Index:
・Part A: Foundations of Intelligence (AGI/ASI)
・Part B: Application to the Universe (Physics)
Part A: Foundations of Intelligence (AGI/ASI)
Optimal Solution of Inductive Inference via Minimization of Unpredictable Information: Towards Artificial Superintelligence
Overview:
How can AI transcend human intelligence (AGI) to reach Artificial Superintelligence (ASI)? As long as AI relies on human evaluations (e.g., RLHF), it cannot exceed human cognitive limits. This paper provides a purely mathematical and objective formalization of "inductive inference," eliminating arbitrary prior probabilities by introducing the "Unknown (?)" placeholder. By defining the optimal solution as the minimization of "Total Unpredictable Information" (E=L(R)+H(P)), it resolves the trade-offs of overfitting and sample scarcity. This is the absolute objective function for the "System 2 (Rational Reasoning)" of ASI.
Key Achievements:
- Elimination of arbitrary prior probabilities using the "Unknown (?)" placeholder.
- Formulation of a parameter-free entropy calculation based on the total number of samples.
- Definition of the optimal solution for inductive inference via the minimization of "Total Unpredictable Information."
Abstract:
For artificial intelligence to surpass human intelligence and reach Artificial Superintelligence (ASI), an objective and mathematical optimal solution for inductive inference, independent of subjective human evaluations or arbitrary prior probabilities, is indispensable. In this paper, we propose a novel formalization that reduces inductive inference to a deductive framework by embedding the inference target into the population as an information-less placeholder called the "Unknown" (?). In this method, the probability distribution and the unknown rate of the target are derived based on the spatial relationships between known samples and the target. Furthermore, to mathematically eliminate the combinatorial explosion (overfitting) associated with infinite variable generation and coordinate transformations, we redefine the optimal solution of inductive inference as the minimization of the "total unpredictable information," which is the sum of the "information content of the rule" and the "entropy of the inference result." By calculating the rule's information content as the number of symbol selections in the sum-of-products standard form, and by defining entropy through a parameter-free general formula based on the total number of samples, we completely eliminate dependence on programming language syntax and physical resolution. This theory resolves the trade-offs among inference purity, sample size, and rule complexity without any arbitrariness. Implementing this objective evaluation criterion as the absolute objective function for the AI's "System 2" (rational reasoning) paves a definitive path toward realizing ASI that transcends human cognitive biases and autonomously discovers true laws.
How to Cite:
<>Bibtex
@misc{kato_2026_22955788,
author = {Kato, Yusuke},
title = {Optimal Solution of Inductive Inference via
Minimization of Unpredictable Information: Towards
Artificial Superintelligence
},
month = sep,
year = 2026,
publisher = {Zenodo},
doi = {10.5281/zenodo.22955788},
url = {https://doi.org/10.5281/zenodo.22955788},
}
Part B: Application to the Universe (Physics)
Overview of the Intergeometric Theory:
The Intergeometric Theory consists of two foundational papers. Part I focuses on the microscopic scale (particle physics), deriving the Standard Model from geometric first principles. Part II expands this framework to the macroscopic scale (cosmology), resolving major cosmological paradoxes. Together, they form a self-consistent Theory of Everything spanning from the Higgs scale to the Hubble scale.
Geometric Unification of Spacetime and Particles (I): First-Principles Derivation of Standard Model Parameters based on Phase Interference and Topology
Key Achievements:
- Mathematical proof of parity violation in weak interactions.
- Derivation of 3-generation fermion masses and CKM/PMNS mixing matrices from topological volume ratios.
- Geometric derivation of the gravitational constant (G).
