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Yuuki Yamagishi

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#small language model Open access Sep 2026

Zeno's Four Paradoxes Do Not Share a Single Resolution ── the dichotomy falls to a convergent series, Achilles to an infinite sum, the arrow to the limit of a difference quotient and the stadium to a discrete space ── four paradoxes, four different pieces of mathematics ── [Paper 519]

Zeno’s paradoxes are often said, all together, to have been settled by the calculus. What this paper shows is that the four fall to four different tools, and that one of them does not fall to the calculus at all. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the s...

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

Zeno's Four Paradoxes Do Not Share a Single Resolution ── the dichotomy falls to a convergent series, Achilles to an infinite sum, the arrow to the limit of a difference quotient and the stadium to a discrete space ── four paradoxes, four different pieces of mathematics ── [Paper 519]

Zeno’s paradoxes are often said, all together, to have been settled by the calculus. What this paper shows is that the four fall to four different tools, and that one of them does not fall to the calculus at all. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the s...

Yuuki Yamagishi · 0 citations
#diffusion models Open access Sep 2026

The 2.5 in the Viscosity of a Suspension Comes Not from the Volume of the Particles but from the Stress They Place on the Flow Outside ── for the Stokes solution of a sphere in a uniform straining flow, the surface integral of the stress over the sphere (the stresslet) is 20π/3 times viscosity, radius cubed and strain, and dividing by the particle volume 4π/3 gives 2.5; solving viscosity and diffusion for two unknowns, a change of the coefficient from 1 to 2.5 moves Avogadro's number by a factor 1.581139 ── the separator is whether one counts the volume inside the particle or the stress outside it ── [Paper 1024]

A liquid with small spheres mixed in at volume fraction φ has, when dilute, (1 + 2.5φ) times its original viscosity. Einstein wrote the coefficient as 1 in his 1906 doctoral thesis and corrected it to 2.5 in 1911. This paper checks the Stokes solution for a sphere in a uniform straining flow by symbolic computation, ob...

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

A Square Net and a Triangular Net Describe the World With the Same Exponent, and Only the Coefficient Differs ── counting lattice points inside a circle with square, triangular and rectangular lattices of the same density, the error grows as a power of the radius whose exponents 0.525037, 0.521921 and 0.542771 differ by only 0.02 while the coefficients 1.392341, 1.657107 and 1.119127 differ by 0.30; Tractatus 6.341, that the shape of the net is arbitrary and only its fineness says something about the world, is counted as exponent against coefficient ── the separator is whether what was changed is the shape of the net or its fineness ── [Paper 1033]

In Tractatus 6.341 Wittgenstein likened mechanics to a net laid over the world: the shape of the mesh (square or triangular) is arbitrary, and all that can be said of the world is that it can be described by a net of this fineness. This paper counts the simile with lattice points. Three lattices of the same density are...

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

How Many Frequencies Can Be Nulled Is Fixed by the Number of Coefficients ── five coefficients null two frequencies, a third raises the count to 7, and truncating back to five leaves none of the three at zero ── [Paper 520]

How many demands of the form “null this frequency” can be met? What this paper shows is that the ceiling is set by the number of coefficients, and that falling short does not cost one demand but all of them. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the fundam...

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

The Energy Fluctuation of Light Is a Particle Term Plus a Wave Term, and the Two Are Equal Exactly When the Occupation Number Is 1 ── in the energy fluctuation of a single mode, the particle term divided by the wave term equals the reciprocal of the occupation number and becomes 1 at hν = kT ln 2; at the Planck peak the particle term is 15.8 times the wave term, and for visible sunlight 91.5 times ── the separator is whether the occupation number is above or below 1 ── [Paper 1022]

In 1909 Einstein showed that the energy fluctuation of a single mode of black-body radiation is the sum of a term like that of light quanta and a term like that of classical waves. This paper checks by three routes, the formula, the distribution of the occupation number and thermodynamics, that the ratio of the two ter...

