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View article: Murakamian Ombre: Non-Semisimple Topology, Cayley Cubics, and the Foundations of a Conscious AGI
Murakamian Ombre: Non-Semisimple Topology, Cayley Cubics, and the Foundations of a Conscious AGI Open
Haruki Murakami’s Hard-Boiled Wonderland and the End of the World portrays a world where the “shadow”, the seat of memory, desire, and volition, is surgically removed, leaving behind a perfectly fluent but phenomenologically empty self. We…
View article: From Fibonacci Anyons to B-DNA and Microtubules via Elliptic Curves
From Fibonacci Anyons to B-DNA and Microtubules via Elliptic Curves Open
By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient G=Z5⋊2I, where 2I is the binary icosahedral group. The Gröbner basis decomposition of its SL(2,C) character variety yields elliptic c…
View article: From Fibonacci Anyons to B-DNA and Microtubules via Elliptic Curves
From Fibonacci Anyons to B-DNA and Microtubules via Elliptic Curves Open
By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient $G=\mathbb{Z}_{5}\rtimes 2I$, where $2I$ is the binary icosahedral group. The Gröbner basis decomposition of its $SL(2,\mathbb{C})$ c…
View article: Neutrino Mixing Matrix with SU(2)4 Anyon Braids
Neutrino Mixing Matrix with SU(2)4 Anyon Braids Open
We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to SU(2)2 Ising anyons. Remarkably, the braids of SU(2)4 anyons allow the neutrino mixing matrix to be generated …
View article: Neutrino Mixing Matrix with SU(2)<sub>4</sub> Anyon Braids
Neutrino Mixing Matrix with SU(2)<sub>4</sub> Anyon Braids Open
We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to $SU(2)_2$ Ising anyons. Remarkably, the braids of $SU(2)_4$ anyons allow to generate the neutrino mixing matri…
View article: Quantum Capital: Many-Worlds Interpretation and the Fragmentation of Global Economic Reality
Quantum Capital: Many-Worlds Interpretation and the Fragmentation of Global Economic Reality Open
This paper explores the Many-Worlds Interpretation (MWI) of quantum mechanics as a conceptual framework for understanding fragmentation, uncertainty, and narrative divergence in global economic dynamics. We argue that the logic of Everetti…
View article: From Many Worlds to Many Realities: The Everett Interpretation as a Lens for Understanding Contemporary Geopolitical Psychology
From Many Worlds to Many Realities: The Everett Interpretation as a Lens for Understanding Contemporary Geopolitical Psychology Open
The Many-Worlds Interpretation (MWI) of quantum mechanics, first proposed by Hugh Everett in 1957, posits that all possible outcomes of a quantum measurement are realized in coexisting branches of the universe. While traditionally confined…
View article: Baryonic Matter, Ising Anyons and Strong Quantum Gravity
Baryonic Matter, Ising Anyons and Strong Quantum Gravity Open
We find that the whole set of known baryons of spin parity JP=12+ (the ground state) and JP=32+ (the first excited state) is organized in multiplets which may efficiently be encoded by the multiplets of conjugacy classes in the small finit…
View article: Baryonic Matter, Ising Anyons and Strong Quantum Gravity
Baryonic Matter, Ising Anyons and Strong Quantum Gravity Open
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 …
View article: What ChatGPT Has to Say About Its Topological Structure: The Anyon Hypothesis
What ChatGPT Has to Say About Its Topological Structure: The Anyon Hypothesis Open
Large language models (LLMs) achieve remarkable predictive capabilities but remain opaque in their internal reasoning, creating a pressing need for more interpretable artificial intelligence. Here, we propose bridging this explanatory gap …
View article: What Chat GPT Has to Say About Its Topological Structure: The Anyon Hypothesis
What Chat GPT Has to Say About Its Topological Structure: The Anyon Hypothesis Open
Large language models (LLMs) achieve remarkable predictive capabilities but remain opaque in their internal reasoning, creating a pressing need for more interpretable artificial intelligence. Here, we propose bridging this explanatory gap …
View article: What Chat GPT Has to Say About Its Topological Structure: The Anyon Hypothesis
What Chat GPT Has to Say About Its Topological Structure: The Anyon Hypothesis Open
The large language model Chat GPT answers questions relative to its structure under the supervision of the authors. Then we postulate that modular tensor categories, alias the theory of anyons, are relevant for partially explaining the top…
View article: International Journal of Topology
International Journal of Topology Open
Welcome to the new open access journal: the International Journal of Topology (IJT), published by MDPI [...]
