Diego Luis Tentor — ArXe Research — 2026
There are questions physics does not ask — either because it considers them answered, or because it considers them ill-formed. Why do physical laws have the form they have and not another? Where does time come from? What is space, before there is anything to occupy it? Why do the fundamental constants have the values they have — and not slightly different ones?
The standard answer oscillates between two positions. Either the questions are empirical and answered by measurement. Or they are metaphysical and not answered at all. In neither case are they derived.
ArXe is an attempt to derive them. Not from a deeper physics — from the only thing that requires no prior explanation: that logical nothingness is inviable. What follows is an account of the points at which that attempt produces structurally new results.
I. No Preexistences
The first question any ontology must answer is this: what does it presuppose?
ArXe presupposes one thing: that logical nothingness is inviable. It does not presuppose numbers. It does not presuppose laws. It does not presuppose particles, space, time, or observer. What is called “the universe” is not a mathematical structure that exists — it is the active process by which the inviability of nothingness escapes into structure.
This distinguishes ArXe from Platonism, which presupposes mathematical entities as foundation. From physicalism, which presupposes substance. From idealism, which presupposes a prior mind or concept. In all three cases the question remains intact: and that which you presuppose — where does it come from?
ArXe does not answer that question. It dissolves it: the only starting point that requires no prior explanation is the impossibility of not beginning.
Mathematics is not the foundation of reality. It is the grammar of the unfolding of distinction.
II. Undecidability as Mechanism, Not Limit
Undecidability is not an epistemological problem. It is not what the observer cannot know. It is the generative mechanism of geometry.
Space emerges because order is undecidable: there is no structural reason to prefer one phase ordering over another. Time emerges as decided order: the succession recorded as historical fact at T³. Time and space are not two dimensions of the same continuum — they are contraries. Time is decided order. Space is undecidable order.
Simultaneity is not an accident of perception. Each level of arity generates a distinct form of simultaneity: what can co-occur without contradiction at T⁻¹ is not what can co-occur at T². Quantum entanglement is not paradox — it is the structural simultaneity of T⁻¹ misread through the categories of T².
Probability enters the system the same way: not as a mathematical tool imposed from outside, but as a consequence of the open boundary condition of T⁻¹. At T⁰ there are no possible orderings. At T¹ succession is trivial — no structural alternative exists. At T⁻¹ six equiprobable orderings appear for the first time. Variance is born here. The entire probabilistic edifice of physics is the statistical manifestation of this architecture.
III. The Formulas Are Found, Not Built
A phenomenological model with enough parameters reproduces any data. The question is not whether the model fits — it is whether it could fail to fit.
In ArXe, the arities that appear in the expression of a physical constant are not chosen. They come from the ontological table of the system or they do not come. That restriction is what gives the result its weight: when the formula appears, there is no room in which it was hidden.
The lexicon of 25 arity operators was confirmed by two independent programs that did not communicate. This is not convergent fitting — it is independent detection of the same structure. Across ~119 constants analyzed, the average error is around 0.002%. More significant: the chronological deltas of fundamental constants across decades of measurement show ArXe-arity structure in the variations — and conventional arities where human protocol decisions intervened.
The distinction is not quantitative. It is of kind.
IV. Nature and Convention Can Be Separated
A physical constant has digits. Not all of them are of the same type.
The leading digits express the ontological unfolding: the irreducible structure of the corresponding level, encoded in ArXe arities. The trailing digits express the history of those who measured: conventional choices of units, systems, and measurement protocols, encoded in arity numbers that do not belong to the ontological table.
This is not a metaphor. It is the Naturality-by-Digit Principle: given threshold d, the digits up to d carry pure ArXe P-structure; the digits beyond d* carry P-structure with human arities. The Layer C / Layer D distinction formalizes this.
The consequence is philosophically non-trivial: physics does not speak of reality with a uniform voice. Each constant is a superposition of two languages. ArXe separates them.
V. The Observer Does Not Get Postulated — It Emerges
The observer is not an external element added to the system to do physics. It is a condition of possibility that the system generates internally.
