The Connecting Thread Theory (TBP): An Ab Initio Geometric Framework for Fundamental Constants

By: Cefiyana | Independent Interdisciplinary Researcher

Abstract

Contemporary models in high-energy physics and cosmology frequently utilize phenomenological parameterization to constrain the limits of the Standard Model and General Relativity. This article outlines the Connecting Thread Theory (TBP), a proposed discrete 6-dimensional topological matrix framework that models fundamental constants analytically. By formulating a quantized spatial capacity bounded by an absolute thermodynamic ceiling, TBP suggests a deterministic pathway to derive particle masses, coupling strengths, and cosmological budgets with minimal reliance on empirical fitting.

​1. Introduction and Methodological Scope

​The reliance on phenomenological free parameters remains a recognized analytical challenge in fundamental physics. While the Standard Model incorporates over nineteen empirical constants, these values are typically constrained by observation rather than derived from first principles. The Connecting Thread Theory (TBP) provides an alternative formal framework aimed at addressing these challenges by evaluating the fundamental operational space as a discrete mechanical substrate.

​Within its domain of validity, TBP does not invalidate the established macroscopic equations of General Relativity or Quantum Field Theory, but rather aims to provide a geometric basis that mathematically reproduces their empirically measured values.

​2. Foundational Matrix Postulates

​The analytical derivations within TBP are built upon a specific set of geometric parameters, evaluated fractionally to maintain computational consistency. The foundational postulates include:

• ​Spatial Dimension (d=6): The postulated degrees of freedom required to accommodate internal gauge symmetries while maintaining macroscopic stability.
• ​Active Loop Constant (\mu=88): Defined as the baseline topological load of the spatial matrix.
• ​Critical Vacuum Ceiling (R_{crit}): The theoretical upper bound of interaction density, derived as R_{crit} = \frac{\mu^2}{d^2} = \frac{1936}{9} \approx 215.111 GeV.
• ​Geometric Friction Limit (H_{lim}): The modeled spatial attenuation for wave propagation, derived as H{lim} = \frac{1}{d^2 \cdot \sqrt{R{crit}}} = \frac{1}{528} \approx 0.00189.

​3. Formal Action and UV-Finiteness Regulation

​TBP proposes a unified geometric action (\mathcal{S}{TBP}) that evaluates interaction strengths as transmission limits across discrete matrix plaquettes. To address ultraviolet (UV) divergences, the framework integrates a Heaviside step function (\Theta) bounded by the critical ceiling (R{crit}).

​As localized energy density (E_i) approaches the modeled topological limit of \approx 215.11 GeV, the probability amplitude of the operational matrix is fundamentally nullified. This operation suggests a potential mathematical pathway to intrinsically restrict UV-divergences by resolving unbounded S-Matrix integrals into finite, closed summations.

​4. Sectoral Derivations of the Standard Model

​Operating strictly within the theoretical domain of the d=6 manifold, TBP derives the following limits for the Standard Model:

​4.1. The Electromagnetic Sector and Observer Bias

The framework derives a pristine ideal geometric density for the inverse fine-structure constant at exactly \alpha^{-1}{ideal} = 137.036000. This theoretical derivation exhibits a fractional deviation from the empirical CODATA measurement of 137.035999. The model explicitly attributes this \sim \mathcal{O}(10^{-7}) gap to localized observer bias (Terrestrial Vacuum Microlensing), where the macroscopic gravitational potential (\Sigma\Phi{local}) of the Milky Way, Sun, and Earth relativistically compresses the measurement metric.

​4.2. Electroweak and Scalar Bosons

Through the evaluation of the active loop constant (\mu) and derived electroweak mixing angle (\sin^2 \theta_W = \frac{2}{9}), TBP yields highly specific mass boundaries:

• ​Z Boson: Derived analytically as a closed propagation loop at 91.187047 GeV.
• ​W Boson: Incorporating a first-order geometric kinematic attenuation (\Delta M_W = \frac{1}{24} GeV), the observable mass converges at 80.377751 GeV.
• ​The Higgs Boson: Modeled as a stationary topological defect, the base topological sum yields a physical scalar mass equilibrium of exactly 125.222... GeV. This formulation suggests scalar equilibrium can be established without introducing a phenomenological negative mass-squared parameter.

​4.3. Fermion Mass Hierarchy and Neutrino Dissipation

TBP models leptons as propagating kinematic waves and quarks as statically bound geometric regimes. Utilizing a metric scale operator (S \approx 2.151 MeV), the derivations yield structural alignments for the electron (0.510999 MeV), muon (105.66 MeV), and tau (1776.72 MeV) masses.

​Furthermore, neutrinos are modeled not as condensed kinematic fermions, but as thermal dissipations of geometric manifold friction. By projecting generational friction against the squared absolute vacuum capacity (R_{crit}^2), the mass dissipations are mathematically constrained to the sub-electronvolt regime. Specifically, the electron neutrino is derived at 0.2568 eV, consistent with current empirical upper limits.

​5. Deterministic Cosmology and Gravitational Dilution

​The model proposes an alternative perspective on the hierarchy problem by evaluating gravity as a dimensional volumetric dilution of the 6D manifold's internal tension.

• ​Macroscopic Gravity: The derived macroscopic gravitational constant (G_{Final}) is calculated at \approx 6.67184 \times 10^{-11} m$^3kg^{-1}s^{-2}$, incorporating a proposed 3-dimensional volumetric bias.
• ​The Dark Sector: The cosmological energy budget is evaluated as a proportional outcome of the spatial dimension ratios. The framework analytically predicts a Dark Energy budget (vacuum loop residue) of \approx 68.67\% and a Dark Matter budget of \approx 26.68\%. These formulations exhibit strong geometric convergence with Planck satellite empirical metrology without the necessity for phenomenological particulate parameters.

​6. Limitations, Reproducibility, and Falsification

​The exact fractional derivations within the TBP framework reflect the deterministic nature of its mathematical axioms rather than empirical exactitude. The model is explicitly falsifiable; if current or future collider programs observe macroscopic matter configurations or scalar excitations above the theoretical limit of \approx 215.11 GeV, the foundational topological truncation proposed by this model is invalidated.

​To ensure absolute computational reproducibility, the complete custom Python source code utilized to verify the fractional matrix computations, dimensional mass derivations, and perturbative stability is openly deposited on GitHub. Extrapolation of this matrix framework beyond current metrological and collider validation remains theoretical, pending independent empirical testing.

​7. Conclusion

​The Connecting Thread Theory provides an analytical exploration of discrete spatial geometries. By bounding a 6-dimensional manifold with an absolute thermodynamic ceiling, the model outlines a deterministic method for evaluating the parameters of the Standard Model and General Relativity. While the derivations align closely with current CODATA and Planck observations, definitive validation is contingent upon high-resolution collider binning and asymptotic zero-potential astrophysical metrology.

full manuscript read:

[embed]*The Connecting Thread Theory: An Ab Initio Geometric Matrix Framework for Standard Model and Gravitational Parameters *Contemporary theoretical physics frequently utilizes phenomenological parameterization to constrain the Standard Model and the cosmological metrics of General Relativity. This manuscript introduces the Connecting Thread Theory (TBP), a discrete 6-dimensional topological matrix framework that models the fundamental constants of nature ab initio, structurally minimizing reliance on empirical parameter fitting. doi.org

ORCID:

[embed][*ORCID

orcid.org](https://orcid.org/0009-0008-4324-9515)