Mathematical Materiality (MM) in brief. MM starts from one thesis: the laws of physics are not rules that something makes matter obey; matter is the relations of mathematics itself. In logic, nothing exists on its own: to exist means to exist in relation to another logical entity, and outside this web of relations nothing can exist, not even other universes. In the first logical nexus between space and time, which with Einstein became homogeneous, there is a non-local phase, made only of a logical distinction: space is not time, with no relation of quantitative calculation between the two, except the common logical entity they share, which is needed to make them exist for each other. It is not a distant level: it is present in every phase of reality, in every place and at every instant. It shows in entanglement, where two distant systems remain correlated more strongly than any explanation with separate properties and no influence faster than light allows, without anything travelling between them. In this non-local phase the two distinct terms, space and time, share only one logical element, which we shall call their greatest common divisor (GCD), just as the numbers 3 and 5 share only 1. The local world arises when a relation is counted through this GCD: its multiples and its fractions form a matrix. Read by an observer inside it like us, the multiples appear as time and the fractions as space. That same multiple, when it is directly contained in the matrix of the point of observation, turns into mass, that is, into concrete matter as it is ordinarily understood. Time and mass are therefore closely related, in agreement with Einstein's relativity, which ties mass to spacetime. The observed objects, while being logically autonomous entities in their local relations, are related to the observer through a logical diffraction, in fractions, of the observer's matrix. Quantum mechanics offers a further confirmation, as MM reads it. Here the non-local phase and the logical mirror reciprocity between the two ends of the nexus account for the probabilistic behaviour of matter. When the observed object is large enough, its mass fixes it in the matrix of the point of observation: we see it in one place and at one instant. When it falls below a certain mass level, the principal GCD, that of the point of observation, and the GCD of the diffraction that generates the object are forced to become equal, as in a mirror: the object no longer occupies a single point of the spacetime generated by the observer but spreads over several possible positions, and we observe it as probability. It is like having to describe a 10 using only the number 1: the only way is to distribute the 1 over ten positions, one for each unit of the 10. The idea that the passage from quantum to classical behaviour depends on mass is close to that of Penrose and Diósi; in MM the threshold is the point where the two GCDs, the principal one and that of the local diffraction, become equal. For all these reasons the universe behaves like a simulation without being one. It follows exact rules, made of counts, everywhere and at every instant, but no machine runs them and no programmer wrote them: a structure of mathematical relations does not need to be computed in order to exist. That such a simulation need not be run had already been noted by Tegmark (2008); Vazza (2025) estimated that running it on a machine would require resources that the laws of the universe do not allow. This record develops one aspect of the framework. Four-page summary: DOI 10.5281/zenodo.23535916. Entry page, with the list of all records: DOI 10.5281/zenodo.22667516. This record. Physics already ties mass to time: every mass carries a rhythm, the Compton frequency mc²/h, and all bodies fall in the same way within a few parts in 10¹⁵. This deposit tests one thesis of the framework: the same counting is time when it is read, and mass when it stays contained. Read: it becomes a row of distinct events, like the ticks of a clock. Contained: it stays inside the thing as a rhythm that produces no distinct events, like a top spinning in a closed box. In this reading mass is made of time, time held inside the thing; and what weighs is the value of the rhythm, the total energy including binding, not the count of the pieces. It is the twin of deposit 2.62 on observed objects (DOI 10.5281/zenodo.23609967): in the counting, fractions give objects and distances, multiples give time and mass. How it was tested. Eleven translations of the thesis into measurable quantities, a reference (standard physics), a neutrino threshold, seven criteria and the outcome rules were registered before any calculation, then confronted with MICROSCOPE, lunar laser ranging, a neutron-interferometer geometry, the AME2020 atomic masses, the Margolus–Levitin and Lloyd bounds, JUNO 2026 and DESI. Excluded: the count of the pieces weighs (titanium and platinum would fall with a difference of 7.5 × 10⁻⁴, 2.7 × 10¹¹ standard deviations from MICROSCOPE; at most a fraction 5.3 × 10⁻¹² of gravity can act on the count; aluminium against iron, 1.3 × 10¹⁰ times the lunar-laser limit on active mass; Earth and Moon, 1.7 × 10⁴ standard deviations); masses growing with the age of the cosmos (1.5 × 10⁴ standard deviations, with a declared mapping); mass as the number of distinct states per second counted from rest (it gives zero to a particle at rest). Compatible, and coinciding with standard physics: mass as the Compton rhythm; as the Komar mass; as a value that, seen from far away, drops with the rate of clocks; and as the ceiling on distinct states, counting energy from the vacuum: at most two distinct states per Compton cycle in a long sequence (Margolus–Levitin), four logical operations per cycle (Lloyd). Not concluded: whether the Compton rhythm leaves a readable copy at every cycle (about 25 copies of difference in the neutron-interferometer geometry; the sources disagree on how to read the observed gravitational phase). Not testable today: the mass-dependent fall of the checkerboard of deposit 2.40, about 10⁻⁴² for titanium and platinum with the Planck step; with a free step MICROSCOPE requires a step shorter than about 10⁻²¹ m. Neutrinos: the Koide relation of deposit 2.38 (Brannen's prediction) gives Σ = 0.0591 eV with the JUNO 2026 data; decision rules are registered with a deadline of 31 December 2035; the DESI Feldman–Cousins limit (0.053 eV) lies below the minimum of the normal ordering. No translation gives a distinctive prediction today. Prior work, first. Margolus and Levitin (1998) and Lloyd (2000) on energy and the maximum rate of distinct states; Zych, Costa, Pikovski and Brukner (2011) on proper time and interferometric visibility; Wolf et al. (2011) on the Compton frequency in atom interferometers; Lan et al. (2013), the Compton clock; Greenberger (2010); Margalit et al. (2015), a self-interfering clock; Pikovski et al. (2015) and Zych and Brukner (2018) on the mass of composite systems; MICROSCOPE (Touboul et al. 2022); Singh et al. (2023); Komar (1959); Nordtvedt (1968); Koide (1982-1983); Brannen (2006); Dirac quantum walks (Bialynicki-Birula 1994; Meyer 1996; Arrighi, Nesme and Forets 2014; D'Ariano and Perinotti 2014). What is not claimed. No mass is derived and no mass value is fitted: particle masses remain measured data. The framework is not claimed to explain mass; the compatible readings coincide with standard physics by identity or by construction and are not independent proofs. The neutrino prediction is not new. The neutron fringes are not claimed to exclude copies of the Compton rhythm. Contents. README.md (English) and LEGGIMI_IT.md (Italian), with the full text and a glossary; AUTHOR_BACKGROUND.md with the author's sentences; the registered protocol, two corrections and the outcome notes; three Python programs with their results; three verification reports by a second AI (gpt-6-luna via Codex), two on the calculations and one on the package, with the answers; registers with SHA-256 fingerprints and UTC times; run_all.py, which re-runs everything in a few seconds and compares the results with the registered ones (the AME2020 table is downloaded from the IAEA and checked by its fingerprint). The author is not a physicist; translations, programs and calculations were made with Claude (Anthropic). The work has not been reviewed by a human referee.
No takes yet. Share an insight, caveat, or question.
Ugo Lanciano (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: