLOM","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TJ6QMLOMPCULYIVN3HXFXCYTXM","target":"record","payload":{"canonical_record":{"source":{"id":"1707.07229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-22T22:55:54Z","cross_cats_sorted":[],"title_canon_sha256":"39c6506be4eb9f9eed831367c754575dd306c8300e483afc6a1dcf917e86a0d2","abstract_canon_sha256":"90ded4b9b24ce0084924163d39991298043cd1b6db597f202e6a08098d41f075"},"schema_version":"1.0"},"canonical_sha256":"9a7d062dcc78a8bc22add9ee5b8b13bb20dd864d14ce3191072e8bd85ca91009","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:11.589040Z","signature_b64":"TT2P0bbhbqiln5lw28VAy0KVXP0U3sX472hJt1f4LHGOouLHb2MdkAr681ztKdtfuhAZ7ShaD/RViOrSeYVWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a7d062dcc78a8bc22add9ee5b8b13bb20dd864d14ce3191072e8bd85ca91009","last_reissued_at":"2026-05-18T00:25:11.588138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:11.588138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.07229","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":"2026-05-18T00:25:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHf6+qnyba8nNmDjvnxcRjAcSfUO5hstpUf3LgbFNXDststm/46dDkcpAJ4oKuIfB1tSV5WDHbYPbTCX8ukEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:10:33.363728Z"},"content_sha256":"1b4d24b1f2a2b19ae5a7580e825848562ba19d2e9418ee02512fab12e7a523af","schema_version":"1.0","event_id":"sha256:1b4d24b1f2a2b19ae5a7580e825848562ba19d2e9418ee02512fab12e7a523af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TJ6QMLOMPCULYIVN3HXFXCYTXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a problem of Pillai with Fibonacci numbers and powers of 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florian Luca, Mahadi Ddamulira, Mihaja Rakotomalala","submitted_at":"2017-07-22T22:55:54Z","abstract_excerpt":"In this paper, we find all integers c having at least two representations as a difference between a Fibonacci number and a power of 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07229","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":"2026-05-18T00:25:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NugY7RH/1JxU/T5XuzmN/PL/AQvhWuMBf/4jG5N2AFj4lhA3ORJ2jhL0NoE80V7IT+brJ/levzk04uMBQfdCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:10:33.364433Z"},"content_sha256":"b9a8f94c09e64814e71894ff10358841fae226c9fff415e53788f61f342d03c4","schema_version":"1.0","event_id":"sha256:b9a8f94c09e64814e71894ff10358841fae226c9fff415e53788f61f342d03c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJ6QMLOMPCULYIVN3HXFXCYTXM/bundle.json","state_url":"https://pith.science/pith/TJ6QMLOMPCULYIVN3HXFXCYTXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJ6QMLOMPCULYIVN3HXFXCYTXM/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":"2026-05-25T16:10:33Z","links":{"resolver":"https://pith.science/pith/TJ6QMLOMPCULYIVN3HXFXCYTXM","bundle":"https://pith.science/pith/TJ6QMLOMPCULYIVN3HXFXCYTXM/bundle.json","state":"https://pith.science/pith/TJ6QMLOMPCULYIVN3HXFXCYTXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJ6QMLOMPCULYIVN3HXFXCYTXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TJ6QMLOMPCULYIVN3HXFXCYTXM","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":"90ded4b9b24ce0084924163d39991298043cd1b6db597f202e6a08098d41f075","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-22T22:55:54Z","title_canon_sha256":"39c6506be4eb9f9eed831367c754575dd306c8300e483afc6a1dcf917e86a0d2"},"schema_version":"1.0","source":{"id":"1707.07229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07229","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07229v1","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07229","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"TJ6QMLOMPCUL","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TJ6QMLOMPCULYIVN","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TJ6QMLOM","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:b9a8f94c09e64814e71894ff10358841fae226c9fff415e53788f61f342d03c4","target":"graph","created_at":"2026-05-18T00:25:11Z","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 find all integers c having at least two representations as a difference between a Fibonacci number and a power of 2.","authors_text":"Florian Luca, Mahadi Ddamulira, Mihaja Rakotomalala","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-22T22:55:54Z","title":"On a problem of Pillai with Fibonacci numbers and powers of 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07229","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":"sha256:1b4d24b1f2a2b19ae5a7580e825848562ba19d2e9418ee02512fab12e7a523af","target":"record","created_at":"2026-05-18T00:25:11Z","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":"90ded4b9b24ce0084924163d39991298043cd1b6db597f202e6a08098d41f075","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-22T22:55:54Z","title_canon_sha256":"39c6506be4eb9f9eed831367c754575dd306c8300e483afc6a1dcf917e86a0d2"},"schema_version":"1.0","source":{"id":"1707.07229","kind":"arxiv","version":1}},"canonical_sha256":"9a7d062dcc78a8bc22add9ee5b8b13bb20dd864d14ce3191072e8bd85ca91009","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a7d062dcc78a8bc22add9ee5b8b13bb20dd864d14ce3191072e8bd85ca91009","first_computed_at":"2026-05-18T00:25:11.588138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:11.588138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TT2P0bbhbqiln5lw28VAy0KVXP0U3sX472hJt1f4LHGOouLHb2MdkAr681ztKdtfuhAZ7ShaD/RViOrSeYVWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:11.589040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b4d24b1f2a2b19ae5a7580e825848562ba19d2e9418ee02512fab12e7a523af","sha256:b9a8f94c09e64814e71894ff10358841fae226c9fff415e53788f61f342d03c4"],"state_sha256":"87693e11dfc43d87349aae491bc8088d6cbf5d1c64b6004ec10350187257a899"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSGKNzviUbAAVPJAdrC44YKayBP+3/d3qO1K+0e/HKoQlFNkTGeOrZWZsPk3dHP2mwlFncOohJ77mS0ndVuhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:10:33.368168Z","bundle_sha256":"8cd23daac59fae42f3c467257b49ff055164ade998c647bd83f9ba1ec3681e3a"}}