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Carmichael,On the numerical factors of the arithmetic formsα n ±β n, Annals of Mathematics15 (1913), 49–70","work_id":"ed54e069-0e98-4ac1-bf87-9a4de6decede","year":1913}],"snapshot_sha256":"cd96ca11339e07836e5247056b52a24fe2488b54f065eb84b2bb37a13d48af4d"},"source":{"id":"2605.17699","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T21:56:11.963897Z","id":"d8a9f7a3-bd6c-4238-8ebd-204a22e15a5d","model_set":{"reader":"grok-4.3"},"one_line_summary":"For the k-generalized Pell sequence defined by the given recurrence, the only multiplicatively dependent pairs P_n^(k) and P_m^(k) occur for small listed values of k, m, n.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"For k at least 2, the k-generalized Pell sequence has multiplicatively dependent terms only for a short list of small indices.","strongest_claim":"For k ≥ 2 the only solutions with n > m ≥ 0 such that P_n^(k) and P_m^(k) are multiplicatively dependent occur for very small k, m, n which are listed explicitly.","weakest_assumption":"That the combination of Matveev's lower bounds and the Baker-Davenport reduction produces an explicit finite bound small enough for exhaustive computational verification, with no missed large solutions outside the reduced range."}},"verdict_id":"d8a9f7a3-bd6c-4238-8ebd-204a22e15a5d"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6afb669aad13448289a89eecc21ebc1efec9f45dcb5f77a38834633a1c3f2260","target":"record","created_at":"2026-05-20T00:04:53Z","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":"97c6d1f62c7fbb61d9318a889be8ca6b914366a5e8e2126290eeac8d6d7494ed","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-17T23:44:44Z","title_canon_sha256":"e83077717febe8576e8212da22e99007067bcec5262cb03288d8c8e45c5ccdd8"},"schema_version":"1.0","source":{"id":"2605.17699","kind":"arxiv","version":1}},"canonical_sha256":"c3a7b8e3b434a1112f8691db4c5e2995426638a08849fa673f6e4f512dc75a1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3a7b8e3b434a1112f8691db4c5e2995426638a08849fa673f6e4f512dc75a1d","first_computed_at":"2026-05-20T00:04:53.453217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:53.453217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/IXTD+SYYA/E9/ueKoeh/L6JPrFPL4szj9NWA2cqWYKG+cf4Qm4klJozTeYpXBHXEuVctzLYijlUDb8IndxUAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:53.454039Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6afb669aad13448289a89eecc21ebc1efec9f45dcb5f77a38834633a1c3f2260","sha256:63f78b57751f0a5f1946962aa1acca4bdb08162b2368edd07a1fd4026b3e0a7e"],"state_sha256":"3644030d3f6a7ddcf9a3fe14a85302cf42cdea5fccbb2b46d36b20ae931b3ef6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRKxSVaFyZABFZnLs6i7QQWnW6/EduO3EnqGKDqMZv2vsbZ5w5DjEpXNuljrSY0cOagzzmmjAZZJxq7lw+I5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:21:38.464971Z","bundle_sha256":"fe781776567a4d2aed7cf20e317bd8253b19930c98d996e40b020625824b62b1"}}