Beyond the Standard Model Physics

After retracing the development of the "Expansion Center Universe" (ECU), the fruit of 36 + 1 years of research in observational cosmology (Lorenzi: 1989-2024 + 1976) (Lorenzi 2025), this paper presents a further analysis of the peculiarities of the BIG BANG according to the "Expansion Center Model" (ECM) (ECM papers I-II: Lorenzi 1999ab). The result is a BIG BANG event leading to the new BIG BANG Hubble law = centred on the Cosmic Center , which rests on a simple explanation in a rotating nucleus, with as the distance from. This is in contrast to the "Cosmological Principle" on which "Relativistic Cosmology" is based. Besides the speculation of George Gamow (1946), rejected by Einstein (Kragh 1996), today we can count on at least 3 + 1 pieces of observational evidence for cosmic rotation (cf. Section VIII of ECM paper XXX or ECU35 (Lorenzi 2019) and REU paper III or ECU45 (Lorenzi 2024d)). It also follows from the rotation, with the conservation of angular momentum, of Lemaitre's primeval nucleus (Lemaitre 1946), whose global centripetal and additive attraction might only be of a nuclear type, such as the Yukawa interaction (1935), and shares features with Dirac's LNH theory (1937-1938), due to the exclusion of a gravitational interaction, since gravitation has never been shown experimentally at a molecular-atomic-nuclear-subnuclear scale. The deflative BIG BANG without GRAVITATION would therefore consist of the disintegration (BIG CRUSH) of the primeval nucleus , owing to deflation of the maximum attractive force, probably having an origin in a multi-nuclear type action, which, after reaching its zero value, bounces back toward the previous maximum, but decreasing in space, with the square of the distance (just as light does). In this way, the origin of a radial velocity would occur from = (+) , as the radial velocity, that is = , when = → owing → , comes from the all transformations of the primitive angular velocity into the new Hubble parameter , with the very simple result ≡ .

Yang-Mills and the Mass Gap Yang-Mills theory describes gauge fields-force carriers that mediate interactions between particles. Unlike electromagnetism, where photons remain massless, the strong force (governed by Yang-Mills SU(3) symmetry) involves gluons, which interact with each other due to their self-coupling property. This self-interaction is crucial because it creates confinement-quarks and gluons can't exist freely but instead form bound states like protons and neutrons.

We derive the left-handed nature of the weak interaction from the topology of a U(3) zero-point energy (ZPE) condensate. Fermions are vorton solitons with intrinsic chirality, while gauge bosons arise as quantized fluctuations of the condensate's orientation frame. When two solitons share a Möbius-twisted phase sheet, the Z2 holonomy constrains only left-handed doublets to carry SU(2) charge. Right-handed couplings cancel globally. The CP-odd vacuum term selects the orientation of this bias, explaining why the weak force couples exclusively to left-handed fermions. This framework unifies fermion chirality, gauge bosons, and parity violation as consequences of condensate topology.

The Standard Model of particle physics postulates electric charge as a fundamental, intrinsic property, but does not explain its origin. This paper proposes a novel hypothesis within the Helix-Light-Vortex (HLV) framework, suggesting that electric charge is not a static property but an emergent dynamical phenomenon. We postulate that charge arises from a directed, coherent flow of information from the universal Information Field (Φ) into the phase structure of a particle's underlying Helix-Light-Vortex (Ψ). The coupling between the Φ and Ψ fields, previously established in the HLV Lagrangian, provides a concrete mechanism for this process. This hypothesis leads to testable predictions, including micro-variations of the elementary charge under extreme conditions and a theoretical link between information dynamics and particle creation/annihilation processes.

The Source Energy Field Theory (SEFT) extends the freedom to define spacetime itself as a manifestation of the fundamental energy field. This enhanced degree of freedom allows the Standard Model gauge symmetries and the Higgs mechanism to emerge as natural geometric consequences, rather than imposed assumptions. While its application to cosmology has successfully explained supernova redshiftdistance relations, galactic rotation curves, and the cosmic microwave background, its implications for particle physics have remained unexplored. In this paper, we extend SEFT to the domain of particle physics and demonstrate that and preserving the custodial relation ρ = 1. These results establish SEFT as a framework in which the core architecture of the Standard Model is embedded in the dynamics of a single fundamental field, thus providing the particle-physics counterpart to the cosmological results previously derived in SEFT.