An observer requires four structural conditions: it must be able to distinguish states, record history, perform operations on that history, and construct models of itself. The minimum level satisfying all four is T⁻⁵, corresponding to arity 11.
This has consequences. The observer cannot be at just any level. It is not contingent. Its position in the hierarchy is derived, not postulated. And that position determines what it can see: the observer at T⁻⁵ has direct access to adjacent levels and mediated access — always with information loss — to distant ones.
The observer problem in quantum mechanics is not a problem of interpretation. It is a problem of structural placement that ArXe resolves without an ad hoc wavefunction collapse.
VI. π and φ Are Not Postulated — They Are Derived
π and φ appear throughout physics. The question is why.
In ArXe, both are the geometric limits of logical ambiguity at T³. π is the closed boundary condition anchor at that level. φ is the open boundary condition anchor. They are not inserted into the system as convenient constants — they emerge as the only geometric ratios compatible with the boundary conditions of the third degree of freedom of the contradiction.
The recurrence of these constants in physics is not a mysterious coincidence. It is the signature of level T³ in all phenomena that depend on its boundary conditions.
VII. The Periodic Table and the Lanthanide Series
ArXe does not reproduce the periodic table in the sense of fitting its periods to a formula. It derives the conditions of possibility of its structure.
The periods are projections of T⁻⁵. The lanthanide series is a concrete realization of the phase-ordering principle at T⁻³: when the number of electrons in the 4f shell exceeds the arity of the level (7), the spatial mode T² collapses. That collapse is always exactly 4 orderings — because T² as a complete mode either holds or does not, with no intermediate. The observable signature: number of Kramers doublets = n − 4 for ions with n > 7. Verified in Dy³⁺ and Er³⁺.
This is not elegant postdiction. The formula was derived from the phase-ordering principle before the data were checked.
VIII. Physics as the Dominant Statistical Layer
Physical reality is not “what there is.” It is the statistically most probable layer of the structural possibility space of each level.
The Principle of Probabilistic Freedom establishes that the universe privileges no configuration. The consequence is that simpler configurations are more abundant — not because the universe favors them, but because more configurations satisfy them. Relative Logical Necessity establishes that once a configuration is actual, its implications are inescapable.
These two principles, together with the scale of n-ary logics, answer a question standard physics does not ask: why do physical laws have the form they have? They are not laws imposed from outside. They are the dominant statistical layer of the unfolding of the primordial contradiction.
IX. No Absolute Truths — No Binary Refutation
ArXe does not adopt a binary refutation criterion because it rejects the presupposition that makes it possible: that there is an absolute truth which the system either reaches or does not.
The system adopts a mapping criterion: an assignment is good if it is internally coherent, systematically applicable, parsimonious, and corresponds with experiment within stated error tolerances. This criterion has degrees. It has no all-or-nothing threshold.
This is not relativism. It is the logical consequence of the fact that the universe does not weigh truths — it processes distinction. A theory that adopts absolute truth as its criterion is importing a category the system does not contain.
The tension stays open: if the mapping criterion has no binary threshold, how does one distinguish a theory that works from one that does not? ArXe’s answer is cross-coherence: the same lexicon of 25 arities found by two independent programs, chronologically pure structural deltas, dimensional equivalences that emerged without being sought. The coincidence hypothesis becomes progressively less plausible. Not impossible. Progressively less plausible.
X. The Physical Dialogue Has Grammar
Physical constants are not given numbers. They are expressions in the grammar of the unfolding.
Grammar ALO is the reading method: each constant is read as a combination of arity operators from the ontological lexicon, plus boundary condition anchors where the level requires them. Dimensional constants (masses in Planck units) are expressed with arities alone — no anchors needed. Dimensionless constants require π and φ anchors at the positions that correspond to their level.
The result is that the corpus of ~119 constants is not a list of data. It is a structured conversation between levels of the hierarchy. Each constant is a sentence. The grammar is derivable. The observer reading from T⁻⁵ can distinguish which part of each sentence is the unfolding speaking — and which part is itself answering.
“We do not prove. We show: how complexity emerges from the impossibility of nothingness.”
ArXe Theory V4.2 — March 2026
Diego Luis Tentor — ArXe Research
License: CC BY-SA 4.0