Abstract:
Although the Standard Model in modern particle physics agrees with experiments to an extremely high precision, the origins of ”local gauge invariance,” ”parity violation,” ”neutrino masslessness,” and dozens of free parameters (mass ratios, coupling constants, and mixing angles) are treated as phenomenological assumptions rather than theoretical inevitabilities. In this paper, starting from the first principle that the universe is a ”minimal entity of existence rather than nothingness,” we present a geometric framework based on spatial directionality and wave phase interference. In this theory, gauge interactions and the Higgs mechanism are reconstructed as geometric compensation mechanisms for phase shifts accompanying particle propagation, and the left-handed selectivity of the weak interaction (parity violation) is mathematically proven as a theorem regarding the radiation causality of space. Furthermore, by formulating spacetime as a 4-dimensional tensor product Hilbert space (degrees of freedom N = 81), and utilizing the trace of the projection tensor for the spatial metric and topological measure integrals in phase space, we derive the coupling constants, fermion masses, mixing matrices (CKM and PMNS), and the gravitational constant from first principles. Except for the calibration of the Higgs scale using the electron mass and the identification of the cosmological environmental variable (decay rate χ0), this model calculates all major parameters of the Standard Model within 1σ accuracy without employing any arbitrary parameter fitting. This study suggests that a superstring-like geometric approach functions extremely powerfully even as a low-energy effective theory, and that the Standard Model is a topological inevitability of space itself.
How to Cite:
<>Bibtex
@misc{kato_2026_22805072,
author = {Kato, Yusuke},
title = {Geometric Unification of Spacetime and Particles
(I): First-Principles Derivation of Standard Model
Parameters based on Phase Interference and
Topology
},
month = sep,
year = 2026,
publisher = {Zenodo},
doi = {10.5281/zenodo.22805072},
url = {https://doi.org/10.5281/zenodo.22805072},
}
Geometric Unification of Spacetime and Particles (II): Resolution of Hubble Tension via Scale Illusion and Identification of Dark Matte
Key Achievements:
- Complete resolution of the Hubble tension and \(S_8\) tension via "Scale Illusion" accompanying vacuum decay.
- Geometric resolution of the 120-order-of-magnitude cosmological constant problem.
- Identification of dark matter as "Transverse Leptons" whose pair creation is strictly prohibited by superselection rules.
Abstract:
Although the modern standard cosmology (ΛCDM model) is in good agreement with observational data, it harbors fundamental paradoxes such as the cosmological constant problem, the Hubble tension, the identity of dark matter, and baryon asymmetry. In this paper, we extend the concepts of ”fractal hierarchical structure of space” and ”cosmic energy decay rate χ0,” which derived all parameters of the particle Standard Model in the previous report, to macroscopic cosmological scales, comprehensively resolving these intractable problems from a unified geometric principle. First, by redefining inflation as a tensor-product hierarchical creation process of spatial information and setting the true natural unit at the Higgs scale, we geometrically resolve the 120-order-of-magnitude discrepancy in the vacuum energy density. Next, we introduce the decay dynamics of the vacuum in the energy budget of the universe. By formulating the ”geometric scale illusion” caused against true background evolution by the standard distance rulers assuming an invariant dark energy, we proved that the increase of H0 in the late universe (Hubble tension) and the S8 tension are consecutively resolved without altering the laws of physics. Furthermore, we identify dark matter geometrically as a ”Transverse Lepton” whose pair creation is strictly prohibited by superselection rules in quantum field theory, and derive the baryon number density and the energy density ratios (Ωm,ΩΛ) from first principles based on the spin budget of the early universe. Through this theory, the entire history of the universe—from a singularity-free birth to a ”Big Reset” at the end of its life—is elucidated without invoking any unknown dark fluids or ad-hoc parameter adjustments.
How to Cite:
<>Bibtex
@misc{kato_2026_22805497,
author = {Kato, Yusuke},
title = {Geometric Unification of Spacetime and Particles
(II): Resolution of Hubble Tension via Scale
Illusion and Identification of Dark Matter
},
month = sep,
year = 2026,
publisher = {Zenodo},
doi = {10.5281/zenodo.22805497},
url = {https://doi.org/10.5281/zenodo.22805497},
}