International Journal of Topology

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Int. J. Topol., Volume 2, Issue 2 (June 2025) – 2 articles

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39 pages, 401 KiB

Open AccessArticle

Computational Holography

by Logan Nye

Int. J. Topol. 2025, 2(2), 5; https://doi.org/10.3390/ijt2020005 - 15 Apr 2025

Viewed by 132

Abstract

We establish a comprehensive framework demonstrating that physical reality can be understood as a holographic encoding of underlying computational structures. Our central thesis is that different geometric realizations of the same physical system represent equivalent holographic encodings of a unique computational structure. We formalize quantum complexity as a physical observable, establish its mathematical properties, and demonstrate its correspondence with geometric descriptions. This framework naturally generalizes holographic principles beyond AdS/CFT correspondence, with direct applications to black hole physics and quantum information theory. We derive specific, quantifiable predictions with numerical estimates for experimental verification. Our results suggest that computational structure, rather than geometry, may be the more fundamental concept in physics. Full article

(This article belongs to the Special Issue Feature Papers in Topology and Its Applications)

16 pages, 890 KiB

Open AccessArticle

Baryonic Matter, Ising Anyons and Strong Quantum Gravity

by Michel Planat

Int. J. Topol. 2025, 2(2), 4; https://doi.org/10.3390/ijt2020004 - 4 Apr 2025

Viewed by 210

Abstract

We find that the whole set of known baryons of spin parity

J^{P} = {\frac{1}{2}}^{+}

(the ground state) and

J^{P} = {\frac{3}{2}}^{+}

(the first excited state) is organized in multiplets which may efficiently be encoded by the [...] Read more.

We find that the whole set of known baryons of spin parity

J^{P} = {\frac{1}{2}}^{+}

(the ground state) and

J^{P} = {\frac{3}{2}}^{+}

(the first excited state) is organized in multiplets which may efficiently be encoded by the multiplets of conjugacy classes in the small finite group

G = (192, 187)

. A subset of the theory is the small group

(48, 29) ≅ G L (2, 3)

whose conjugacy classes are in correspondence with the baryon families of Gell-Mann’s octet and decuplet. G has many of its irreducible characters that are minimal and informationally complete quantum measurements that we assign to the baryon families. Since G is isomorphic to the group of braiding matrices of

S U {(2)}_{2}

Ising anyons, we explore the view that baryonic matter has a topological origin. We are interested in the holographic gravity dual

A d S_{3} / Q F T_{2}

of the Ising model. This dual corresponds to a strongly coupled pure Einstein gravity with central charge

c = 1 / 2

and AdS radius of the order of the Planck scale. Some physical issues related to our approach are discussed. Full article

(This article belongs to the Special Issue Feature Papers in Topology and Its Applications)

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Int. J. Topol., Volume 2, Issue 2 (June 2025) – 2 articles

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