Quantum Fractal Geometry: Rigorous Foundations, Unifying Framework, and Comprehensive Experimental Program
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2026
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| _version_ | 1866901879974264832 |
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| author | Portelli, Christopher |
| author_facet | Portelli, Christopher |
| contents | <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Version 2 (April 2026). This paper presents the QFG theoretical framework including formal axioms, projection operator, three master theorems deriving the Born rule, Einstein field equations and Schrödinger equation, no-signalling theorem, and quantitative falsifiable predictions for Bell tests, CMB, black hole scaling, and galaxy dynamics.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Three targeted updates relative to Version 1 (DOI: 10.5281/zenodo.19510514): (1) The companion empirical paper citation has been corrected — the prior preprint (DOI: 10.5281/zenodo.19523163) was withdrawn because it employed a proxy statistic not faithful to the formal CTI definition; it is superseded by a new paper implementing the theoretically correct CTI using the QFG projection operator directly. (2) Section 8.1 reports the first result of that proper CTI test: coefficient δ = −0.357 (p = 0.0083) on N = 70 galaxies, consistent with the QFG sign prediction. (3) Section 7 cosmological numerical predictions are explicitly identified as parameter-dependent estimates requiring first-principles derivation of α, λ, and Lc before definitive tests can be formulated. The theoretical framework is entirely unchanged from Version 1.</p> <blockquote class="ml-2 border-l-4 border-border-300/10 pl-4 text-text-300"> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]"><strong>Foundation paper (19510513 V2)</strong></p> <blockquote class="ml-2 border-l-4 border-border-300/10 pl-4 text-text-300"> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]"><strong>Note (April 2026).</strong> Subsequent empirical testing of the CTI implementation indicates that the current operationalisation does not demonstrate independent signal beyond morphological structure when profiles are richly characterised. The theoretical framework remains intact and untouched by these results. The framework is empirically unconfirmed pending improved observables or first-principles derivation of the free parameters α, λ, and Lc.</p> </blockquote> </blockquote> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19562759 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Quantum Fractal Geometry: Rigorous Foundations, Unifying Framework, and Comprehensive Experimental Program Portelli, Christopher quantum gravity quantum entanglement Bell theorem black hole thermodynamics cosmology fractal geometry observer resolution General Relativity Quantum Mechanics <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Version 2 (April 2026). This paper presents the QFG theoretical framework including formal axioms, projection operator, three master theorems deriving the Born rule, Einstein field equations and Schrödinger equation, no-signalling theorem, and quantitative falsifiable predictions for Bell tests, CMB, black hole scaling, and galaxy dynamics.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Three targeted updates relative to Version 1 (DOI: 10.5281/zenodo.19510514): (1) The companion empirical paper citation has been corrected — the prior preprint (DOI: 10.5281/zenodo.19523163) was withdrawn because it employed a proxy statistic not faithful to the formal CTI definition; it is superseded by a new paper implementing the theoretically correct CTI using the QFG projection operator directly. (2) Section 8.1 reports the first result of that proper CTI test: coefficient δ = −0.357 (p = 0.0083) on N = 70 galaxies, consistent with the QFG sign prediction. (3) Section 7 cosmological numerical predictions are explicitly identified as parameter-dependent estimates requiring first-principles derivation of α, λ, and Lc before definitive tests can be formulated. The theoretical framework is entirely unchanged from Version 1.</p> <blockquote class="ml-2 border-l-4 border-border-300/10 pl-4 text-text-300"> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]"><strong>Foundation paper (19510513 V2)</strong></p> <blockquote class="ml-2 border-l-4 border-border-300/10 pl-4 text-text-300"> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]"><strong>Note (April 2026).</strong> Subsequent empirical testing of the CTI implementation indicates that the current operationalisation does not demonstrate independent signal beyond morphological structure when profiles are richly characterised. The theoretical framework remains intact and untouched by these results. The framework is empirically unconfirmed pending improved observables or first-principles derivation of the free parameters α, λ, and Lc.</p> </blockquote> </blockquote> |
| title | Quantum Fractal Geometry: Rigorous Foundations, Unifying Framework, and Comprehensive Experimental Program |
| topic | quantum gravity quantum entanglement Bell theorem black hole thermodynamics cosmology fractal geometry observer resolution General Relativity Quantum Mechanics |
| url | https://doi.org/10.5281/zenodo.19562759 |