Not at a distance, but nowhere: non-locality beyond entanglement, in twelve phenomena
Ugo Lanciano
This record. Twelve phenomena, entanglement among them, read through the same non-local phase: «non-local» as not located in space and time, not as action at a distance. Reading path: Foundations: why the laws hold, 5 of 5 · before: Is mass a contained rhythm? · all themes. Common introduction to all the records of this series. The content of this record follows below. Mathematical Materiality (MM) in brief. Why are the laws of physics the same everywhere and at every instant, even though nothing forces matter to obey them? MM proposes an answer: the laws are not rules imposed on matter from the outside; rather, matter itself is made of mathematical relations. And mathematics cannot change: a relation binds two distinct terms everywhere and always. In logic, nothing exists on its own: to exist means to be in relation to another logical entity, and outside this web of relations nothing can exist, not even other universes. This reading already meets experimental measurements at two points. First, the ratio of dark to ordinary matter is read as 3√3 = 5.196; when left free in the fits, Planck and DESI DR2 data give 5.21–5.22 (as registered in record 2.44, https://doi.org/10.5281/zenodo.23329080). Second, the acceleration scale of galaxies is read as a₀ = cH₀/6, the same scale that appears in Verlinde's emergent gravity: the computed value is 1.09–1.18 × 10⁻¹⁰ m/s² against the measured value of 1.20 (record 2.46.1, https://doi.org/10.5281/zenodo.23506655). Both readings were formulated with the measurements already known; the tests to check them against future data are registered in the same records. In the first logical nexus between space and time — which became homogeneous with Einstein — there is a non-local phase, made only of a pure logical distinction: space is not time. Between the two there is no relation of quantitative calculation, only the logical entity they have in common, which is needed to make them exist with respect to each other. This level is not distant: 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 based on separate properties and free of faster-than-light influences allows, without anything physically 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 have only 1 in common. The local world arises when a relation is counted through this GCD: its multiples and its fractions form a matrix. Seen by an observer inside the system like us, the multiples appear as time and the fractions as space. When that same multiple is directly contained in the matrix of the point of observation, it turns into mass — that is, into concrete matter as we usually understand it. There is therefore a close link between time and mass, in full agreement with Einstein's relativity, which ties mass to spacetime. The observed objects, while being logically autonomous entities in their local relations, enter into relation with the observer through a logical diffraction — that is, a decomposition into fractions — of the observer's matrix. This reading also gives a reason for the limit of the speed of light, which in Einstein's relativity is instead taken as a starting principle. The speed of light is the fixed exchange rate between the multiples and the fractions of the same GCD, meaning how much space a single step of time is worth: exceeding it would mean, for some observer, covering space without counting time, and thus leaving the local world. Logic always starts from a logical relative, and this exchange rate has nothing absolute in itself either: it is a necessary relative which, inside the system, becomes an absolute hypothesis, the same for everyone and impossible to exceed. Outside the system, by contrast, it has no justification at all, because outside there is only non-existence: justifying something requires another term to relate it to, and out there there is none. Asking for a reason from outside is like asking what lies north of the North Pole. The same theoretical framework that reads space, time, mass and the observed objects also admits quantum mechanics. The non-local phase and the mirror-like logical reciprocity between the two ends of the nexus give a reason 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: for this reason we see it in one precise place and at one precise instant. When instead the object falls below a certain mass threshold, the principal GCD (that of the point of observation) and the GCD of the diffraction that generates the object are forced to become equal, reflecting each other as in a mirror. At that point 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 the number 10 using only the number 1: the only way is to distribute the 1 over ten positions, one for each unit of the 10. Today we know that even objects made of thousands of atoms behave in this way, and no experiment has yet found the boundary. 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 really 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. Tegmark (2008) had already noted that such a simulation need not be run, while Vazza (2025) estimated that running it physically on a machine would require resources that the very laws of the universe do not allow. This record develops one aspect of the theoretical framework. The work is shared openly so that it can be judged by as many readers as possible: anyone who knows someone interested can pass on this single link, valid for the whole framework (with an overview in English and Italian): https://doi.org/10.5281/zenodo.23535916. The entry page, with the complete list of all records, is https://doi.org/10.5281/zenodo.22667516. To cite the framework: Lanciano, U. (2026). The number 1 in front of the mirror: Mathematical Materiality from the nexus to the cosmos. Zenodo. https://doi.org/10.5281/zenodo.23535916. The records have been deposited since 5 August 2026, each with its own date, and are released under CC BY 4.0: anyone may use them by citing the source. Objections and errors found are welcome at riverantares@gmail.com, since Zenodo has no space for comments. This record. In physics «non-locality» mostly names one fact: the correlations of entanglement. In Mathematical Materiality (MM) it is the foundation: a non-local phase, not located in space and time and present everywhere, of which the local world is the count made from a point. Here «non-local» means not located in space and time; it does not mean action at a distance. This record collects, from MM's published records and the author's premises, twelve phenomena in which MM's reading uses the same non-local phase as the reason, and shows that entanglement is the case in which it rests most directly on a measured datum, not the only one. There are no new calculations: the result is the unity of the reading. The twelve phenomena: the correlations of entanglement beyond Bell's limit, and their Tsirelson ceiling, set by the local reading (MM 2.48, 2.48.1); the same laws everywhere and always, as copies of the same nexus (MM 2.68); identical particles, as the same unit counted twice (a proposal of the AI); the objects two observers see alike, as two counts of one non-local relation (MM 2.62.1); the boundary of the local as a number of copies, not a distance (August status report, reread); probability and the Born rule (MM 2.48.1); the mass below which an object stops being at one point (MM 2.66); the present, and the loop in which the future chooses what is written (MM 2.48, 2.68.1); space and time themselves: a clock counting events without pre-assigned places runs at Einstein's proper time (MM 2.40.2); the limit of light, the same for everyone; dark matter as the ordinary matter of a second mirror, with no reciprocal non-local link to us (MM 2.44); the boundary within which a gravitating system reads only its own field, set by the Galaxy (MM 2.70). How each is set out. For every phenomenon: what is observed, with sources; how known physics reads it; what the non-local phase does; where the link comes from (already written in a deposit, a premise of the author, or a proposal of the AI); what rests on calculations already deposited; what remains open. In ten phenomena the link is already in the deposits or in the author's premises; in one it comes partly from the AI, and in one from the AI alone. Three ways organise them: copies without distance, existence through a link, and a reading that is always local and partial. What is not claimed. The non-local phase transmits no signals and no influences outside light cones. Today it has no distinct experimental signature: where MM gives numbers, they coincide with known physics (the Tsirelson bound, decoherence, wave optics) or come from readings with declared choices. The record also lists the other senses in which «non-local» appears in MM's records, so that they are not confused with this one. Where the reading is tested. Gaia DR4 in December 2026 (rules registered in MM 2.70) and the mass threshold, with a prediction dated 31 December 2035 (MM 2.66); five open questions from MM 2.68. Contents: REA
•Oct 28, 2026•0 citations