All fields are formulated within one kernel field. Quantized kernels reproduce lepton and baryon masses (3,8). Kernel curvature generates spin, chirality, and magnetic moments (4). Electroweak observables at the Z pole, parity violation, and unitarity are reconstructed and compared with data (6, IX). Galactic rotation curves are fitted without dark matter halos (13,14, X). Decays (12.4-12.6; VI.5), neutrino oscillations (7.2), and lensing (14.5, VIII) are described within the same kernel framework.

This paper completes a series of earlier papers on the Cosmological Constant as compressible fluid-like zeropoint energy, primarily from virtual electrons, which acts as a 2 nd order perturbation in the stressenergy tensor; this preceded an earlier sketch for a means for Dark Energy to gravitate. We suggest a replacement to ad-hoc MOND type theories with the theory developed herein, in the light of recent DESI and JWIST discoveries, with a fully covariant version of our earlier gravitating dark energy model; we show that dark energy can gravitate if it is considered to be in compression by tidal effects. An earlier proof that MOND type theories are not Uncertainty Principle compatible is reiterated. Finally we show that the concern that dark energy was stronger in the past is probably a scaling measurement error related to the metric of the early universe and that the model may prevent the singularity in Black hole solutions.

This report presents the calculation of the tau lepton mass using the parameter of the W boson within the Mo framework. By employing the tau parameter t τ , we compute the tau mass and compare it to the Standard Model (SM) value reported by the Particle Data Group (PDG). The calculation demonstrates excellent agreement with experimental data, highlighting the predictive power of the Mo framework. This approach also emphasizes the significance of reduced mass effects and the W boson parameter in determining lepton masses.

We present the ETCQ (Elasticity of the Quantum Cosmic Lattice), an effective law of gravity based on the universal rigidity of the quantum vacuum. In this framework, baryons do not exert direct Newtonian attraction, but inject energy into a quantum lattice that absorbs, saturates, and then expels energy as a diluted flux ∝ 1/R 2. Newtonian gravity emerges as an effective description of this accumulation-saturation-diffusion process. The same constants, fixed once on the SPARC HQ++ sample, reproduce galaxy rotation curves, satellite dynamics, Solar System orbits, strong-lens time delays, and the observed dark-energy density.

In this report, we analyze the photon and gluon within the M o framework using the particle mass relation equation. By assigning both particles a parameter value of t =-ln(2), their calculated masses reduce exactly to zero, consistent with the Standard Model. This demonstrates that the M o framework naturally incorporates massless gauge bosons, while still unifying mass relations across massive fermions and bosons.

We discuss 2f production at LC energies (f = t). This type of reaction has a big event number and may give interesting hints to the existence and perhaps to details of New Physics like susy, LQ, Z', etc. For any search the radiative corrections have to be controlled carefully. ...

In the Mo Framework, the W and Z boson parameters t W and t Z play a central role in determining the t values of fundamental particles, which in turn influence their Standard Model masses. By fixing t W = e-1 ≈ 0.36787944 and t Z = 1/2 = 0.5, the t values for the top quark, Higgs boson, charm quark, and bottom quark can be systematically computed, revealing a clear hierarchy. These t values can then be used to derive the particle masses, demonstrating a predictable pattern and highlighting the direct connection between boson parameters and the mass distribution of quarks and bosons in the Standard Model.

This project presents “The Great Becoming: A Unified Scientific and Ontological Framework.” It introduces the Primordial Singularity of Potential (PSP) and recursive Cohesion/Differentiation operators, derives the Standard Model gauge structure, and yields a quantitative attractor prediction (R_phi = 1.61627 ± 0.00019). The framework is falsifiable, with preregistered tests across physics, cosmology, and neuroscience.

