Worknote TT-DAV: Discrete Temporality from 2I and NODE-EV
Year: 2026
Type: article
Abstract: We examine whether the geometry of the 600-cell supports a discrete temporality,without yet postulating a complete structural time. Two structures are distinguished. Thefirst is a clock: the binary icosahedral group 2I (120 elements) acts freely by leftField ValueTitle Worknote TT-DAV: Discrete Temporality from 2Iand NODE-EVAuthor DanielAssistance Drafted with Claude (Sonnet 5.5) from joint work inthe sessionCreated 4 November 2026Last revised 5 November 2026Document type Technical worknote (working draft, not apublication)Reference framework TT-DAV Edition 29 (Rev. 6.2); TT-DAV: structural,physical and relational time (PDF)Computing environment Python 3 and NumPy; Colab run with Python 3.13.18and NumPy 2.4.6 (script 1)Attached material 6 complete scripts (Appendix A) and their fulloutputs (Appendix B)Language English (translation of the Spanish originalworknote)Worknote TT-DAV: Discrete Temporality from 2I and NODE-EVPage 1 of 52multiplication on the 120 vertices, 720 edges and 600 tetrahedra, and yields exactrecurrence with periods {1, 2, 3, 4, 5, 6, 10} and least common multiple 60. The second is anarrow: the NODE-EV relaxation s(k) = 1 − c_N^(k+1) with c_N = 0.3065, which is monotoneand convergent but has no recurrence. No numerical relation between the 2I periods andc_N exceeds chance. Return by conjugacy class produces rich period hierarchies, but abattery of 22 finite subgroups of SU(2) shows that they are a property of non-abeliangroups in general, not of the 600-cell. We recommend defining recurrence by exact returnand keeping the clock and the arrow as separate structures. The geometric derivation ofc_N and of the factor 2π/15 remains open.Keywordsdiscrete temporality; structural time; 600-cell; binary icosahedral group 2I; exactrecurrence; conjugacy classes; finite subgroups of SU(2); tetrahedral angular deficit;NODE-EV relaxation; arrow of time; TT-DAV
Author: Chillemi, Daniel Andres
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225318077