We present principles of Measurement Quantization (MQ) and approaches to measurement that support the discreteness of measure. Several claims are addressed. Notably, that measure is discrete with respect to the internal frame, non-discrete with respect to the system frame and that length is contracted due to the discreteness of measure. We address the relation of angular measure to momentum, the physical significance of count bounds and that the fundamental measures — more precise expressions for Planck’s units — are an emergent property of the internal frame. Quantum experiments by Shwartz, et. al and CODATA provide physical support. We predict and derive values for elementary charge and the gravitational, Hubble, reduced Planck, electric, magnetic, Coulomb, and fine structure constants. We then correlate gravity with electromagnetism (unification). We present expressions for galactic rotation, dark matter, dark energy, and accelerating expansion. MQ advances over Loop Quantum Gravity with two frames, the difference which leads to the physical constants and the laws of nature. We correlate the quantum and cosmological, describing an inflation free quantum epoch, why it ceases and expansion. Therein are solutions to the horizon problem and homogenous, isotropic properties of the universe. Predictions include length contraction unrelated to special or general relativity (SR/GR), 13-digit measures of the gravitational constant, the Planck momentum, and universal mass accretion.

This preprint introduces the Quantum Continuous Present Theory (QCPT), a conceptual framework proposing that time is an emergent physical property generated by the quantum-state transitions of matter. Instead of treating time as a pre-existing background parameter, QCPT postulates that each material system generates micro-time pulses arising from its internal quantum evolution, and that the global structure of cosmic time emerges from the collective synchronization—partial, imperfect, relativistic, and gravity-modulated—of all these microscopic quantum pulses. The objective of QCPT is not to provide a complete mathematical formalization, which remains open, but to articulate a coherent conceptual model that invites mathematical development and potential experimental exploration. QCPT seeks to bridge the conceptual gap between relativity and quantum mechanics by reinterpreting temporal flow as a property emergent from matter rather than a fundamental backdrop. Version 0.2 expands this framework by introducing a conceptual explanation for the emergence of space. In this view, time arises from the internal rhythm of a single system, whereas space appears only when many such rhythms synchronize and form an ordered structure. This addendum also suggests that the Higgs field acts as the physical medium that enables this synchronization. Taken together, these ideas offer a unified conceptual lens that connects quantum discreteness, relativistic geometry, and phenomena such as interf

Abstract Discrete spectra are traditionally postulated as axiomatic in quantum theory. Here we demonstrate that discreteness can emerge generically as a consequence of dynamical stability in reversible, non-integrable systems under weak perturbations. We identify robust parameter plateaus (locking shelves) across quantum Floquet chains, classical area-preserving maps, and wave-transfer matrices. Crucially, every tested system follows the same boundary logic: shelves occur only within elliptic stability islands and collapse under irreversibility, strong noise, or hyperbolic instability. We do not derive quantum theory; we identify a cross-domain stability mechanism that generically selects discrete responses. This stability-selection principle provides a concrete bridge between classical mode-locking, Floquet many-body scars, discrete time crystals, and dynamical localization—suggesting that discreteness is a selected dynamical outcome rather than a fundamental axiom.

Scanning the structure of ill-known spaces: Part 1. Founding principles about mathematical constitution of space Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal properties originating from nonwellfounded properties of the empty set is demonstrated. This lattice provides a substrate with both discrete and continuous properties, from which existence of physical universes can be proved, up to the function of conscious perception. Spacetime emerges as an ordered sequence of mappings of closed 3-D Ponicare sections of a topological 4-space provided by the lattice. The possibility of existence of spaces with fuzzy dimension or with adjoined parts with decreasing dimensions is raised, together with possible tools for their study.

We develop a pre-geometric cosmological framework in which existence is identified with a finite amount of unstructured energy possessing vibration as its only intrinsic property. This vibrational substrate occupies an open, bounded spectral interval $(\omega_{\min},\omega_{\max})$, ensuring finiteness of total energy and excluding infinitely stable configurations. The substrate evolves under two fundamental and competing tendencies---excitation, which amplifies coherence, and randomization, which scrambles it. Their balance produces a metastable unstructured regime in which rare fluctuations may form long-lived self-consistent spectral configurations. Because the substrate is finite and subject to competing order--disorder dynamics, no coherent configuration can be perpetually stable. We show that the only mechanism capable of sustaining long-lived organization is a replication instability: a coherent unit may reproduce into multiple offspring according to a general $1\!\to n$ rule. Replication consumes energy from the finite substrate, breaks the metastable symmetry, and induces a discrete notion of event time through the replication tick $\Delta\tau$. Temporal succession is defined through correlation ordering of spectral microstates, producing an intrinsic pre-causal structure. The compactness of the spectral domain imposes minimal and maximal timescales, bounds the internal coherence of emergent units, and limits their proliferation. These spectral constraints serve as p

The weak-field, quasi-static regime of gravity is commonly described by the Newton-Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1-AX5 (including conservation) and standard DEC refinement, the Newton-Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency-wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source-potential relation characterized by a power-law kernel wker(k)=1+C(k0/k)α in Fourier space. The kernel exponent α=12(1-φ-1)≈0.191, where φ=(1+5)/2, is derived from self-similarity of the discrete ledger closure; the amplitude C=φ-2≈0.382 is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed M/L=1, no per-galaxy tuning, conservative σtot), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves median(χ2/N)=3.06 over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization/screening.

Discreteness provides unique opportunities for controlling the flow of light. As in solidstate physics, optical discrete or lattice configurations are known to exhibit a succession of allowed Floquet-Bloch bands and forbidden bandgaps. In weakly coupled systems, the Floquet-Bloch states can be accurately described by local modes, and thus the tight-binding approximation or coupled-mode theory is applicable. As a result, the field dynamics become effectively discretized. In optics, arrays of evanescently coupled waveguides, photonic crystal fibers, chains of coupled microresonators, and photonic crystals are prime examples of such structures where discrete wave dynamics can be experimentally investigated. Perhaps the most exciting outcome of the interplay between discreteness and optica nonlinearity is the existence of self-localized entities better known as discrete solitons. This class of optical solitons were first suggested in the late 1980s and successfully observed in AlGaAs waveguide arrays a decade later. Since then, discrete optical solitons have been observed in many other material systems such as in optically induced lattices, in quadratic waveguide arrays, and in liquid-crystal cells. This experimental work has not only resulted in a deeper understanding of nonlinear processes in periodic environments, but it has also helped to assess the potential of these self-trapped states toward future applications. Nowadays, the field of discrete optical dynamics in nonlinear lattices is at an exciting stage of development. Even though some of the basic concepts in this area have been around for a while, much remains to be explored and discovered.