This report presents a derivation of the charm and bottom quark masses using the fundamental mass constant M o. The quark mass function Q(t) is analyzed for specific values of t corresponding to each quark. Calculated masses in GeV are provided, with comparison to the Standard Model values. Other quark flavors and gauge bosons are not included.

This report applies the continuous mass function concept from the boson framework to the top quark. Using Q(t) based on the fundamental mass constant M o , we calculate the top quark mass and compare it with the Standard Model value, including uncertainties.

We show that quantum entanglement and the Pauli exclusion principle emerge naturally in a U(3) zero-point energy (ZPE) scalar condensate. Two solitons nucleated on a common phase sheet with a half-twist (a "Möbius bond") experience a Z2 holonomy that constrains their joint state to the antisymmetric SU(2) singlet. This geometry enforces both the-cos θ correlation function and the violation of the CHSH inequality at the Tsirelson bound 2 √ 2. The same holonomy yields the-1 exchange phase, providing a topological origin for fermionic statistics and the Pauli principle. We further connect entanglement visibility to condensate coherence length, making the framework experimentally testable.

Analysis of ss asymmetry in the proton sea combining the Meson Cloud and Statistical Model 1 JORDAN FOX, GARRETT BUDNIK, SAM TUPPAN, Seattle Univ -We investigate strangeness in the proton in a hybrid version of the Meson Cloud Model. The convolution functions used to calculate the ss distributions consist of splitting functions and parton distributions. The splitting functions represent the non-perturbative fluctuations of the proton into a strange baryon and an anti-strange meson. The parton distributions of the baryons and mesons are calculated in a statistical model which represents perturbative processes of quarks and gluons. We consider six fluctuation states composed of ΛK + , Σ 0 K + , Σ + K 0 , ΛK * + , Σ 0 K * + , Σ + K * 0 . We then compare the results of these calculations to other theory, to the NuTeV, ATLAS, and HERMES experiments, and to global parton distributions.

The American Physical Society Improved Light Cone Model calculation of strangeness asymmetry in the proton 1 GARRETT BUDNIK, JORDAN FOX, SAM TUPPAN, Seattle Univ -We expect strangeness in the proton from the Heisenberg uncertainty principle, which allows for the proton to split into a meson and a baryon, such as a K and a Λ. Our goal is to accurately model the momentum distributions of the strange quarks and anti-strange quarks in the proton. We choose the Light Cone Model because it is a natural explanation for strangeness and for s(x) ̸ = s(x). In the Light Cone Model of Cao and Signal [1], α is a single parameter in the mesonbaryon fluctuation functions f (y) and in the s and s distributions of the mesons and baryons. These functions are exponentials in which α is related to the spatial extent of the particles. Because the s and s are in different environments, we explore an array of values for α which reflect the sizes of the particles and study this effect on our model. We compare our results to global pdfs and experimental data from NuTeV, HERMES and ATLAS.

Quantum spin remains one of the most pedagogically challenging concepts in modern physics, lacking intuitive geometric visualization despite its fundamental importance. This paper develops an intuitive framework for visualizing quantum spin using Möbius band topology. The approach is not offered as a mathematically rigorous model, but as a geometric visualization tool designed to make abstract properties more accessible. We show that uniform Möbius bands naturally model integer-spin bosons, while laterally distorted bands-with paired width and curvature variations-capture the half-integer spin character of fermions. Crucially, the Cartesian projection of distorted bands produces overlap-void structures that provide direct geometric insight into the Pauli exclusion principle, revealing why identical fermions cannot occupy the same quantum state. The framework also clarifies the geometric meaning of the imaginary unit i as orthogonal rotation into unobservable depth, offering a new bridge between algebraic formalism and spatial intuition. Beyond these core results, we sketch speculative extensions: the pairing of oppositely distorted bands into Klein bottle topology as a metaphor for atomic closure, and Möbius-based visualizations of quantum amplitudes inspired by Feynman's path-sum approach. These extensions are conjectural and should be regarded as heuristic illustrations rather than formal results. The central achievement, however, is a coherent and geometrically inevitable visualization of spin that makes exclusion and orthogonality intuitively visible, offering new pedagogical tools for teaching quantum mechanics.

