Foundations

Mathematical Demonstration of the Continuity of Time and Space: Limits, Smoothness, and Finite Resolution

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Mathematical Demonstration of the Continuity of Time and Space

Mathematical Demonstration of the Continuity of Time and Space presents a rigorous, self-contained analysis showing that a limit point added at infinity can be reached with full continuity, differentiability, and infinite smoothness. Using a simple refinement sequence and a standard change of variables, the work proves that the limiting value is not a singular boundary: the function is continuous at infinity, its derivative at infinity exists and equals zero, and all higher-order derivatives vanish as well. Beyond the formal result, the paper clarifies a common conceptual error in physics: finite measurement resolution does not imply ontological discreteness. “Minimum measurable” intervals reflect experimental limitation, not a breakdown of continuity. The article is written to be readable, rigorous, and directly relevant to debates on spacetime granularity, limits, and the logic of inference from finite observations.

Mathematical_Demonstration_of_the_ContinDownload

DOI: 10.5281/zenodo.18093432

Date: Dec 26, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Replacing Parameters with Physical Necessity: Quarkbase Cosmology

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Replacing Parameters with Physical Necessity

Replacing Parameters with Physical Necessity presents a minimal-ontology framework that replaces parameter fitting with physical necessity. The theory is grounded on a single postulate: the physical vacuum is a continuous, non-dissipative pressure medium described by a scalar field Ψ. All physical entities arise as discrete compactations of this medium, and all interactions emerge as responses to pressure gradients and structural recomposition. From this single substrate, the framework provides unified physical explanations for: conditional irreversibility via vacuum recomposition; neutrino oscillations without intrinsic neutrino masses; the charged-lepton spectrum as resonant modes of a finite compactation; color confinement as a consequence of topological continuity; matter–antimatter asymmetry as geometric phase-orientation selection rather than CP-driven baryogenesis; and the filamentary large-scale structure of the universe as anisotropic instability of the Ψ-field, without invoking dark matter. The work is explicitly falsifiable. It states what must be false if the framework is correct and identifies decisive points where experimental evidence would refute it. No new particles, sectors, or symmetries are introduced. Instead, much of the existing theoretical scaffolding is shown to be unnecessary if a physical substrate is taken seriously. The conclusions are plain. You may take them or leave them; curiosity has been satisfied.

Replacing_Parameters_with_Physical_NecesDownload

DOI: 10.5281/zenodo.18064740

Date: Dec 26, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Conditional Irreversibility and the Emergence of the Time Arrow from Vacuum Recomposition

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Conditional Irreversibility and the Emergence of the Time Arrow from Vacuum Recomposition

Conditional Irreversibility and the Emergence of the Time Arrow from Vacuum Recomposition presents a medium-based physical criterion for when reversible dynamics become irreversible. The work distinguishes mathematical time-reversal invariance from physical reconstructibility, proposing that the arrow of time emerges only when the vacuum medium can no longer recompose a previously coherent configuration after coherence is lost through dispersion, phase decorrelation, or leakage into non-recomposable vacuum modes. The paper includes a mode-coupling toy model and threshold analysis to show how irreversible behavior can arise without breaking fundamental reversibility.

Conditional_Irreversibility_and_the_Emergence_of_the_Time_Arrow_from_Vacuum_RecompositionDownload

DOI: 10.5281/zenodo.18041285

Date: Dec 24, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Law of Antimatter Emergence in Quarkbase Cosmology

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Law of Antimatter Emergence in Quarkbase derives a structural, medium-based criterion for the existence of antimatter within the framework of Quarkbase Cosmology. Antimatter is not postulated as a parallel sector nor as a remnant of a primordial symmetry, but emerges conditionally from the dynamics of the Ψ-field. A single operational principle-the conjugation of phase and orientation combined with mechanical admissibility-determines whether a given excitation admits a distinct antiparticle, is self-conjugate, or is structurally forbidden from having an antimatter counterpart. The criterion is applied systematically to leptons, neutrinos, electromagnetic modes, baryons, mesons, and composite nuclear states, yielding a unified classification that accounts for the observed pattern of antimatter and leads to explicit, falsifiable predictions beyond the Standard Model.

Law_of_Antimatter_Emergence_in_QuarkbaseDownload

DOI: 10.5281/zenodo.17991454

Date: Dec 19, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Chemistry of Quarkbase III: Emergence of periods and chemical groups from geometric closures of the Vacuum Pressure Field (Ψ)

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Emergence of periods

Emergence of periods and chemical groups from geometric closures of the Vacuum Pressure Field (Ψ) derives the periodic structure of the chemical elements from first principles within the Quarkbase framework. Starting from a single variational functional of a vacuum pressure field, the theory produces a discrete ladder of admissible stable configurations whose finiteness, ordering, and repetition follow from geometric closure and phase-coherence constraints, without invoking electronic shells, orbitals, or empirical fitting. Chemical periods emerge as closure intervals of this ladder, while chemical groups arise from the underlying geometric and spectral structure. The observable atomic number is linked to a physical compactation charge through a single global calibration, yielding a finite periodic table with seven complete periods and a predicted subsequent closure beyond the currently known elements.