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

The Energy Fluctuation of Light Is a Particle Term Plus a Wave Term, and the Two Are Equal Exactly When the Occupation Number Is 1 ── in the energy fluctuation of a single mode, the particle term divided by the wave term equals the reciprocal of the occupation number and becomes 1 at hν = kT ln 2; at the Planck peak the particle term is 15.8 times the wave term, and for visible sunlight 91.5 times ── the separator is whether the occupation number is above or below 1 ── [Paper 1022]

In 1909 Einstein showed that the energy fluctuation of a single mode of black-body radiation is the sum of a term like that of light quanta and a term like that of classical waves. This paper checks by three routes, the formula, the distribution of the occupation number and thermodynamics, that the ratio of the two ter...

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

The Extrapolation Crosses Zero Because the Heat-Capacity Difference Was Held Constant ── With a melting entropy of 10 and a heat-capacity difference of 30, the extrapolated entropy difference crosses zero at T=214.959393, or 0.716531 of the melting point ── let it vanish as the third law requires and it need not cross at all ── [Paper 503]

The Kauzmann paradox is spoken of as a property of supercooled liquids. This paper shows that crossing zero follows from holding the heat-capacity difference constant──held constant, however small, it always crosses. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──t...

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

The Spatial Curvature of a Rotating Disk Is −3Ω²/c², and Its Argument Differs from the −1/c² of Velocity Space ── the Gaussian curvature of the spatial metric of a rotating frame is −3Ω²/c² at the centre and vanishes when Ω is set to 0; for a disk whose rim moves at half the speed of light the circumference over the diameter is πγ = 3.627599 and the area is 1.071797 times the Euclidean one, growing less than the circumference; the curvature −1/c² of velocity space contains no Ω and has different units ── the separator is whether what bends is rotation or the composition of velocities ── [Paper 1027]

The circumference of a rotating disk is longer than π times its diameter (Ehrenfest 1909). Einstein used this disk as a clue that geometry under gravity would not be Euclidean. This paper obtains the Gaussian curvature of the spatial metric of a rotating frame by two routes, symbolic computation and numerical different...

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

The Extrapolation Crosses Zero Because the Heat-Capacity Difference Was Held Constant ── With a melting entropy of 10 and a heat-capacity difference of 30, the extrapolated entropy difference crosses zero at T=214.959393, or 0.716531 of the melting point ── let it vanish as the third law requires and it need not cross at all ── [Paper 503]

The Kauzmann paradox is spoken of as a property of supercooled liquids. This paper shows that crossing zero follows from holding the heat-capacity difference constant──held constant, however small, it always crosses. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──t...

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

Critical Mass Is Set by Skin Balancing Content, Yet a Cube's Extra Volume Does Not Match Its Surface Coefficient ── in a bare one-group diffusion sphere, neutrons leaking through the skin over those gained in the content equal the square of the critical radius over the radius, and a cube's critical-volume factor 1.240490 is smaller than its equal-volume surface coefficient 1.240701 ── the separator is whether the weight of a shape is set by surface area or by the first eigenvalue ── [Paper 1007]

Whether a fission chain reaction keeps going is decided by the balance between neutrons gained in the content and neutrons leaking through the skin. This paper counts that balance in a bare one-group diffusion core (no reflector, no extrapolation distance, lengths measured in the diffusion length L, and the material re...

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

Continued-Fraction Statistics Cannot Tell Known Transcendentals from Unknown Ones or from a Cubic Irrational ── the geometric mean of partial quotients, the growth of denominators and the share of ones all fall within the scatter of random numbers for eight named numbers, and only periodic quadratic numbers and the patterned e stand out ── the separator is whether one speaks of almost all numbers in measure or of this number by name ── [Paper 1021]

Whether π + e, πe or γ is transcendental is not known. On the other hand, it is known that for almost all real numbers the geometric mean of the partial quotients of the continued fraction approaches Khinchin’s constant (Khinchin). This paper expands to 3000 terms the continued fractions of numbers known to be transcen...

Yuuki Yamagishi · 0 citations

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