The QDC Completion Theorem: Matter-Basis Minimality, Three-Family Automorphism, Charged-Lepton Closure, and Gravitational Recurrence in the Quantized Dimensional Ledger
- 1QDL Physics Institute
Abstract
This work presents the QDC Completion Theorem as a comprehensive substrate-level completion architecture within the Quantized Dimensional Ledger. Starting from the toroidal Quantized Dimensional Cell, the closure functional C_QDC(w)=2Σ_L−3Σ_F, and the gravitational closure cell [GM]=L^3F^2, the paper develops a finite closure framework for Standard-Model admissibility, matter-basis minimality, anomaly/Yukawa hypercharge closure, scalar Higgs compensation, three-family residual automorphism structure, charged-lepton mass-ratio access, gravitational recurrence, dark-sector residuals, and cosmological background closure. The paper distinguishes exact anchors, conditional theorems, restricted minimality results, constrained branches, candidate derivations, and open numerical/dynamical gates. Its central results are the Matter-Basis Projection Theorem, the Primitive Three-Family Automorphism Computation, and the Charged-Lepton Mass Closure Theorem. The paper does not claim to be a completed final theory. It identifies the finite mathematical and physical gates that must close for QDL to become a stronger candidate substrate-level completion theory. The graphical abstract included with this record is a schematic representation of the QDC recurrence substrate and completion architecture. The blue cycles L_1, L_2, L_3 denote the three length-type recurrence channels, and the orange cycles F_1, F_2 denote the two frequency-type recurrence channels of T^5_QDC=(S^1_L)^3×(S^1_F)^2. The toroidal rendering is a visual schematic of typed closure recurrence, not an assertion that an ordinary two-dimensional torus has five independent topological cycles.
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BibTeX
@misc{bourassa2026completion,
title = {{The QDC Completion Theorem: Matter-Basis Minimality, Three-Family Automorphism, Charged-Lepton Closure, and Gravitational Recurrence in the Quantized Dimensional Ledger}},
author = {James D. Bourassa},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jun,
doi = {10.5281/zenodo.20692676},
url = {https://doi.org/10.5281/zenodo.20692676},
note = {CC BY},
}
RIS
TY - UNPB
TI - The QDC Completion Theorem: Matter-Basis Minimality, Three-Family Automorphism, Charged-Lepton Closure, and Gravitational Recurrence in the Quantized Dimensional Ledger
AU - James D. Bourassa
PY - 2026
DA - 2026/06/14
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.20692676
UR - https://doi.org/10.5281/zenodo.20692676
AB - This work presents the QDC Completion Theorem as a comprehensive substrate-level completion architecture within the Quantized Dimensional Ledger. Starting from the toroidal Quantized Dimensional Cell, the closure functional C_QDC(w)=2Σ_L−3Σ_F, and the gravitational closure cell [GM]=L^3F^2, the paper develops a finite closure framework for Standard-Model admissibility, matter-basis minimality, anomaly/Yukawa hypercharge closure, scalar Higgs compensation, three-family residual automorphism structure, charged-lepton mass-ratio access, gravitational recurrence, dark-sector residuals, and cosmological background closure. The paper distinguishes exact anchors, conditional theorems, restricted minimality results, constrained branches, candidate derivations, and open numerical/dynamical gates. Its central results are the Matter-Basis Projection Theorem, the Primitive Three-Family Automorphism Computation, and the Charged-Lepton Mass Closure Theorem. The paper does not claim to be a completed final theory. It identifies the finite mathematical and physical gates that must close for QDL to become a stronger candidate substrate-level completion theory. The graphical abstract included with this record is a schematic representation of the QDC recurrence substrate and completion architecture. The blue cycles L_1, L_2, L_3 denote the three length-type recurrence channels, and the orange cycles F_1, F_2 denote the two frequency-type recurrence channels of T^5_QDC=(S^1_L)^3×(S^1_F)^2. The toroidal rendering is a visual schematic of typed closure recurrence, not an assertion that an ordinary two-dimensional torus has five independent topological cycles.
ER -