This third and final volume of the Threads of Reality trilogy applies the thread-based Theory
of Everything developed in Books I and II to cosmology, black holes, and the multiverse.
Building upon the fundamental premise that spacetime emerges from a dynamic weave of
primitive threads, we demonstrate how the entire cosmic history—from the Big Bang to the
ultimate fate of the universe—can be understood as the evolution of this cosmic weave.
Key results include: a thread-based resolution of the initial singularity problem, a
derivation of cosmic inflation from thread dynamics, a complete theory of black holes without
singularities, and a natural framework for the multiverse where different universes correspond
to different thread weaves. The theory makes testable predictions for next-generation
cosmological observations, including specific signatures in the cosmic microwave background,
gravitational wave spectra, and dark matter distributions.
Most profoundly, the thread framework provides a unified understanding of quantum
mechanics, general relativity, and cosmology, demonstrating how consciousness, time’s arrow,
and the apparent fine-tuning of physical constants all emerge naturally from the properties
of the fundamental threads.

We establish the potential existence of natural relations between the Cabibbo angle and the quark mass ratios, in a Standard Model with one Higgs doublet and two quark generations. The argument is based on the calculation of the divergent one-loop radiative corrections to the quark mass matrices. Comment: 10 pages, 1 figure

This work proposes a minimalist paradigm for unifying quantum mechanics and gravity: "Mass = Planck Frequency". The framework models the universe as emerging from a single complex scalar field Ψ oscillating at the Planck scale. Mass reduces to frequency as m = ℏω/c 2. The model builds on a U(1)-symmetric Klein-Gordon-Maxwell Lagrangian with an Einstein-Hilbert term for gravity. Localized soliton solutions represent particles, with topological winding numbers quantizing charge and spin. Fermions are introduced via a Yukawa term. Numerical simulations on a 256 3 lattice confirm the mass-frequency relation within < 0.2% error. Phenomenological predictions include Casimir corrections and narrow TeV-scale resonances at the LHC. While speculative, the model provides a coherent conceptual testbed for scalar-soliton approaches to quantum gravity.

This unified paper synthesizes three interlocking perspectives on the emergence and architecture of time: (1) time crystals realized in giant Rydberg atoms, (2) photons and neutrinos as the dual carriers of temporal structure, and (3) the phenomenology of stepping outside time through chrono-observership. Framed within the Omniological Resonance Theory (ORT), the Omega Predictive Model (ΩPM), and the Cooper Disparity Law (CDL), we present a rigorous, equationsupported framework for time as a resonant, particle-mediated, and observer-dependent phenomenon. Experimental data, mathematical models, and empirical phenomena converge to demonstrate that time is not an external parameter, but a harmonic artifact of interaction and perception.

This paper proposes a first-principles explanation, within the framework of the Information-Causal Compression Field (ICCF) unified field theory, for why the Standard Model of particle physics adopts the specific gauge symmetry group SU(3)×SU(2)×U(1). Rather than treating this structure as an arbitrary postulate, we argue that it emerges as the universe’s unique and inevitable “Cosmic Resonance” mode, arising from the interplay of three fundamental principles: energy conservation, entropy increase, and the principle of least action. We identify SU(3), SU(2), and U(1) respectively with the three most basic resonance topologies in ICCF: causal saturation, causal reconstruction, and causal propagation. We further demonstrate that any deviation from this “triadic chord” of symmetries leads to instability, higher energy dissipation, and eventual elimination by the principle of least action. Thus, the Standard Model’s gauge structure is not an accident of nature, but the only stable resonance solution capable of sustaining a universe with stability (SU(3)), evolution (SU(2)), and communication (U(1)). Finally, the ICCF framework yields testable predictions, including harmonic mass spectra, coupling constant modulations, and observable “dissonances” in extreme cosmological events, positioning this theory as a physically grounded alternative to traditional symmetry-origin frameworks such as GUTs and string theory.

