{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VHD3BSF5O2HZ7JR256TFRDBOXL","short_pith_number":"pith:VHD3BSF5","canonical_record":{"source":{"id":"1903.01313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-04T15:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"08be74feea85551d6c3db010e5512b02b856ae689e5fa35ffcff4c32ee31bf14","abstract_canon_sha256":"da9405e751a4700b6bc8818a3b7c6457c3f677ba263454f720ef2250604a8471"},"schema_version":"1.0"},"canonical_sha256":"a9c7b0c8bd768f9fa63aefa6588c2ebaef4f0c3387b64ba8d1017df431e1c8ea","source":{"kind":"arxiv","id":"1903.01313","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01313","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01313v1","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01313","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"VHD3BSF5O2HZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VHD3BSF5O2HZ7JR2","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VHD3BSF5","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VHD3BSF5O2HZ7JR256TFRDBOXL","target":"record","payload":{"canonical_record":{"source":{"id":"1903.01313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-04T15:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"08be74feea85551d6c3db010e5512b02b856ae689e5fa35ffcff4c32ee31bf14","abstract_canon_sha256":"da9405e751a4700b6bc8818a3b7c6457c3f677ba263454f720ef2250604a8471"},"schema_version":"1.0"},"canonical_sha256":"a9c7b0c8bd768f9fa63aefa6588c2ebaef4f0c3387b64ba8d1017df431e1c8ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:09.121561Z","signature_b64":"sIhoPnGmlP6t1A2k1UxW9Q8nb3N8gmZpP4bx2BdxEGnlJz4jkiyBvZnMeB3N53Maz0rDM8YIX8a30lXsFgMOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9c7b0c8bd768f9fa63aefa6588c2ebaef4f0c3387b64ba8d1017df431e1c8ea","last_reissued_at":"2026-05-17T23:52:09.120991Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:09.120991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.01313","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":"2026-05-17T23:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJjqWJXXbJlxcciFemoqCC7Se8AH52TlrPmzvXz4QqxM69PV+86X8DjRSdbTGq4rkYLzXNRODGJ2fLsw7brpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:54:23.248108Z"},"content_sha256":"c3e48a5228f7597d069553f405231067481ecc4c110fcd38dafcc9a53ad15b26","schema_version":"1.0","event_id":"sha256:c3e48a5228f7597d069553f405231067481ecc4c110fcd38dafcc9a53ad15b26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VHD3BSF5O2HZ7JR256TFRDBOXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simson Identity of Generalized m-step Fibonacci Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Y\\\"uksel Soykan","submitted_at":"2019-03-04T15:45:44Z","abstract_excerpt":"One of the best known and oldest identities for the Fibonacci sequence $F_n$ is  $F_{n+1}F_{n-1}-F_{n}^2=(-1)^n$ which was derived first by R. Simson in 1753 and it is now called as Simson or Cassini Identity. In this paper, we generalize this result to generalized m-step Fibonacci numbers and give an attractive formula. Furthermore, we present some Simson's identities of particular generalized m-step Fibonacci sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01313","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":"2026-05-17T23:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+C5i1ZoQ/Kzi9sFQfBlL9NE3olsLpX8QiMhO0bunZLVSyGYQk76oFTXFautrgzAeG1/v1jXFrdELFk9PnJvvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:54:23.248662Z"},"content_sha256":"59e54e21f5079546f0e987d7e3a2b91c826aab8a944536f10ab0ab274e75e4f6","schema_version":"1.0","event_id":"sha256:59e54e21f5079546f0e987d7e3a2b91c826aab8a944536f10ab0ab274e75e4f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHD3BSF5O2HZ7JR256TFRDBOXL/bundle.json","state_url":"https://pith.science/pith/VHD3BSF5O2HZ7JR256TFRDBOXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHD3BSF5O2HZ7JR256TFRDBOXL/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":"2026-05-31T04:54:23Z","links":{"resolver":"https://pith.science/pith/VHD3BSF5O2HZ7JR256TFRDBOXL","bundle":"https://pith.science/pith/VHD3BSF5O2HZ7JR256TFRDBOXL/bundle.json","state":"https://pith.science/pith/VHD3BSF5O2HZ7JR256TFRDBOXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHD3BSF5O2HZ7JR256TFRDBOXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VHD3BSF5O2HZ7JR256TFRDBOXL","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":"da9405e751a4700b6bc8818a3b7c6457c3f677ba263454f720ef2250604a8471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-04T15:45:44Z","title_canon_sha256":"08be74feea85551d6c3db010e5512b02b856ae689e5fa35ffcff4c32ee31bf14"},"schema_version":"1.0","source":{"id":"1903.01313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01313","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01313v1","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01313","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"VHD3BSF5O2HZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VHD3BSF5O2HZ7JR2","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VHD3BSF5","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:59e54e21f5079546f0e987d7e3a2b91c826aab8a944536f10ab0ab274e75e4f6","target":"graph","created_at":"2026-05-17T23:52:09Z","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":"One of the best known and oldest identities for the Fibonacci sequence $F_n$ is  $F_{n+1}F_{n-1}-F_{n}^2=(-1)^n$ which was derived first by R. Simson in 1753 and it is now called as Simson or Cassini Identity. In this paper, we generalize this result to generalized m-step Fibonacci numbers and give an attractive formula. Furthermore, we present some Simson's identities of particular generalized m-step Fibonacci sequences.","authors_text":"Y\\\"uksel Soykan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-04T15:45:44Z","title":"Simson Identity of Generalized m-step Fibonacci Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01313","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:c3e48a5228f7597d069553f405231067481ecc4c110fcd38dafcc9a53ad15b26","target":"record","created_at":"2026-05-17T23:52:09Z","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":"da9405e751a4700b6bc8818a3b7c6457c3f677ba263454f720ef2250604a8471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-04T15:45:44Z","title_canon_sha256":"08be74feea85551d6c3db010e5512b02b856ae689e5fa35ffcff4c32ee31bf14"},"schema_version":"1.0","source":{"id":"1903.01313","kind":"arxiv","version":1}},"canonical_sha256":"a9c7b0c8bd768f9fa63aefa6588c2ebaef4f0c3387b64ba8d1017df431e1c8ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9c7b0c8bd768f9fa63aefa6588c2ebaef4f0c3387b64ba8d1017df431e1c8ea","first_computed_at":"2026-05-17T23:52:09.120991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:09.120991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sIhoPnGmlP6t1A2k1UxW9Q8nb3N8gmZpP4bx2BdxEGnlJz4jkiyBvZnMeB3N53Maz0rDM8YIX8a30lXsFgMOBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:09.121561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3e48a5228f7597d069553f405231067481ecc4c110fcd38dafcc9a53ad15b26","sha256:59e54e21f5079546f0e987d7e3a2b91c826aab8a944536f10ab0ab274e75e4f6"],"state_sha256":"100af836cef2dd4c42c25a6dd433dccd2310719c1aa926b11db6d4712709e4b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxgoxY+en3fPqwRUAwPIAuGdy40SOd2jtptAlw1Qc2CMVtnFyYYevBMLnZWPSAxKYGLUlq0IK9kKu7nGyZJ9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:54:23.252900Z","bundle_sha256":"a1e6b7ce2882600c59098966f84c909cf5de00d501422f20914c48482036d1b1"}}