Mathematical Materiality 2.32: An AI-Assisted Cosmological Model Survives Its First Joint Test Across Three Cosmological Probes
Abstract
A model of the universe developed with the assistance of GPT-6 Astra and Claude has survived its first global confrontation with cosmological data. Across supernovae, DESI measurements and the geometry of the cosmic microwave background, it obtains almost the same fit as the standard cosmological model: a chi-square of 1420.02, compared with 1421.19 for ΛCDM. This is not a statistical victory over ΛCDM. The news is that the construction did not collapse. Starting from a fundamentally different account of cosmic acceleration, Mathematical Materiality 2.32 reached almost the same agreement with three major families of observations. From four open problems to a formalized ontology Mathematical Materiality did not begin as an isolated attempt to explain dark energy. The proposal grew out of four problems that contemporary physics describes with great precision but still leaves open at a fundamental level: why physical laws retain the same regularity across different places and epochs; what produces the phenomena currently attributed to dark matter; what physical mechanism lies behind the cosmic acceleration associated with dark energy; what structure of reality could make quantum behaviour and the role of observation intelligible. MM asks whether these apparently separate difficulties may point to a missing level in our description of the world. Its proposal is not to add another particle or substance, but to change what the theory treats as fundamental. Objects, space and observers are described as configurations of the same material relational structure. This is the intended meaning of the name Mathematical Materiality. Mathematics is not merely applied from the outside to a world assumed to be already constituted. It is logically materialized: every distinction used in the mathematics must correspond to an operation that could occur within the proposed ontology. A sign requires a register capable of retaining it; a comparison requires a connection between registers; a memory requires a persistent configuration; and a transformation requires an explicit rule specifying which states may follow one another. On this basis, MM constructs a formalized ontology of registers, relational links, comparisons, memories and permitted transformations. Once these operations have been fixed, their mathematical consequences are not selected to obtain a preferred result. They follow from the composition of the relations and from the probabilistic rules governing their evolution. The theory therefore produces calculable quantities, growth regimes, bounds and failure conditions. The transition from the formal relational structure to cosmology is declared separately. Explicit physical postulates connect the capacity of the structure to volume and its active configurations to energy. This bridge produces a cosmological component with a density, pressure and evolutionary history that can be compared with observations. Version 2.32 does not claim to have solved all four motivating problems. It directly addresses the third — the origin of the effect attributed to dark energy — and submits a cosmological consequence of the formalized ontology to a global observational comparison. The form of the predictions was not adjusted to the observations after the fact: only three dark-sector parameters were fitted, and the shape of the history arises from the formalized ontological architecture together with explicitly declared physical postulates that connect the relational structure to cosmological volume and energy. The comparison with cosmological data The global test uses three observational blocks: 1,590 Pantheon+ light curves, corresponding to 1,473 distinct supernovae above redshift 0.01; 13 compressed geometrical measurements from DESI DR2; three Planck 2018 distance priors summarizing the geometry of the cosmic microwave background at last scattering. The ordinary cosmological parameters were not fixed to their Planck values. They were allowed to vary and were inferred together with the parameters specific to Mathematical Materiality. The best point found by the global chain reaches a total chi-square of 1420.02. ΛCDM, evaluated with the same code, on the same data and with the same freedom in the ordinary cosmological parameters, reaches 1421.19. Chi-square measures the overall mismatch between predictions and observations: a lower value indicates a better fit. Mathematical Materiality, however, introduces three additional parameters in its dark sector. An improvement of approximately 1.17 chi-square units does not compensate for this additional freedom, and statistical model-selection criteria continue to favour ΛCDM. The result should therefore be stated precisely. Mathematical Materiality has not defeated ΛCDM. It has reached the standard model’s level of observational agreement while deriving the shape of its recent cosmic history from a constrained internal construction rather than fitting an arbitrary function of redshift. The first observational bound on the relational parameter The parameter p controls how far the relational dark component departs from the behaviour of a cosmological constant. The global sampling produces the one-sided upper bound p < 0.0724 at 95 per cent credibility. This is not a detection of a departure from ΛCDM. It is the first observational restriction, within this framework, on the permitted amplitude of the relational component. The ordinary cosmological parameters also emerge from the fit. Their posterior medians are: h = 0.6764; ωb = Ωbh2 = 0.02258; Ωm = 0.3066. Within the adopted cosmological framework, these values lie within approximately one standard deviation of the corresponding Planck 2018 results. A prediction capable of ruling out the model Mathematical Materiality exposes a clear failure condition. Its relational dark component cannot cross the threshold w = −1. If future observations were to establish convincingly that cosmic evolution requires the dark component to fall below this value, the model in its present form would be excluded. The deposit also pre-registers the next test, concerning the inhomogeneous sector. Its decision rule and three possible outcomes are stated before the calculation is performed. A global chain made possible by an emulator A direct evaluation of the complete cosmological solver required approximately fifteen minutes. A conventional global Markov-chain analysis would therefore have been impractical. To overcome this limit, a lightweight Gaussian-process emulator was trained on full evaluations of the model. The emulator was tested by repeatedly retraining it without the point it was required to predict. Across 4,608 validation decisions, it produced no false acceptances. Sampling was restricted to the declared domain in which this certification was valid. The final chain used 32 walkers for 8,000 steps. It reached N/τ = 77.4, exceeding the convergence criterion fixed before the run, and yielded an estimated 2,300 independent samples. The chain minimum of 1420.02 agrees with the value of 1420.05 obtained from a separately computed profile that did not use the emulator. Four computational routes recover compatible bounds on p, including two that do not share the same numerical machinery; two of the four are chains that were not run to convergence and serve only as cross-checks. What remains to be tested The reported result concerns primarily the background geometry of cosmic expansion. The cosmic microwave background enters through three Planck 2018 distance priors, not through the complete temperature and polarization spectra. The following have not yet been tested or derived in the global comparison: the growth of cosmic structure; the late integrated Sachs–Wolfe effect; the complete cosmic microwave background spectra; a unique microscopic rule for the entire construction; the value of the vacuum residue. The Friedmann–Lemaître–Robertson–Walker framework, the cosmological history before the transition and the physics of recombination are imported. The recent evolution of the relational dark component is calculated by the model. The earlier restricted comparison using 1,448 DES-Dovekie supernova candidates, retained in Appendices G–H, is separate from the new global fit and preserves the limitations declared in its original analysis. The role of artificial intelligence GPT-6 Astra assisted stages of the physical and mathematical development and independently checked parts of the construction. Claude supplied the source notes and prototypes credited in the article and assisted the later formalization, implementation, global inference, verification and release preparation. Both worked under the direction of the author. AI assistance is not presented as evidence that the model is correct. It is one of the features that makes this case unusual and open to examination: AI systems helped transform an ontological proposal into a cosmological model capable of producing numerical predictions, confronting real observations and declaring in advance the conditions under which it could fail. To support external scrutiny, the deposit includes configurations, code, chain samples, emulator certification, convergence diagnostics and a final audit. How to read the deposit The one-page Press and Expert Note presents the main result, the essential numbers and the first checks that an independent expert may wish to perform. Pages 1–25 of the main article explain the argument without requiring the reader to follow the technical derivations. Appendices S–V contain the global cosmological fit, the MCMC chain, the emulator certification and the limits of the comparison. The two companion reports and the research-materials archive support a more detailed technical examination. Independent cosmologists and other specialists are invited to reproduce, criticize or falsify the result. Mathematical Materiality 2.32 does no
