Why Three Generations? Fermion Family Closure as a Generational-Saturation Corollary of Mass as Structural Inconsistency in the Fractal Consistency Law
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| _version_ | 1866901398294102016 |
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| author | Reyna Ugarriza, César Daniel |
| author_facet | Reyna Ugarriza, César Daniel |
| contents | <p>This paper develops a focused corollary of the broader Fractal Consistency Law (FCL) mass-spectrum programme: the problem of why the Standard Model contains exactly three fermion generations. The point of departure is not an isolated three-point fit, but the validated quadratic mass law of the main FCL mass manuscript, which identifies distinct family floors and slopes together with a shared negative fermionic curvature. We argue that this curvature can be reinterpreted as a dynamical saturation mechanism acting on a discrete generational ladder. To formalize that idea we introduce a minimal stacking ansatz in which the mass of the nth generation is controlled by a productive compression term and a competing fatigue term. In the charged-lepton sector, this yields a natural and transparent proof-of-concept for short-ladder closure; in the quark sectors, the same mechanism survives only in dressed form, consistent with the QCD-aware treatment and Bayesian stabilization already required by the main mass paper.</p> <p>The manuscript is deliberately disciplined in scope: it does not claim a full first-principles derivation of the Standard Model, nor a universal exclusion theorem for every imaginable fourth-generation scenario. Its central claim is narrower and stronger: the validated shared negative curvature of the FCL fermionic spectrum admits a nontrivial generational reading, according to which family replication is finite because structural complexity accumulates under saturation. We provide the conceptual dictionary linking the global mass fit to the generational ladder, develop the quark extension, address predictable hostile objections, and specify the precise epistemic status of the result. The outcome is a robust, falsifiable and publication-oriented theory note that should be read explicitly as a derived mechanism paper subordinate to the flagship mass-spectrum manuscript.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20090225 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Why Three Generations? Fermion Family Closure as a Generational-Saturation Corollary of Mass as Structural Inconsistency in the Fractal Consistency Law Reyna Ugarriza, César Daniel Fractal Consistency Law Principle of Minimum Inconsistency three generations fermion generations fermion families fermion family closure mass hierarchy particle mass hierarchy Standard Model Standard Model flavor problem Yukawa hierarchy charged leptons quark masses quark dressing fourth generation mass as structural inconsistency shared fermionic curvature negative fermionic curvature generational saturation structural saturation substrate fatigue productive compression fractal mass ladder generational closure <p>This paper develops a focused corollary of the broader Fractal Consistency Law (FCL) mass-spectrum programme: the problem of why the Standard Model contains exactly three fermion generations. The point of departure is not an isolated three-point fit, but the validated quadratic mass law of the main FCL mass manuscript, which identifies distinct family floors and slopes together with a shared negative fermionic curvature. We argue that this curvature can be reinterpreted as a dynamical saturation mechanism acting on a discrete generational ladder. To formalize that idea we introduce a minimal stacking ansatz in which the mass of the nth generation is controlled by a productive compression term and a competing fatigue term. In the charged-lepton sector, this yields a natural and transparent proof-of-concept for short-ladder closure; in the quark sectors, the same mechanism survives only in dressed form, consistent with the QCD-aware treatment and Bayesian stabilization already required by the main mass paper.</p> <p>The manuscript is deliberately disciplined in scope: it does not claim a full first-principles derivation of the Standard Model, nor a universal exclusion theorem for every imaginable fourth-generation scenario. Its central claim is narrower and stronger: the validated shared negative curvature of the FCL fermionic spectrum admits a nontrivial generational reading, according to which family replication is finite because structural complexity accumulates under saturation. We provide the conceptual dictionary linking the global mass fit to the generational ladder, develop the quark extension, address predictable hostile objections, and specify the precise epistemic status of the result. The outcome is a robust, falsifiable and publication-oriented theory note that should be read explicitly as a derived mechanism paper subordinate to the flagship mass-spectrum manuscript.</p> |
| title | Why Three Generations? Fermion Family Closure as a Generational-Saturation Corollary of Mass as Structural Inconsistency in the Fractal Consistency Law |
| topic | Fractal Consistency Law Principle of Minimum Inconsistency three generations fermion generations fermion families fermion family closure mass hierarchy particle mass hierarchy Standard Model Standard Model flavor problem Yukawa hierarchy charged leptons quark masses quark dressing fourth generation mass as structural inconsistency shared fermionic curvature negative fermionic curvature generational saturation structural saturation substrate fatigue productive compression fractal mass ladder generational closure |
| url | https://doi.org/10.5281/zenodo.20090225 |