Emergence_of_periods_and_chemical_groups_from_geometric_closures_of_the_Vacuum_Pressure_FieldDownload

DOI: 10.5281/zenodo.17957261

Date: Dec 16, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Chemistry of Quarkbase Cosmology -II: Emergence of Electronegativity

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Emergence of Electronegativity

Emergence of Electronegativity derives electronegativity from first principles within Quarkbase Cosmology as an emergent, relational property of phase control in the Ψ-field. Without introducing chemical axioms, orbital postulates, or empirical fitting, electronegativity is shown to arise from nuclear phase rigidity and external-mode sensitivity. The framework naturally reproduces bond polarity, ionic and covalent limits, and periodic trends as consequences of resonance and phase coherence, providing a unified theoretical foundation for chemistry consistent with the Quarkbase Cosmology framework

Chemistry_of_Quarkbase_Cosmology___II__Emergence_of_ElectronegativityDownload

DOI: 10.5281/zenodo.17930306

Date: Dec 14, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Relativistic Invariance and Experimental Constraints on Quarkbase Cosmology

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Relativistic Invariance and Experimental Constraints on Quarkbase Cosmology

Relativistic Invariance and Experimental Constraints on Quarkbase Cosmology presents the updated English version of a quantitative consistency analysis of Quarkbase Cosmology with current experimental tests of Lorentz invariance. Using the latest Standard-Model Extension (SME) Data Tables (January 2025), experimental bounds on the variation of the fine-structure constant and on photonic SME coefficients are translated into direct numerical constraints on the operative combination ε∂μΨ. The analysis is carried out component by component, clearly distinguishing laboratory and astrophysical limits and identifying the conditions required to suppress birefringent projections. The results show that Quarkbase Cosmology preserves effective local Lorentz invariance, remains compatible with all existing experimental constraints, and yields explicit, falsifiable predictions for future high-precision tests.

Relat_Invariance_Experimental_Constraints_on_Quarkbase_CosmologyDownload

DOI: 10.5281/zenodo.17928150

Date: Dec 14, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Chemistry of Quarkbase Cosmology — I: Emergence of Atomic Valence

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Chemistry of Quarkbase Cosmology

Chemistry of Quarkbase Cosmology — I: Emergence of Atomic Valence presents a foundational derivation of atomic valence within the Quarkbase Cosmology framework. The work shows that chemical structure arises as a geometric and dynamical consequence of stationary torsional modes of a continuous, frictionless Ψ-field, without invoking quantum-mechanical postulates, electronic orbitals, or Pauli exclusion. Discrete shell capacities (2, 8, 18, 32), valence saturation in noble gases, variable valence, and standard molecular geometries are deduced as universal, parameter-independent outcomes. Quantitative predictions for bond energies, electronegativity gradients, and spectroscopic shifts are deferred to subsequent papers, where torsional coupling strengths and Ψ-field stiffness parameters are derived

Chemistry_of_Quarkbase_Cosmology_I_Emergence_of_Atomic_ValenceDownload

DOI: 10.5281/zenodo.17926245

Date: Dec 14, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Gravitation Without Mass – A Geometric Pressure Interpretation of Curvature

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Gravitation Without Mass

Gravitation Without Mass – A Geometric Pressure Interpretation of Curvature raises the question: Can mass be defined if only one object exists in the universe? 
This work argues that it cannot: mass is a relational quantity with no physical meaning in a one-object universe. Using the ADM 3+1 formalism, gravitational acceleration is expressed as the orthogonal projection of the curvature gradient—a structure formally equivalent to a pressure gradient.

This leads to a reinterpretation of gravity as geometric pressure acting on the compact volume displaced by an object, rather than a force sourced by mass. The framework leaves Einstein’s equations untouched while replacing the classical mass→curvature linkage with a volume→pressure mechanism that is ontologically consistent, operationally definable, and naturally compatible with quantum descriptions.

The result clarifies the conceptual foundations of General Relativity, dissolves the classical–quantum discontinuity without introducing gravitons, and avoids unwarranted unification claims by explicitly restricting the interpretation to gravity alone.

Gravitation_Without_MassDownload

DOI: 10.5281/zenodo.17873312

Date: Dec 10, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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Relativity as a Pressure Phenomenon in the Quarkic Ether

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Relativity as a Pressure Phenomenon in the Quarkic Ether

Relativity as a Pressure Phenomenon in the Quarkic Ether reformulates Relativity as a macroscopic pressure phenomenon of the quarkic ether. Instead of interpreting time dilation, length contraction, and inertial growth as geometric postulates of spacetime, this work shows that they arise naturally from the delayed volumetric recovery of a perfect-pressure medium. A moving quarkbase generates frontal compression and a trailing wake whose finite propagation speed cΨ reproduces the full Lorentz factor, the relativistic energy relations, and the velocity-addition law. Gravity appears as a gradient of the etheric index nΨ(x), yielding an effective metric formally identical to general relativity but rooted in physical pressure dynamics. All classical relativistic effects—including Doppler shift, aberration, Shapiro delay, lensing, and cosmological redshift—emerge from the hydrodynamic behaviour of a frictionless continuum. Thus, relativity does not replace the ether: it reveals its macroscopic shadow

And_Ether_said_Let_there_be_Relativity__and_it_was_RelativityDownload

DOI: 10.5281/zenodo.17717027

Date: Nov 18, 2025

Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827

Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International

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