Many known numbers, one reading: a census of the constants touched by a two-mirror geometry, with a registered prediction for the dark-to-baryon ratio

Standard physics leaves many numbers free. This record lists the known numbers touched by the readings of the author's framework, Mathematical Materiality (MM), and asks which of them MM reads in a form that no other work we found gives. The work goes from the data to MM. A reading chosen after looking at the data is admitted if its choices are declared; only a fixed reading applied to data not yet seen is called a prediction. (1) One rule, two distant numbers. A single geometric factor, √3 per spatial direction between two mirror images, reads the cosmic dark-to-baryon ratio Ω_c/Ω_b = 3√3 = 5.196 and the galactic acceleration scale a₀ = cH₀/6. The two most recent CMB combinations, which share data, read 3√3 within 2σ: P-ACT-LB2 gives 5.199 and CMB-SPA + DESI DR2 gives 5.254 ± 0.037, with the correlations of the published chains. Planck 2018 alone is at 2.1σ. SPARC reads cH₀/6 within its systematic uncertainty. The reading was chosen knowing these values and its choices are declared: it is a coherent reading, not a derivation. (2) The census. The census is a selection from a working catalogue that is still partial. It has 18 entries compatible with the measurements, or not excluded, under conditions stated row by row. They include: 3√3 and cH₀/6, with the cluster baryon fraction as a rewriting of 3√3; the shape of a₀(z); Koide's 2/3, and a mirror Koide relation for down quarks; Σm_ν = 0.0593 eV, from a relation already proposed by Brannen, allowed by the ΛCDM bounds that allow the normal ordering; M_W at 0.7σ, λ(M_P) at 1.3σ and the first-row CKM deficit at 1.5σ, with the conditions stated in the table; γ = β = 1, if R is a pure ratio of units; the Tsirelson bound; the maximum compactness 0.466 of an ideal uniform-density star with the isotropic variable. Seven entries have a future check, and the unfavourable outcomes are reported too. The strong coupling itself is not read: α_s enters as data, and readings that return it through the ratio R of the inverse strong and weak couplings are discarded by construction. Two non-circular relations remain, both chosen after looking at the data. The first, α₃ = (α₂ + 2α_Y)/3 at the Planck scale, has its fixed point at 0.11625 with the PDG 2025 inputs and 0.11666 with the PDG 2026 inputs: z = −1.08 against the world average, and z = −2.02 with the ALPHA 2026 lattice value as input (tension, not exclusion). Its prospective test on the next PDG edition and the next FLAG review is registered and included; a compatibility counts as precise only if σ_tot ≤ 0.070. The second, Y/W = (F/W)^(3/2), is in tension with ALPHA (3.3σ) and is not tested further. The entries are not independent numbers. Where standard physics or another author gives the same number or relation (general relativity, quantum mechanics, Koide, Brannen, Rivero, Verlinde), the table says so: there MM is compatible, not distinctive. (3) The distinctive form. Among the precedents we identified, only Verlinde's emergent gravity (2016) gives both relations: a_M = cH₀/6, and Ω_D² = (4/3)Ω_B. He presents the second as a conjectural extension; here it is taken as exact with Ω_D = Ω_c. It gives ω_c/ω_b = 2h/√(3ω_b), equal to 3√3 only for Ω_b = 4/81, i.e. for h = (9/2)√ω_b, about 0.675. In MM the ratio is 3√3 for any h. A test was registered before the calculation, using ΛCDM parameters from Planck 2018, P-ACT-LB2 and CMB-SPA + DESI DR2 and a declared grid of correlations. Today it does not separate the two forms: P-ACT-LB2 gives a hint towards MM, CMB-SPA + DESI a hint towards Verlinde, and Planck is undecided. Rerun with the correlations of the published chains (for P-ACT-LB2, which has no public chain, those of P-ACT-LB with DESI DR1 BAO, as a proxy), each combination falls in a single zone (Planck then gives a hint towards Verlinde), and none reaches a preference. (4) A registered prediction. Two future data sets may decide between the two forms, or leave the comparison open: the first DESI BAO release beyond DR2 combined with the CMB, and the first Simons Observatory parameters combined with DESI. The rules for them are fixed in advance and applied by a program, which passes 71 edge-case tests. Only articles posted after 16 October 2026, 02:22:54 UTC are admitted; a query of the arXiv API at 01:49 UTC that day found none among the indexed articles. The rules, in short: A relation falls if χ² > 9. A relation also falls if χ² > 4 while the other is preferred (Δχ² beyond 4) and compatible, unless a single matrix of another admissible combination favours it. The MM reading of the ratio receives an A-confirmation, on a parameter already used to choose it, if MM is preferred and compatible and no single matrix of another admissible combination gives a contrary hint. «7.51 favoured» is the symmetric outcome. A confirmation in one block does not hold overall if the other block contradicts it. Numbers made public before registration lower a confirmation to grade B*. If the MM reading falls, what falls is the MM reading of the ratio. The procedure, data and program of today's test were registered with SHA-256 before the calculation; outcome notes and revised versions of the prediction were registered afterwards, each with its time; the rules of the prediction were fixed before any target data. These registrations are local. The public timestamp is the publication date of this record. The test and the prediction went through four rounds of checks by AI reviewers (Codex/GPT-6 and Gemini), whose numbers were rechecked by code. python codice/run_all.py reruns every program and compares its output with the reference files, in under a minute. Before publication, every number of the census that can be recomputed from public inputs was recomputed by code, and the Standard Model running was checked against the couplings at the Planck mass and their derivatives published by Buttazzo et al. (2013, eq. 61): 10 checks out of 10 within thresholds fixed in advance. The author is not a professional physicist; computations were done with AI assistants (Claude, with checks by Codex and Gemini), not reviewed by a human referee.