Can one hidden-sector reading cover several dark-matter puzzles? Consistency checks of Ω_c/Ω_b = 3√3 against Planck and DESI DR2, the evolution of the RAR scale, and limits on uniform decay

This record asks whether one reading of dark matter suggested by the author's framework (Mathematical Materiality, MM) can connect several dark-matter puzzles, and confronts the parts that give numbers with public data. The cosmological ratio fit, the evolution of the radial-acceleration-relation (RAR) scale, the decay analysis and the hidden-sector constructions are separate investigations; no joint likelihood or complete dynamical model is presented. Hypothesis (declared, not derived): the effective gravitating cold-dark-matter density represents hidden-sector matter with its own internal interactions — in MM terms the ordinary matter of a «mirror», normal in its own laws, with constants read relative to ours, left generic — with the mean ratio ρ_c/ρ_b = 3√3 imposed separately. It is additionally postulated that hidden radiation does not source our expansion; no covariant implementation is provided. Consistency checks (python riproduci.py: 745 checks; the cosmological minimisations are archived, not re-run): (1) in flat ΛCDM, imposing ω_cdm = 3√3·ω_b costs T_B = 0.17 with Planck 2018 lite + low-ℓ + DESI DR2 BAO and 0.23 adding the Planck lensing reconstruction (CLASS + Cobaya); free ratios 5.22 and 5.21 — a retrospective check, with a prospective test registered; (2) in the four MUSE-DARK III bins the RAR scale increases with redshift; among constant, H(z) and inverse-age laws H(z) has the lowest χ² (5.48 with bars as 1σ, 21.04 as 95 %), not uniquely selected; registered for future data; it replaces, as working law, the inverse-age law of MM 2.42 (reassessed in version 2.42.1); (3) no preference for constant-rate decay of almost all dark matter into dark radiation; nominal provisional bounds on the comoving loss of about 2.6 % (with lensing) and 3.8 % (without); (4) the baryon fraction 0.161 is a rough match to cluster baryon budgets, while the galaxy RAR does not describe clusters. A table states which puzzles the reading tries to connect (dark-to-baryon ratio, cosmological scale of a0, absence of direct-detection signals, cold cosmology with galaxy RAR), the quantitative status of each, and related approaches. The case for the reading rests on this consilience, and it grows only as more links become quantitative (today two of four). A worked one-factor realisation of the hidden sector satisfies two approximate screening inequalities but does not establish a viable sector. Part of an earlier unpublished draft (the MM algebra of hidden sectors and the separation of light) is included. Withdrawn statements are recorded. The author is not a professional physicist; the framework and its premises are his. Computations and code by Claude (Anthropic) with dated protocols and SHA-256 content hashes; cross-checks by a second AI assistant (Astra, GPT-6), whose corrections are applied and documented. No human referee has reviewed this record.