{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R3GWSVUUUSUJOIONU45MYU57PL","short_pith_number":"pith:R3GWSVUU","canonical_record":{"source":{"id":"1407.8086","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2014-07-30T15:22:52Z","cross_cats_sorted":[],"title_canon_sha256":"d35b032d7579978bdbe86538d2fbf270fc29c081e59020383a86d30a867693b7","abstract_canon_sha256":"3ffdbe8e4e662123a5813506143f4bf16bf286116a7c9d6c3512ba17aa712ca5"},"schema_version":"1.0"},"canonical_sha256":"8ecd695694a4a89721cda73acc53bf7adea1439ad9d0b98365af011f18f19a50","source":{"kind":"arxiv","id":"1407.8086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8086","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8086v1","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8086","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"R3GWSVUUUSUJ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R3GWSVUUUSUJOION","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R3GWSVUU","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R3GWSVUUUSUJOIONU45MYU57PL","target":"record","payload":{"canonical_record":{"source":{"id":"1407.8086","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2014-07-30T15:22:52Z","cross_cats_sorted":[],"title_canon_sha256":"d35b032d7579978bdbe86538d2fbf270fc29c081e59020383a86d30a867693b7","abstract_canon_sha256":"3ffdbe8e4e662123a5813506143f4bf16bf286116a7c9d6c3512ba17aa712ca5"},"schema_version":"1.0"},"canonical_sha256":"8ecd695694a4a89721cda73acc53bf7adea1439ad9d0b98365af011f18f19a50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:13.637499Z","signature_b64":"sRTry+E+bfxHciCM4KOcHGhngcqPO+dFKFpFJZloTLGgtLSs3XIBGgsLP7fr3fOKa4HnsOhzJh1eDrZhMayCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ecd695694a4a89721cda73acc53bf7adea1439ad9d0b98365af011f18f19a50","last_reissued_at":"2026-05-18T02:46:13.636748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:13.636748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.8086","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":"2026-05-18T02:46:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8EiVMPfcK+uFkmN1wBJmGRasnAwMYuVa/SyYdAlCUjI6tZnDgMeU3vZhDLUvE1JoUdFkFOmq9Lh4Q4JxzO2oBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:04:09.962344Z"},"content_sha256":"59e93419771a5f14843626f3d4e2861cfc78d2982b7b578f8b6d5e8f2d9f1683","schema_version":"1.0","event_id":"sha256:59e93419771a5f14843626f3d4e2861cfc78d2982b7b578f8b6d5e8f2d9f1683"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R3GWSVUUUSUJOIONU45MYU57PL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic properties of generalized Fibonacci sequences","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Soohyun Park","submitted_at":"2014-07-30T15:22:52Z","abstract_excerpt":"The generalized Fibonacci sequences are sequences $\\{f_n\\}$ which satisfy the recurrence $f_n(s, t) = sf_{n - 1}(s, t) + tf_{n - 2}(s, t)$ ($s, t \\in \\mathbb{Z}$) with initial conditions $f_0(s, t) = 0$ and $f_1(s, t) = 1$. In a recent paper, Amdeberhan, Chen, Moll, and Sagan considered some arithmetic properites of the generalized Fibonacci sequence. Specifically, they considered the behavior of analogues of the $p$-adic valuation and the Riemann zeta function. In this paper, we resolve some conjectures which they raised relating to these topics. We also consider the rank modulo $n$ in more d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8086","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":"2026-05-18T02:46:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bm/hUEqUfxDreTqtEkjjFepU2LGBJoEC9QiwKEazrJnpPC8DbIV929zZnM7fovQc40mBLIOZZ3XxvrpaFPYhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:04:09.963064Z"},"content_sha256":"d64d364f1c3dfab16704fbc23e6c1458c2c63ad0ec927ce69e2182c340ed4487","schema_version":"1.0","event_id":"sha256:d64d364f1c3dfab16704fbc23e6c1458c2c63ad0ec927ce69e2182c340ed4487"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R3GWSVUUUSUJOIONU45MYU57PL/bundle.json","state_url":"https://pith.science/