Φ ∞ II: Recursive Geometry of Classical Reality

Φ ∞ II: Recursive Geometry of Classical Reality | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 29 May 2025 V1 Latest version Share on Φ ∞ II: Recursive Geometry of Classical Reality Author : Faruk Alpay 0009-0009-2207-6528 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.174854029.91112600/v1 400 views 157 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Building upon the Φ ∞ framework introduced in Φ ∞ I: Stabilization of Quantum Structure, this paper demonstrates how classical reality emerges as the entropy-frozen limit of symbolic recursive deformation. I establish the precise mathematical conditions under which symbolic curvature κ(x) = ∂ 2 H/∂ϕ 2 converges to classical geometric curvature, symbolic time t O (n) reduces to Newtonian and relativistic time, and non-commuting symbolic operators collapse into classical observables. The central result is that classical physics represents the κ → 0 limit of recursive stabilization, where the master equation H ϕ Ψ = 0 enforces a unique, deterministic reality through entropy minimization at the universal fixed point Φ ∞ . Supplementary Material File (phi_infinity_ii__recursive_geometry_of_classical_reality-3.pdf) Download 465.20 KB Information & Authors Information Version history V1 Version 1 29 May 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords alpay algebra categorical fixed points classical emergence coalgebras decoherence entropy minimization recursive stabilization sheaf logic spectral sequence symbolic curvature topos theory φ-infinity theory Authors Affiliations Faruk Alpay 0009-0009-2207-6528 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 400 views 157 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Faruk Alpay. Φ ∞ II: Recursive Geometry of Classical Reality. Authorea . 29 May 2025. DOI: https://doi.org/10.22541/au.174854029.91112600/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! 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