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Author

Yuuki Yamagishi

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#small language model Open access Sep 2026

Most of the Smoke Is Not What Burned but Air the Plume Pulled In, So What Sets the Volume of Smoke Is the Ceiling Height ── A 1000 kW fire burns only 0.076923 kg/s of fuel, yet the plume at a height of 5 m carries 9.216677 kg/s ── the separator is whether the volume of smoke is set by the fuel or by the ceiling height ── [Paper 728]

The smoke in a fire is taken to be what burned. Counted by mass, most of it never burned at all. What burned and what became smoke are set side by side in the same units. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──plume entrainment, smoke layer descent and the...

Yuuki Yamagishi · 0 citations
#small language model Open access Sep 2026

The Oldest Age a Ring Can Read Is Set Not by the Clock but by Whether the Ring Can Be Seen ── at a resolution of 1 mum, daily rings can be read to 3.0060 years and annual rings to 22.1871 years, a difference of 19.1811 years ── the separator is whether the rings are made by a daily or a yearly cycle, and whether the rings can be seen ── [Paper 656]

The small stone in a fish's ear (the otolith) carries rings, like the rings of a tree. In young fish one ring a day (daily rings) can be counted, and in grown fish one ring a year (annual rings), and age is read from them. But the slower the growth, the thinner the rings, until the microscope can no longer tell them ap...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

c as the Ball of Velocity Space ── 2nd ed.: This Was a Result About c, Not About 4 pi (the Yamagishi Patch and Thomas Precession) ── [Paper 60]

c as the Ball of Velocity Space — second edition: this was a result about c, not about four pi. In special relativity the set of admissible velocities is a ball of radius c, and under the metric induced by the velocity-addition law it is hyperbolic space of curvature minus one over c squared (Varicak 1910). Here the re...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

The ABC Conjecture Is a Theorem for Polynomials and a Conjecture for Integers: Integers Lack the Derivative ── for polynomials maxdeg never exceeds the number of distinct roots minus 1 (the Mason--Stothers theorem), so the same inequality never fails ── its proof uses that the Wronskian ab'-a'b is divisible by the repeated part of the roots, and integers have no such derivative ── [Paper 641]

For coprime positive integers a+b=c, write rad(abc) for the product of the distinct primes dividing abc, and define the quality q=log c/lograd(abc). The ABC conjecture says that for every epsilon>0 only finitely many triples have q>1+epsilon. The same question can be posed for polynomials, where it is a theorem. This p...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

"Rare" Is Measured on a Logarithmic Scale ── The Central Limit Theorem Is the Wrong Instrument in the Tail, and the Fence Is the Single Big Jump ── [Paper 190]

When an event is called extremely rare, the next question is on what scale it was measured. When a probability falls through orders of magnitude, saying how many times larger one thing is than another stops meaning anything. This paper shows, against exact combinatorial values, that the right scale for a rare event is...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

Why Does a Maximum Speed Exist? ── The Two Relativities (Galilean and Lorentzian) and the Theorem of Ignatowski ── [Paper 83]

Why Does a Maximum Speed Exist? — The Two Relativities (Galilean and Lorentzian) and the Theorem of Ignatowski. Why does a maximum speed exist at all? Starting only from the relativity principle, the homogeneity and isotropy of space, and group structure (plus causality), the coordinate transformations between inertial...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

The Euler-Characteristic Origin of the 4π Patch ── Reading m = 4π as 2π·χ(S²) via Poincaré–Hopf ── [Paper 67]

The Euler-Characteristic Origin of the 4π Patch: Reading m = 4π as 2π·χ(S²) via Poincaré–Hopf. The constant 4π — the total solid angle of the 2-sphere and the limit mass m=4π of Paper 01 — anchors the Yamagishi system. This paper observes that 4π is topological, not merely geometric: by Gauss–Bonnet ∫K dA = 2π·χ, and b...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

The Qubit as a Hopf Fibration ── Is Born's "2" the Same Root as the Hopf Map's "2"? ── [Paper 68]

The Qubit as a Hopf Fibration: Is Born's "2" the Same Root as the Hopf Map's "2"? — A Disciplined Census of the Twos. The state space of a single qubit is exactly the Hopf fibration: normalised state vectors form S³⊂ℂ², the global phase is the fibre U(1)=S¹, the quotient S³/U(1)=S² is the Bloch sphere, and S³→S² is the...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

The 8π Is an Artefact of the Units ── 3rd Edition: Giving Each of the Three Twos Its Own Address ── [Paper 17]

This paper showed that substituting m=4π into the kinetic term of the Schrödinger equation gives −(1/8π)∇²ψ + Vψ = Eψ, and the first edition claimed that this 8π has the same origin as the 8πG of Einstein's equation. The second edition withdrew that claim by separating three mutually unrelated factors of 2. The 3rd edi...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

The Four Planck Quantities Are Four Instances of One Rule ── 3rd ed.: in the Yamagishi Complete Planck Unit Unpacking Theory, the mass dimension fixes the power of 4π, and l_p/t_p=c holds in every unit system ── [Paper 40]

The Four Planck Quantities Are Four Instances of One Rule: Mass Dimension Fixes the Power of 4pi, and l_p/t_p = c Holds in Every Unit System. Third edition. This paper carried a table showing that under the Yamagishi patch G = 4pi, hbar = 1/(4pi) the four Planck quantities read l_p = c^(-3/2), t_p = c^(-5/2), m_p = sqr...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

The Yamagishi Kinetic Energy Equation ── E_k = 2π v², and the Three Distinct Roots of 2π ── [Paper 18]

Take the classical kinetic energy E_k = (1)/(2)mv² and substitute the Yamagishi patch obtained from the n=2 uniqueness theorem, m = 4π = Vol(S²): the result is E_k = 2π v². The substitution is correct. The coefficient (1)/(2) is the result of the integration ∫_0^v v'dv'=(v²)/(2). This paper examines the identity of the...

Yuuki Yamagishi · 0 citations
#large language models Open access Sep 2026

The Uniqueness Theorem of n = 2 for Spherically Symmetric Density Distributions ── Confirmation from Four Directions (Geometry, Mechanics, Potential Theory, Information Theory) and the Representation m = 4π ── [Paper 01]

For a spherically symmetric power-law density distribution ρ(r) = r^(-n) (n in ℝ) in 3D Euclidean space ℝ³, we prove that the mass added per spherical shell, dm/dr = 4π r^(2-n), is independent of the radius r if and only if n = 2 (Theorem 1). The proof needs nothing more than comparing the values at radius 1 and radius...

Yuuki Yamagishi · 0 citations

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