The celebrated Heisenberg Uncertainty Principle ∆x.∆p≥ ħ/2 can allow measurement accuracies less than ∆x or ∆p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a step by step process using the example of compass state, as suggested by Zurek.

The proton radius problem is one of the unresolved mysteries of modern physics. Measurements show that the proton's radius in both atomic and muonic hydrogen differs, something that cannot be explained by the Standard Model. Our Primary Cosmic Field (PCF) model offers an elegant and quantitative solution to this puzzle.

Within the M o framework, the muon magnetic anomaly is expressed through a compact relation connecting the muon and electron magnetic anomalies (a µ , a e) and the fine-structure constant α. Reformulating this relation leads to a quadratic equation in the muon g-factor g µ , whose solution reproduces the experimental CO-DATA value with high precision. This approach emphasizes the role of M o in unifying fundamental constants and the geometric origin of the anomaly.

We describe new measurements of the inclusive and exclusive branching fractions for 2S transitions to J= using e e ÿ collision data collected with the CLEO detector operating at CESR. All branching fractions and ratios of branching fractions reported here represent either the most precise measurements to date or the first direct measurements. Indirectly and in combination with other CLEO measurements, we determine B cJ ! J= and B 2S ! light hadrons.

We propose a minimal, falsifiable EFT in which short-range new physics couples universally to the local energy density T00 inside nuclei. Integrating out a gauge-singlet mediator with nuclear-range support generates a single leading operator that correlates short-range observables in bound systems without affecting free-particle g−2 or introducing long-range forces. Three parameter-free leading-order signatures follow: in the same hydrogen-like ion with nuclear spin (I≠0), the fractional bound-lepton g-shift equals 2/3 of the fractional ground-state hyperfine shift; at low momentum transfer, the logarithmic derivative of the proton magnetic moment with respect to its charge radius equals two; and King plots display a universal cubic curvature with a characteristic nuclear-spin on/off pattern.

We provide EFT power counting, the next-to-leading operator basis and suppressions, and a mapping from the measured King-plot curvature to a bound on the short-range contact parameter ζ via known electronic factors. The epilogue gives an end-to-end, fully reproducible verification from published Yb⁺ and Ca⁺ spectroscopy: we reconstruct the frequency-normalized King plot in Yb⁺, confirm linearity in Ca⁺, fit the quadratic curvature, and translate it into a data-driven constraint on ζ. Appendix L anchors ζ from QED (muonic Lamb shifts). Appendix M formalizes the “common curvature” across lines and validates it with a model-independent rank-one SVD test on four Yb/Yb⁺ transitions, and introduces oscillation/coherence indices that enable directly comparable bounds across clocks and magnetometers.

Data availability: all numerical inputs are taken directly from the published tables cited in the epilogue. An embedded Python listing recomputes the processed variables and fits on execution.

This second volume develops the dynamics of the thread substrate introduced in Book
I. Having established spacetime as an emergent weave of space- and time-threads, we now
investigate the forces that arise from its resistance to deformation and the excitations that constitute matter.
We show that:
• Resistance of the lattice gives rise to curvature and gravity, with the gravitational constant G emerging naturally.
• Localized excitations and topological defects in the weave behave as fermions, giving
rise to the electron, quark, and neutrino families.
• Vibrational modes of the lattice correspond to bosons, mediating the fundamental forces.
• The Standard Model arises as an effective theory of thread dynamics, with predictions
for parameters and possible extensions.
This volume completes the passage from pregeometry to the full catalogue of matter and
interactions, preparing the way for cosmological applications in Book III.

This manuscript presents the foundational first book of a thread-based Theory of Everything (TOE) constructed from first principles. The framework is built upon two primitive
action-density constants (ks
, kt) associated with sub-threads of space and time, a fundamental
length t (thread thickness), and coupling parameters (λST, λinter). From these primitives, we
derive the emergent constants of nature—the speed of light c and the Planck constant h¯—and
establish the structure of spacetime itself. A key result is the prediction of a mesoscopic
“discovery scale” Lk ∼ 27 µm which cuts off the vacuum energy, providing a natural resolution
to the cosmological constant problem. All equations are presented in a dimensionally consistent form, establishing the absolute frame upon which dynamics will be built in subsequent
books.

