Independent researcher and software engineer (28 years of experience), based in Japan.
I started by translating dense theoretical physics and mathematics papers into geometric language — assembling structures piece by piece, like building a model kit. I used AI extensively as a thinking partner throughout this process. Along the way, several unexpected results emerged.
Hyperbolic Scattering, Riccati Asymptotics, and Fredholm Exclusion
A proof of the Riemann Hypothesis via hyperbolic scattering theory on PSL(2,Z)\H². The core result is the scattering Transmission route of §18: from the Riccati expansion of the Dirichlet-to-Neumann operator (Lemma 18.D) and bridge lemmas, Standing Hypotheses (H1)–(H4) are established unconditionally. Theorem 18.H (off-wall exclusion) yields Corollary 18.I (RH). Bilingual: Japanese + English.
🔗 https://zenodo.org/records/19210658
Structural Unification of Gravity, Electromagnetism, and Quantum Mechanics via Curvature Density ρ
A five-part series establishing structural unification of gravity, electromagnetism, and quantum mechanics through the curvature density of U(1) connections on the null Kerr screen S² ≅ CP¹. The gravitational rotation 1-form, Berry connection, and electromagnetic connection share the universal representation F = ϱ ω_FS on S². The unification is structural — a common geometric grammar across three domains. Einstein's equations are characterized, not derived. 98 pages. Bilingual: Japanese + English.
🔗 https://zenodo.org/records/18912814
Structural Inaccessibility of the ABC Conjecture
A no-go theorem proving that no method in method class C (finite local observation-based methods, encompassing sieves, Baker bounds, Buium arithmetic differential geometry, cyclotomic valuations) can prove the finiteness of super-Wieferich primes. Also proves a density theorem: at least 21% of bases possess a super-Wieferich prime. Formulates the null geometry of Spec Z as an indefinite bilinear form. Bilingual: Japanese + English.
🔗 https://zenodo.org/records/19311094
IUT の ABC 証明に対する方法クラス C による構造的限界分析
Structural analysis of Mochizuki's IUT theory using four necessary conditions N1–N4 derived as the contrapositive of the no-go theorem for method class C. Under the IUT component classification, IUT does not exit class C. By the no-go theorem, methods inside C cannot prove ABC. English and Japanese versions included.
🔗 https://zenodo.org/records/19322884
Geometric Derivation from the Riemann Harmonic Sphere and the Harmonic Structure of Number Space
A first-principles geometric derivation of CP violation (matter-antimatter asymmetry) from the adopted parent geometry G_ado (Klein parent curve + Fano plane + octonion) with zero free parameters. The eight geometric constants {r=π/8, a/r=3/(2π²), Δθ_K=1/12, C_j=π²/128, α=√(π/2), K=2/3, λ_eff=(8/π)⁴-3/4, θ_K,up=rμ_k} reproduce all seven CKM observables within at most 0.45σ of PDG measurements (χ²₇ = 0.461). Three generations enforced geometrically via PSL(2,7) ⊂ SU(3); fourth generation excluded. Maxwell's equations rewritten in null form on the null time direction. 270 pages, 12 main chapters + 20 supplementary chapters, 6 figures. Bilingual: Japanese + English.
🔗 https://zenodo.org/records/19800883
These results were not planned. Each emerged from following a geometric structure wherever it led:
- Started from null geometry on a Kerr screen
- Used AI as a constant thinking partner ("explain this like I'm in elementary school")
- Lined up related equations from different domains to find structural similarities
- Translated everything into geometry piece by piece — like assembling a model kit
The arithmetic showed up uninvited. That's the honest version of how this work happened.
Looking for arXiv endorsers in mathematics (math.NT, math-ph) and physics (hep-th).
This work is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).