Late cosmic acceleration as a reading of the observer's clock tied to the growth of structure: registered tests against DESI DR2, supernovae, CMB distance priors and growth data

In its own combinations with the CMB and supernovae, DESI DR2 prefers an evolving dark energy with w0 > −1 and wa < 0 over ΛCDM at 2.8–4.2σ (DESI Collaboration 2025). This record tests the dark-energy history of the author's framework, Mathematical Materiality (MM), against DESI DR2 BAO, compressed CMB distance priors (Chen, Huang and Wang 2019) and three supernova samples, and against the growth of structure. It then proposes a phenomenological hypothesis, read with MM by coherence: the late acceleration as a reading of the observer's clock that changes with the growth of cosmic structure. Every test was registered with SHA-256 fingerprints before its computation (knowing earlier results on the same data, as each registration states); additions decided after seeing results are labelled; failed predictions are reported. An independent AI system checked each block in one to nine rounds. It is an exploratory, preliminary study. (1) The MM 2.32 family against DESI DR2. The published 2.32 expansion history has w ≥ −1 by construction. With DESI DR2 BAO, the CMB priors and Pantheon+, Union3 or DES-Dovekie supernovae, the three registered readings are "in tension" (2.1–3.1σ). Two of them use an analytic statistic checked against simulations, and the third is calibrated with simulations (runs of 400, some extended to 2000). None meets the criterion "falls". Without DESI BAO the two CPL-type readings hold. (2) What the data ask without MM. Parametric reconstructions in redshift bands place the deviation from ΛCDM at z ≈ 0.4–1, not on the CMB distance. Radial and transverse distance readings separated do not differ beyond 1.8 times their error. (3) The hypothesis. Consider a background of matter and radiation with no dark energy, whose expansion rate, as read by the observer, is raised by a factor 1 + δ0 S(z). S follows the growth of structure, and δ0 is fixed by flatness. With S = (D/D0)^n and the ΛCDM growth curve it fits DESI DR2, the CMB priors and the three supernova samples better than ΛCDM by 6.6–11.6 in χ², close to CPL with one parameter fewer. The collapsed fraction and the growth of a universe without dark energy, used as tracers, are excluded or disfavoured. The distance rule is an additional assumption and the exponent n ≈ 3.5–3.7 is fitted. (4) Built from measured growth. The factor can also be built from measured fσ8 (DESI DR1 or SDSS), fitted jointly with the expansion in the approximation of independence and with growth not faster than in the matter era. This improves on ΛCDM plus a free growth curve by 8–13, with as many parameters as CPL plus the curve; joint covariances of DESI growth and BAO are not treated, so this result is preliminary. With DESI growth, the growth computed with the standard perturbation equations (CAMB-PPF) in the resulting read history agrees with the curve used at the checked redshifts in two of three supernova samples. Today's amplitude agrees within 0.75 % with the one from Planck's adopted A_s; with SDSS growth it does not. That check did not feed the computed growth back into the clock law; point (5) does. (5) Self-consistent closure. The factor can follow the linear growth that the read history itself produces, found as a fixed point, with no external or fitted growth curve and one parameter more than ΛCDM. That version fits better than ΛCDM by 7.0–11.8, within 0.3–2.0 of CPL. Its growth is computed from the central values of Planck's primordial amplitude. It is compatible with SDSS, DESI and 6dFGS growth data, with χ² close to ΛCDM's (σ8 = 0.797–0.808). It is a closure within the adopted linear, scale-independent dynamics. The effective equation of state is ≈ −0.8 today and crosses −1 between z ≈ 0 and 0.5. (6) Growth of structure for the MM 2.32 family. At the tested points and under the declared approximations, with A_s fixed to Planck's central value, the expansion histories tested in (1), with their variants, are compatible with SDSS, DESI DR1 and 6dFGS growth under a registered rule (one case at 2.1σ). The measurements do not distinguish them from ΛCDM. Along 400 samples of the published 2.32 chain, the median σ8 is 0.790 (95 %: 0.771–0.800). It is below paired ΛCDM with the same h, ω_b and Ω_m in every sample; the median paired difference MM − ΛCDM is −0.0069 (95 %: −0.016 to −0.002). No paired Δχ² exceeds 4, and 2 % of the samples are in tension in S1-growth only through the amplitude (at most 2.4σ). At three chain points, the coupled Boltzmann run with the MM kernel agrees with CAMB within the registered thresholds. In the branch with no additional vacuum component, at the tested grid points and with the adopted normalizations, the relative rms-response bounds are 1.1×10⁻⁵ for matter density and 3.8×10⁻⁵ for its derivative with respect to ln a. The calculation uses linear sub-horizon dynamics, without matter back-reaction on the source or relativistic terms. These are not bounds on fσ8. (7) Reading MM 2.32 now. The constraint w ≥ −1 of 2.32 comes from a translation of record counts into energy and pressure, not from the author's premises. The published version stands as computed, and a translation of its counts into the clock reading remains to be specified. The closest precedent is the timescape cosmology of Wiltshire, which attributes apparent acceleration to the clocks of observers in bound structures; the model here uses neither voids nor Buchert averaging. The hypothesis is offered as plausible because one rule answers several requirements at once (acceleration without Λ, a late onset, the evolving-w shape favoured by these parametrizations and data, growth compatible with the data), not because any test decides. It does not distinguish the clock reading from a dark-energy component with the same expansion history. Third-party data are not redistributed; their origins and SHA-256 fingerprints are listed. The author is not a professional physicist; computations were done with AI assistants (Claude and Codex), not reviewed by a human referee.