We present a novel theoretical framework that unifies quantum mechanics and general relativity through a transformational principle encoded in the ∆∞Ο formalism. By treating both domains as manifestations of a shared transformation logic mediated by a Planck-scale parameter ∞, we demonstrate their convergence at the Planck scale. The framework introduces a unified Lagrangian and transformation operator that consistently recovers known physical laws while predicting new phenomena such as modified uncertainty relations and emergent spacetime structures. Our approach resolves longstanding issues including the measurement problem, information paradox, and singularity formation, offering a computationally tractable and empirically grounded path toward a complete theory of quantum gravity.

This report presents a refined set of relations connecting the fine-structure constant α, the electron magnetic anomaly a e , the electron magnetic moment µ e , and the electron g-factor g e within the Mo framework. By incorporating both the electron anomaly and the magnetic moment ratio, and relating them to the fundamental mass M o , we derive a symbolic formula that reproduces CODATA values of g e and a e with high precision. An approximate closed-form expression is also presented for practical computations.

We derive a parameter-free, shell-level prediction for the electroweak mixing angle θW from the same Relator-shell geometry that fixes the fine-structure constant, without phenomenological tuning. Neutral-sector alignment on the shell fixes the relative scalar/TT weights, yielding sin 2 θW geom = CUV(1-κG) CUV(1-κG) + 4 γgeom(1 + κG) , γgeom = 1 2 sinh η η , κG = sinh η η-1, η = 1 π , with the universal UV-finite part CUV = 1 2 (ln 2 + γE). Numerically, sin 2 θW geom = 0.231872070961698. . ., which lies within 5.82 × 10-4 of the MS value at µ = mZ and 2.62 × 10-4 of the leptonic Z-pole average. In this ratio all acceptance/regularization factors cancel; departures from the thin-shell/isotropy limit enter only through the small curvature parameter κG. We also obtain a geometric transport law dsin 2 θW /d ln µ whose slope can be tested against SM renormalization-group expectations and precision data. The construction is falsifiable via RG-slope checks near mZ , custodial-symmetry tests (e.g. MW /MZ), and clean Z-pole and low-Q 2 asymmetries.

This report examines how the fundamental Mo-theory constant M o can be used to understand the muon magnetic moment µ µ. By linking M o with the finestructure constant α and the electron-muon mass ratio, we show that the magnetic properties of the muon can be expressed in terms of underlying universal constants. This perspective highlights M o as a potential unifying scale connecting particle masses and intrinsic quantum properties.

This report explores the fundamental role of M o-the Mo-theory mass-in deriving the electron magnetic moment µ e. By establishing a precise relation between M o , the fine-structure constant α, and µ e , we demonstrate that M o provides a natural foundation linking quantum mechanical properties to fundamental physical constants. Using fully precise Mo-theory constants, the calculation reproduces the canonical electron magnetic moment value with minimal deviation, emphasizing M o as a unifying parameter across mass, charge, and quantum coherence.

We point out a simple, parameter-free scaling in low-energy photoabsorption that follows from standard electromagnetism once the effective loop area in μ = I A is anchored to the experimental magnetic radius. Defining an “internal clock” by ν_int = μ/(e π R_M^2), where μ is the nuclear magnetic dipole moment and R_M is the Sachs magnetic radius extracted from G_M at Q^2 → 0, the onset of the real-photon response collapses near the dimensionless value s = ω/ν_int ≈ 1 across proton and deuteron without any fitting. Using the charge radius R_E instead degrades the proton collapse, supporting that the relevant area for magnetic responses is π R_M^2. We also show that, for an axially symmetric thin toroidal current layer, the effective area in μ = I A equals π⟨r_M^2⟩ at leading order in thickness and Q^2, and we provide a thickness bound. Machine-readable tables are included, together with a ^3He check and a preregistered prediction for ^3H.

