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small language model

3,468 papers

#small language model Open access Sep 2026

What Sets the Life Is the Initial Flaw, Not the Final Size ── With an initial flaw of 0.5 mm and a final size of 25 mm, doubling the final size extends the life only to 1.048244, while halving the initial flaw extends it to 1.482441 ── and an infinite final size buys only 1.164716, approached slowly at that ── [Paper 565]

A tougher material is expected to last longer once a crack is present. What this paper shows is that most of the life is spent while the crack is small, so that enlarging the final size extends the life almost not at all. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claim...

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

An Aperture and Its Complement Make the Same Pattern Only Away From the Forward Direction ── the intensities of a slit and of its complement converge away from the forward direction, while in the forward direction alone they do not agree, the ratio being 18.9055 ── [Paper 546]

Babinet's principle says that an aperture and its complement produce the same diffraction pattern. What this paper shows is that this holds only away from the forward direction, and that why it holds and why it fails follow from one and the same identity. No new theorem or law is claimed. Scope of this paper (scope not...

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

One and the Same "Proportional To" Carries Four Different Kinds of Constant ── a sphere's S/V^2/3 is fixed by geometry, a pendulum's Tsqrt(g/L) moves with amplitude, a power law fitted to the primes moves with the window, and the Catalan coefficient reaches only 0.99988751 of its limit even at n=10000 ── [Paper 530]

When one writes "A is proportional to B", the standing of the constant in front is rarely asked about. What this paper shows is that such constants come in four kinds, some of which move when something is changed and some of which do not. No new theorem or law is claimed. Scope of this paper (scope note): No new theore...

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

Condensation Happens Without Any Attraction: What Decides Is the Wavelength Overtaking the Spacing ── the condensation temperature of an ideal Bose gas contains only constants, the mass and the number density, with no interparticle potential at all ── the separator is whether switching off the interaction makes it disappear ── [Paper 663]

It is natural to think that a phase changes because particles attract one another. But the condensation of bosons happens without any attraction at all. The condensation temperature of an ideal Bose gas is computed in three cases, and what fixes that temperature is examined. No new theorem or law is claimed. Scope of t...

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

PENGEMBANGAN MODUL PEMBELAJARAN BERBASIS KOMIK PADA MATERI AMAN DI DUNIA MAYA DI KELAS VI SD NEGERI 075024 DURIA BALAKI

ABSTRACT The need for learning materials that are closely connected to students’ experiences has become a consideration in Indonesian language learning on the topic of Staying Safe in the Digital World for sixth-grade students at SD Negeri 075024 Duria Balaki. The limited availability of engaging reading materials enco...

Armansyah Zebua, Noibe Halawa, Dernius Hura et al. · 0 citations
#small language model Open access Sep 2026

The Number of Directions You Can Push Is Not the Dimension of Where You Can Go ── going forward, turning, backing and turning back by epsilon each moves it in the unpushed sideways direction, with sideways displacement over epsilon^2 at -0.998334 for epsilon=0.1 and -1.000000 for 0.001 ── the separator is whether the discrepancy from alternating two pushes points outside the directions that can be pushed ── [Paper 777]

A car cannot move sideways. It can only drive forward or back and turn. Yet it can pull into a parking space beside it. How a third direction becomes reachable with only two directions of push is counted. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the kinematic...

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

Whether the Machine Was Given Cases or Inequalities Changes What Kind of Proof It Is ── In the case-splitting kind the work is known before starting (1048576 cases for twenty binary choices), while in the inequality kind the margin decides ── and at a margin of 0 no amount of subdivision settles it ── [Paper 538]

The four colour theorem and the Kepler conjecture are both called proofs by computer. What this paper shows is that whether the machine was handed cases or inequalities decides whether the amount of work is knowable in advance. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is...

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

A Transit of Venus Turns the Sun's Parallax, Too Small as an Angle, into Seconds of Time Through Venus's Parallax ── misreading the time by 1 second shifts the parallax by 0.292107 percent, a fineness that would require 0.025688 arcseconds if read as an angle ── the separator is whether the parallax is read as an angle or as a time ── [Paper 806]

The astronomical unit is fixed by the solar parallax, an angle of less than 9 arcseconds. Using the geometry of circular orbits, it is counted how a transit of Venus across the Sun magnifies that small angle and turns it into a time difference. No new theorem or law is claimed. Scope of this paper (scope note): No new...

Yuuki Yamagishi · 0 citations
#edge computing Open access Sep 2026

A Shadow's Edge Is Soft Not Because Light Bends Around It but Because the Sun Is Not a Point ── Against the Sun's angular diameter of 1919.3 arcseconds (0.533139 degrees), the penumbra widens in exact proportion to distance: 9.305029 mm at 1 m and 93.050290 mm at 10 m ── the separator is whether the gap is larger or smaller than the Sun's image ── [Paper 671]

The edge of a shadow is soft. It is sometimes said that light bends around the obstacle, but in sunlight it is not diffraction that softens the edge. Taking the Sun to be not a point but a disc 0.533139 degrees across, the softness of the edge and the shape of dappled sunlight are counted. No new theorem or law is clai...

Yuuki Yamagishi · 0 citations
#edge computing Open access Sep 2026

The Roche Limit Is Not One Distance: It Differs by a Factor of Two Depending on What Holds the Satellite Together ── in units of the planet's radius times the cube root of the density ratio, the limit is 1.259921 for a solid resisting tides alone and 2.455 for a fluid, a factor of 1.948535 apart ── the separator is whether a satellite holds its shape by fluid self-gravity, solid self-gravity or material strength ── [Paper 784]

A satellite that comes too close to its planet is torn apart by tides. That distance is called the Roche limit and is spoken of as one value. How many distances exist under the same name, by differences in what holds a satellite together, is counted. No new theorem or law is claimed. Scope of this paper (scope note): N...

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

Time and Temperature Can Be Traded, but Because the Rate of Exchange Is Exponential Only the Shortening Side Gains Orders ── With a Z value of 10 ℃, every 10 ℃ of temperature multiplies the time required for the same effect by exactly 0.100000 ── the separator is whether the law of exchange is exponential or linear ── [Paper 717]

In thermal sterilisation, time and temperature can be traded. That they trade at all is not news. What is worth counting is how steep the rate of exchange is. The steepness is put into numbers, and with it the reason high-temperature short-time processing works. No new theorem or law is claimed. Scope of this paper (sc...

Yuuki Yamagishi · 0 citations

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