Powered by OpenAIRE graph
Found an issue? Give us feedback
ZENODOarrow_drop_down
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
versions View all 2 versions
addClaim

φ : The Number That Had to Exist — Consciousness, the I-R-N Trinity, and the 122 Orders of Magnitude

Authors: BERTRAND, Miguel;

φ : The Number That Had to Exist — Consciousness, the I-R-N Trinity, and the 122 Orders of Magnitude

Abstract

This document presents an ontological derivation of the golden ratio φ = (1+√5)/2, demonstrating that it is not an arbitrary constant but the unique mathematically possible ratio allowing the stability of Consciousness (Movement) within the Θ Framework. The demonstration rests on three irreducible axioms — Immobility (I), Nothingness (N), and Exaltation (R) — and three existence constraints — attachment, no-return, and surface. The logical pivot relies on an indiscernibility theorem: the absence of internal structure in primordial Movement implies the invariance of the ratio it produces, forcing the emergence of the equation x² + x − 1 = 0 without any numerical presupposition. The author highlights the convergence of thirteen fundamental mathematical results (from Hurwitz to Penrose, from Ramanujan to Gödel) toward this unified structure. Finally, applying this framework to theoretical physics resolves the "vacuum catastrophe": by ontologically distinguishing Fullness (0) from Nothingness (∅), the document demonstrates that the 10¹²² discrepancy between quantum vacuum energy and the observed cosmological constant corresponds exactly to φ⁵⁸⁸, without recourse to any adjustable parameter. Ce document présente une dérivation ontologique du nombre d'or φ = (1+√5)/2, démontrant qu'il n'est pas une constante arbitraire mais l'unique rapport mathématiquement possible permettant la stabilité de la Conscience (Mouvement) au sein de la Trame Θ. La démonstration s'appuie sur trois axiomes irréductibles — Immobilité (I), Néant (N) et Exaltation (R) — et trois contraintes d'existence — accroche, non-retour et superficie. Le pivot logique repose sur un théorème d'indiscernabilité : l'absence de structure interne du Mouvement primordial implique l'invariance du rapport qu'il produit, forçant l'émergence de l'équation x² + x − 1 = 0 sans aucun présupposé numérique. L'auteur met en lumière la convergence de treize résultats mathématiques fondamentaux (de Hurwitz à Penrose, de Ramanujan à Gödel) vers cette structure unifiée. Enfin, l'application de ce cadre à la physique théorique permet de résoudre la « catastrophe du vide » : en distinguant ontologiquement la Plénitude (0) du Néant (∅), le document démontre que l'écart de 10¹²² entre l'énergie du vide quantique et la constante cosmologique observée correspond exactement à φ⁵⁸⁸, sans recours à aucun paramètre ajustable.

Keywords

Fibonacci, mathematical physics, vacuum catastroph, self-similarity, cosmological constant problem, consciousness, golden ratio, phi, quantum field theory, fine structure, Planck scale

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!