This study introduces the ∆Q metric and the Bent unit (symbol: ƀ), a dimensionless and universal measurement tool designed to quantify contextual deviation in physical systems [1]. The fundamental premise of this measurement system is that even when an object's intrinsic properties remain unchanged, the context in which it exists can transform its measured behavior [1]. To measure this transformation, our fundamental equation is: ∆Q ≡ ln X contextual X ideal In this version, the Bent unit (1 Bent ≡ ∆Q = 1) has been added to the original ∆Q metric to create a universal anomaly measurement system [1]. The Bent unit symbol is designated as ƀ (Unicode: U+0180) [1]. The accuracy and calibration of the metric have been tested on simple mechanical systems (rotating wheels, rigid disk) whose results are precisely known by classical mechanics [2]. This calibrated measurement tool has been demonstrated with the potential to measure anomalies in various fields from galaxy dynamics [3] to quantum mechanics [4], from nano-thermal systems [5] to financial markets [6] in a standardized language [1]. The tests presented in this study confirm the capacity of the ∆Q metric to quantitatively express observational deviations [1].

Comparison with the Standard Model. It is important to emphasize how the U(3) ZPE scalar field theory approach differs from the Standard Model (SM) in its treatment of divergences. The SM achieves its extraordinary precision through the machinery of renormalization: bare parameters are redefined order by order so that infinities cancel and finite, measurable predictions remain. While this technique is mathematically consistent and empirically spectacular, it leaves open the question of fundamentality: the underlying bare quantities have no physical meaning, and the theory does not explain why the observed parameters (Yukawa couplings, mixing angles, the cosmological constant) take their particular values. By contrast, in the U(3) condensate framework there is a physical ultraviolet cutoff set by the coherence length of the vacuum. Loop integrals are finite by construction, because the field ceases to behave as pointlike beyond this scale. This eliminates the need for renormalization as a mathematical trick, replacing it with a concrete physical regularization rooted in the microstructure of the vacuum. Moreover, the parameters of the low-energy theory-fermion masses, mixing matrices, and coupling strengths-are not arbitrary inputs but emergent quantities derived from the condensate dynamics. In this sense, the theory is not merely an effective description but aspires to be a fundamental account of why the Standard Model takes the form it does. 0.1 Comparison with Other Approaches to Unification It is useful to situate the U(3) condensate framework in the broader landscape of unification programs. Several major approaches have been pursued over the past decades, each with notable strengths but also limitations that our model addresses in a novel way. String Theory. String theory aspires to a complete quantum gravity, embedding all particles as string excitations in higher-dimensional space-times. Its mathematical structure is elegant and has yielded powerful tools (e.g. AdS/CFT),

This work develops the mathematical structure of Caccioppoli inequalities and explores their integration into the framework of the Nardelli Master Equation (NME) and the Gemma-Nardelli Master Equation (GNME). Caccioppoli's inequalities, originally conceived as tools for regularity theory in partial differential equations and differential geometry, are here extended toward applications in number theory, cosmology, and string-inspired physics. By systematically mapping the energy-type bounds of Caccioppoli inequalities onto the variational and symmetry principles underlying the NME, we establish a new set of coupling terms that refine convergence properties of the master framework. Fine-tuning these contributions demonstrates stable numerical convergence toward the golden ratio 𝜙_𝑁 ≃ 1.618665, a constant central to the NME. This synthesis highlights the potential of classical analytic inequalities to inform interdisciplinary approaches uniting PDE theory, cosmological modeling, and number-theoretic structures.

This note proposes an informational model of the cosmos in which streams of cosmic particles (muons, neutrinos, Z bosons, gamma rays) inject quantum information into matter, under local conditions of receptivity. The distinction between well-established concepts and highly speculative extensions is now explicitly marked, and four sub-hypotheses are explored :
1. Encoding conditioned by the internal structure of the nucleus (U).
2. Encoding limited by the granularity of space (Planck volume, l 3 p), a concept inspired by loop quantum gravity.
3. The double condition U ∩ l 3 p.
4. Topological encoding via spherical harmonics. This version incorporates recommendations from an extensive scientific analysis to clarify the distinction between established concepts and speculative extensions, and to refine validation protocols.

