Candidate 3: An Audited Mixed-Recurrence Cross-Determinant Integer Sequence

This record archives Candidate 3, a well-defined integer sequence constructed from cross-determinants of Fibonacci, Pell, Lucas, Jacobsthal, and Tribonacci-type recurrences. The sequence is defined by Sₙ = D₍F,P₎⁽¹⁾(n) + 2D₍F,T₎⁽²⁾(n) + 2D₍L,J₎⁽¹⁾(n) + 2D₍J,T₎⁽¹⁾(n), where D₍A,B₎⁽ᵏ⁾(n) = AₙBₙ₊ₖ − Aₙ₊ₖBₙ, with the component sequences defined by their stated linear recurrences and initial values in the accompanying reports. The archive contains a reader-friendly PDF summary and a complete ZIP package containing the mathematical reports, audit scripts, selected audit outputs, reproducibility instructions, manifests, and SHA-256 checksums. The accompanying reports document exact generating-function and recurrence audits, an all-n positivity result within the stated computer-assisted certificate, a wider coefficient-family certificate based on FLINT/Arb outward rounding, and structural investigations of the coefficient vector (1, 2, 2, 2). The structural investigation reports NO_KNOWN_REDUCTION_FOUND_WITHIN_INSPECTED_CLASSES and STRUCTURAL_OBSTRUCTION_WITHIN_TESTED_CLASSES. These are scope-limited computational and mathematical findings, not universal impossibility theorems. NOVELTY_UNRESOLVED and HISTORICAL_PRIORITY_NOT_ESTABLISHED remain the conservative classifications. The OEIS record A399323 is preserved as part of the provenance history. Its editorial status is recorded as recycled after an editorial-interest decision that the definition was considered too arbitrary or insufficiently motivated for inclusion. This outcome is not treated as a mathematical disproof of the sequence definition, the calculations, or the accompanying certificates. This record is a technical research artifact. It is not presented as a peer-reviewed publication, a novelty certification, a historical-priority certification, an OEIS acceptance, or an endorsement by Zenodo or CERN. A Zenodo DOI identifies the archival release and does not itself validate the mathematics. The original 2026-08-26 reference snapshot is preserved separately. This post-OEIS release is a dated derivative archive documenting the state of Candidate 3 after the OEIS editorial outcome.