pith/R3GWSVUUUSUJOIONU45MYU57PL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R3GWSVUUUSUJOIONU45MYU57PL/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":"2026-05-31T23:04:09Z","links":{"resolver":"https://pith.science/pith/R3GWSVUUUSUJOIONU45MYU57PL","bundle":"https://pith.science/pith/R3GWSVUUUSUJOIONU45MYU57PL/bundle.json","state":"https://pith.science/pith/R3GWSVUUUSUJOIONU45MYU57PL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R3GWSVUUUSUJOIONU45MYU57PL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R3GWSVUUUSUJOIONU45MYU57PL","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":"3ffdbe8e4e662123a5813506143f4bf16bf286116a7c9d6c3512ba17aa712ca5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2014-07-30T15:22:52Z","title_canon_sha256":"d35b032d7579978bdbe86538d2fbf270fc29c081e59020383a86d30a867693b7"},"schema_version":"1.0","source":{"id":"1407.8086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8086","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8086v1","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8086","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"R3GWSVUUUSUJ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R3GWSVUUUSUJOION","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R3GWSVUU","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:d64d364f1c3dfab16704fbc23e6c1458c2c63ad0ec927ce69e2182c340ed4487","target":"graph","created_at":"2026-05-18T02:46:13Z","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":"The generalized Fibonacci sequences are sequences $\\{f_n\\}$ which satisfy the recurrence $f_n(s, t) = sf_{n - 1}(s, t) + tf_{n - 2}(s, t)$ ($s, t \\in \\mathbb{Z}$) with initial conditions $f_0(s, t) = 0$ and $f_1(s, t) = 1$. In a recent paper, Amdeberhan, Chen, Moll, and Sagan considered some arithmetic properites of the generalized Fibonacci sequence. Specifically, they considered the behavior of analogues of the $p$-adic valuation and the Riemann zeta function. In this paper, we resolve some conjectures which they raised relating to these topics. We also consider the rank modulo $n$ in more d","authors_text":"Soohyun Park","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2014-07-30T15:22:52Z","title":"Arithmetic properties of generalized Fibonacci sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8086","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":"sha256:59e93419771a5f14843626f3d4e2861cfc78d2982b7b578f8b6d5e8f2d9f1683","target":"record","created_at":"2026-05-18T02:46:13Z","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":"3ffdbe8e4e662123a5813506143f4bf16bf286116a7c9d6c3512ba17aa712ca5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2014-07-30T15:22:52Z","title_canon_sha256":"d35b032d7579978bdbe86538d2fbf270fc29c081e59020383a86d30a867693b7"},"schema_version":"1.0","source":{"id":"1407.8086","kind":"arxiv","version":1}},"canonical_sha256":"8ecd695694a4a89721cda73acc53bf7adea1439ad9d0b98365af011f18f19a50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ecd695694a4a89721cda73acc53bf7adea1439ad9d0b98365af011f18f19a50","first_computed_at":"2026-05-18T02:46:13.636748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:13.636748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sRTry+E+bfxHciCM4KOcHGhngcqPO+dFKFpFJZloTLGgtLSs3XIBGgsLP7fr3fOKa4HnsOhzJh1eDrZhMayCDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:13.637499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.8086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e93419771a5f14843626f3d4e2861cfc78d2982b7b578f8b6d5e8f2d9f1683","sha256:d64d364f1c3dfab16704fbc23e6c1458c2c63ad0ec927ce69e2182c340ed4487"],"state_sha256":"c76a32b97747f741057b5d78b6b65cd971df8bb4c6ba64970cc137bba4abe916"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RLyK7PnhhwzOV2I2cNNiUHg2VjiotR2yH1ZuxtKYjeBN4mRBppW9nUvTNejHPq/wlPmfAVUXsCD0zvhW8WWcAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:04:09.967858Z","bundle_sha256":"c3c7487ddba9e4fab8465d4a4dc18a17c720fa692d66276fea1df2f21c7dafd2"}}