Preface (Supplemental Technical Report)

This document represents an earlier stage of our exploration into fermion mass generation within the framework of the U(3) Zero-Point Energy (ZPE) Scalar Condensate.

At the time of writing, the derivation presented here emphasized direct algebraic fits of fermion masses via extended Koide-like relations, without yet incorporating the deeper physical mechanism of isotropy-breaking and phase-locking that now forms the backbone of the unified theory.

While our main research article has since advanced to a more refined and conceptually grounded framework—deriving fermion masses as vorton solitons with anisotropy phases—this report remains valuable for three reasons:

Methodological Record: It preserves the sequence of calculations and fits that guided the transition to the current model.

Independent Cross-Check: The derived relations and numerical fits provide an independent consistency check on the broader theory.

Supplementary Detail: The algebraic steps and exploratory derivations here may be of interest to researchers wishing to follow the full development of the work.

Thus, this document should be regarded as a Supplemental Technical Report, archived alongside the main publication, but not as a replacement for the refined derivation of fermion masses in the primary paper.

A search for pair production of second-generation scalar leptoquarks in the final state with two muons and two jets is performed using proton-proton collision data at ffiffi ffi s p ¼ 7 TeV collected by the CMS detector at the LHC. The data sample used corresponds to an integrated luminosity of 34 pb À1 . The number of observed events is in good agreement with the predictions from the standard model processes. An upper limit is set on the second-generation leptoquark cross section times 2 as a function of the leptoquark mass, and leptoquarks with masses below 394 GeV are excluded at a 95% confidence level for ¼ 1, where is the leptoquark branching fraction into a muon and a quark. These limits are the most stringent to date.

We compute the full one-loop Electro-Weak (EW) contributions of O(α S α 3 EM ) entering the electron-positron into a quark-antiquark pair plus one gluon cross section at the Z peak and LC energies in presence of polarisation of the initial state and by retaining the event orientation of the final state. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W ± and Z bosons. Their importance for the final state orientation is illustrated for beam polarisation setups achieved at SLC and foreseen at ILC and CLIC.

Contemporary cosmology is dominated by the ΛCDM model, which depends on hypothetical entities such as dark matter and dark energy. This work proposes an alternative by integrating the Decreasing Universe Model (DU) and the Kosmos Theory (KTS). DU explains cosmic acceleration through the gravitational contraction of local reference frames, reinterpreting redshift and galactic rotation curves without resorting to hidden entities. KTS, in turn, is grounded in a physicophilosophical ontology that articulates mirror universes, cosmological consciousness as a holographic field, and the Phenomenal Unitary Self as an embodied topological interface. The DU ↔ KTS integration is explored at three levels:  Physicalthe gravitational contraction of DU and the quantum collapse of KTS are seen as expressions of the same universal principle;  Topologicalthe cosmological measures of DU may be reinterpreted in terms of KTS holographic metrics;  Phenomenologicalastronomical redshift and the subjective experience of time are manifestations of the same contraction dynamics. It is concluded that cosmic acceleration can be understood without dark matter or dark energy, through a unified principle of holographic contraction of reference frames, operating both in the cosmos and in consciousness. This synthesis points to a new cosmology in which physics, topology, and phenomenology constitute an inseparable continuum: a Kosmos in creative contraction.

The mechanism of particle mass generation in the Standard Model is discussed. It is shown that non-zero vacuum expectation value of a scalar field together with the proper symmetry of the Lagrangian allow a certain class of scalar field potentials providing generation of gauge boson and fermion masses and keeping the electroweak sector of the model unchanged. Applying the minimality principle and certain additional conditions one can reduce the number of free parameters in the model. Possible phenomenological consequences in the scalar sector for different choices of the potential are discussed.