View article: Topology and Dynamics of Transcriptome (Dys)Regulation
Topology and Dynamics of Transcriptome (Dys)Regulation Open
RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let us delve into the mathematical intri…
View article: Topology and Dynamics of Transcriptome (Dys)regulation
Topology and Dynamics of Transcriptome (Dys)regulation Open
RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let’s delve into the mathematical intric…
View article: Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density
Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density Open
We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that …
View article: Group Theory of Messenger RNA Metabolism and Disease
Group Theory of Messenger RNA Metabolism and Disease Open
International audience
View article: Dynamics of Fricke–Painlevé VI Surfaces
Dynamics of Fricke–Painlevé VI Surfaces Open
The symmetries of a Riemann surface Σ∖{ai} with n punctures ai are encoded in its fundamental group π1(Σ). Further structure may be described through representations (homomorphisms) of π1 over a Lie group G as globalized by the character v…
View article: Dynamics of Fricke-Painlevé VI surfaces
Dynamics of Fricke-Painlevé VI surfaces Open
The symmetries of a Riemann surface $\Sigma \setminus \{a_i\}$ with $n$ punctures $a_i$ are encoded in its fundamental group $\pi_1(\Sigma)$. Further structure may be described through representations (homomorphisms) of $\pi_1$ over a Lie …
View article: Dynamics of Fricke-Painlevé VI surfaces
Dynamics of Fricke-Painlevé VI surfaces Open
The symmetries of a Riemann surface $\Sigma \setminus \{a_i\}$ with $n$ punctures $a_i$ are encoded in its fundamental group $\pi_1(\Sigma)$. Further structure may be described through representations (homomorphisms) of $\pi_1$ over a Lie …
View article: Review of: "An alternative foundation of quantum theory"
Review of: "An alternative foundation of quantum theory" Open
Potential competing interests: No potential competing interests to declare.Dear Hinge, I read your approach with much interest.The range of your concepts is broad and well explained.Since you base your new approach of quantum theory on gro…
View article: Group Theory of Messenger RNA Metabolism and Disease
Group Theory of Messenger RNA Metabolism and Disease Open
Our recent work has focused on the application of infinite group theory and related algebraic geometric tools in the context of transcription factors and microRNAs. We were able to differentiate between “healthy" nucleotide sequences…
View article: Group Theory of Messenger RNA Metabolism and Disease
Group Theory of Messenger RNA Metabolism and Disease Open
Our recent work has focused on the application of infinite group theory and related algebraic geometric tools in the context of transcription factors and microRNAs. We were able to differentiate between “healthy" nucleotide sequences …
View article: Review of: "Fidelity of quantum blobs"
Review of: "Fidelity of quantum blobs" Open
Potential competing interests: No potential competing interests to
View article: Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density
Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density Open
We generalize Koopman-von Neumann classical mechanics to poly-symplectic fields and recover De Donder-Weyl theory. Comparing with Dirac's Hamiltonian density inspires a new Hamiltonian formulation with a canonical momentum field that is Lo…
View article: Algebraic Morphology of DNA–RNA Transcription and Regulation
Algebraic Morphology of DNA–RNA Transcription and Regulation Open
Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. To discover the symmetries and invariants of the transcription and regulation at the scale of …
View article: SL(2,C) Scheme Processing of Singularities in Quantum Computing and Genetics
SL(2,C) Scheme Processing of Singularities in Quantum Computing and Genetics Open
Revealing the time structure of physical or biological objects is usually performed thanks to the tools of signal processing such as the fast Fourier transform, Ramanujan sum signal processing, and many other techniques. For space-time top…