A finite-data criterion for Feigenbaum convergence in real-analytic unimodal families

We give a finite-data criterion for Feigenbaum parameter scaling in real-analytic unimodal families with a quadratic critical point. Implementation requires supplied holomorphic domains, outward evaluators, mixed jets, and Cauchy majorants. The hypotheses separate a physical restrictive return, exact analytic conjugacy, function-space entry, and transversality to the true stable manifold. An independently validated infinite-dimensional block encloses the fixed point around a degree-64 polynomial and proves 4.6692016091024<δ<4.6692016091036. A full-function central flip marker and a local analytic argument yield ad+j-a_∞=Cδ⁻ʲ(1+O((4/5)^j)), C≠0. The common pipeline certifies quadratic, sine, Ricker, Gaussian, exponential-quadratic, and Hurwitz instances. Separate local flips are certified through pre-flip period 4096; effective tail bounds start at family-dependent exponents K_0=20 to 29. The intervening finite-to-tail gap remains open. We give outward amplitude intervals, but not an optimal onset or a numerical relative-remainder prefactor. The exponential-quadratic example is conjugate to a reparameterized Ricker family. Standard analytic invariant-manifold theory remains a cited input. MSC 2020: Primary 37E20, 37E05; Secondary 37F25, 65G20, 11M35. Version 1.0.0 (2026-09-06). Files: the manuscript (26 pages); the frozen self-contained reproduction archive (repro_package_v1.0.0_frozen.zip, SHA-256 bc77b2474bfa0f7305ba2928f5f8c95cb41392bf8ca344049f5896be6b072b08) with the self-certified renormalisation operator block, fixed-point ball, unstable-eigenvalue enclosure, six-family pipeline certificates, effective envelopes, finite certificates through pre-flip period 4096, tools, tests and reproduce.sh (tier0 verify / tier1 quick / tier2 full; requirements: Python 3.12+, python-flint 0.9.0, mpmath 1.3.0); abstract; README; LICENSE (manuscript CC BY 4.0, programs MIT). Independent reproduction on a separate x86-64 host: tier0/1/2 all PASS.