The Fractal Consistency Law
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2026
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| _version_ | 1866901390599651328 |
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| author | Reyna Ugarriza, César Daniel |
| author_facet | Reyna Ugarriza, César Daniel |
| contents | <h3>This monograph presents a consolidated theorem-bearing proof-skeleton architecture for the mathematical hardening of the Fractal Consistency Law (FCL), a unified fractal framework for quantum theory, gravity, matter, and cosmology. The volume does not claim completed mathematical closure. Its purpose is more precise: to transform the FCL from an ontological and theoretical architecture into an explicit proof program organized through definitions, standing assumptions, propositions, lemmas, target theorems, proof skeletons, technical gaps, and cross-module dependencies.</h3> <h3>The monograph is structured into six modules. Module 1 hardens the microscopic fractal substrate and structural inconsistency functional, defining the admissible configuration space, the tripartite inconsistency decomposition, local stability, minimizer existence, and compatibility with coarse-graining. Module 2 formulates the Principle of Minimum Inconsistency (PMI) as a theorem-bearing variational framework, addressing existence, stability, dynamical selection, gradient-type PMI flows, stationary histories, and physical realizability. Module 3 develops the emergence of quantum structure through quantum-accessible configuration classes, physical equivalence, the Fractal-Hilbert map, tensor-compatible subsystem composition, and a Gleason-type route to the Born rule. Module 4 specifies the proof targets for complete quantization of the fractal substrate, including the kinematic and physical Hilbert spaces, canonical and path-integral routes, global unitarity or probability preservation, operational no-signalling, and emergent Lorentz structure. Module 5 formulates the emergence of matter, gauge structure, and effective quantum field theory through scalar block modes, chiral substrate defects, relational phase-holonomy sectors, structural mass functionals, Standard Model recovery, and controlled fractal corrections. Module 6 converts the observational program into a falsifiable architecture covering background cosmology, structure growth, cosmic topology, gravitational-wave and tensor-sector signatures, the mass and neutrino sector, precision quantum texture signatures, and homogeneous statistical comparability.</h3> <h3>The central contribution of the volume is editorial, mathematical, and programmatic at once. It identifies exactly which pieces of the FCL are already structurally mature, which pieces remain conditional, and which theorem-level gaps must still be closed for the FCL to become a mathematically hardened candidate framework. The monograph should therefore be cited as a theorem-bearing proof-skeleton monograph rather than as a completed final theory.</h3> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19809572 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Fractal Consistency Law Reyna Ugarriza, César Daniel Fractal Consistency Law Principle of Minimum Inconsistency proof skeleton theorem-bearing framework fractal substrate structural inconsistency fractal configuration space variational principle quantum gravity framework emergent quantum mechanics Fractal-Hilbert map Born rule substrate quantization emergent Lorentz invariance emergent matter gauge emergence effective quantum field theory Standard Model emergence cosmology falsifiability <h3>This monograph presents a consolidated theorem-bearing proof-skeleton architecture for the mathematical hardening of the Fractal Consistency Law (FCL), a unified fractal framework for quantum theory, gravity, matter, and cosmology. The volume does not claim completed mathematical closure. Its purpose is more precise: to transform the FCL from an ontological and theoretical architecture into an explicit proof program organized through definitions, standing assumptions, propositions, lemmas, target theorems, proof skeletons, technical gaps, and cross-module dependencies.</h3> <h3>The monograph is structured into six modules. Module 1 hardens the microscopic fractal substrate and structural inconsistency functional, defining the admissible configuration space, the tripartite inconsistency decomposition, local stability, minimizer existence, and compatibility with coarse-graining. Module 2 formulates the Principle of Minimum Inconsistency (PMI) as a theorem-bearing variational framework, addressing existence, stability, dynamical selection, gradient-type PMI flows, stationary histories, and physical realizability. Module 3 develops the emergence of quantum structure through quantum-accessible configuration classes, physical equivalence, the Fractal-Hilbert map, tensor-compatible subsystem composition, and a Gleason-type route to the Born rule. Module 4 specifies the proof targets for complete quantization of the fractal substrate, including the kinematic and physical Hilbert spaces, canonical and path-integral routes, global unitarity or probability preservation, operational no-signalling, and emergent Lorentz structure. Module 5 formulates the emergence of matter, gauge structure, and effective quantum field theory through scalar block modes, chiral substrate defects, relational phase-holonomy sectors, structural mass functionals, Standard Model recovery, and controlled fractal corrections. Module 6 converts the observational program into a falsifiable architecture covering background cosmology, structure growth, cosmic topology, gravitational-wave and tensor-sector signatures, the mass and neutrino sector, precision quantum texture signatures, and homogeneous statistical comparability.</h3> <h3>The central contribution of the volume is editorial, mathematical, and programmatic at once. It identifies exactly which pieces of the FCL are already structurally mature, which pieces remain conditional, and which theorem-level gaps must still be closed for the FCL to become a mathematically hardened candidate framework. The monograph should therefore be cited as a theorem-bearing proof-skeleton monograph rather than as a completed final theory.</h3> |
| title | The Fractal Consistency Law |
| topic | Fractal Consistency Law Principle of Minimum Inconsistency proof skeleton theorem-bearing framework fractal substrate structural inconsistency fractal configuration space variational principle quantum gravity framework emergent quantum mechanics Fractal-Hilbert map Born rule substrate quantization emergent Lorentz invariance emergent matter gauge emergence effective quantum field theory Standard Model emergence cosmology falsifiability |
| url | https://doi.org/10.5281/zenodo.19809572 |