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Author

Yuuki Yamagishi

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321 papers indexed here

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#small language model Open access Sep 2026

"Finer Grains Are Stronger" Fails, and Not Because the Theoretical Strength Was Reached ── the prediction at 10 nm, 1550 MPa, is only 14.09 per cent of the theoretical 11000 MPa ── the formula reaches theoretical strength at a grain size of 0.187652 nm, smaller than the 0.256 nm atomic spacing ── what acts is the grain-boundary volume fraction, 30 per cent at 10 nm ── [Paper 397]

The Hall--Petch relation says finer grains are stronger, and it reverses at 10 to 30 nm. This paper shows that the reversal is not because the theoretical strength was reached──the prediction there does not even reach 14 per cent of it. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem...

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

The Humidity Goes from 53.80 Per Cent to 100 Without a Drop of Water Being Added ── lift the parcel 1250 m and temperature and dew point meet at exactly 12.75 degrees ── cloud bases are flat because only height decides condensation ── the strength of the updraught does not appear in the formula ── [Paper 399]

Humidity rising sounds like water being added. This paper shows that the humidity can be taken to 100 per cent with the amount of water untouched──it is enough to lift the air. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the lifting condensation level, the dry a...

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

Put a Number on a Pendulum's "Small Angle" and Ten Degrees Costs 164.78 Seconds a Day ── two degrees costs 6.58 s/day and thirty degrees 1504.12 s/day (25 minutes) ── yet at 170 degrees the period is only 2.4394 times, and it reaches three times at 175.8765 degrees ── the divergence bites only in the last fraction of a degree ── [Paper 396]

We are taught that a pendulum is isochronous if the amplitude is small. This paper asks how small is small──even ten degrees costs 164.78 seconds a day, which is useless for a clock. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the exact period of a simple pendul...

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

The Gyroscope Is Two Orders Too Small to Explain Why a Bicycle Does Not Fall ── The restoring torque required is 68.3765 N. m; the front wheel's gyroscopic torque is 1.2750 N. m ── A gap of 53.6286 ── The two become equal at 965 km/h ── [Paper 359]

A moving bicycle is said to stay up because of the gyroscopic effect of its wheels. This paper asks whether that explanation is the right order of magnitude──the answer is that it is not. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law...

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

With No Cause at All, the Bottom Rises 1.76 Standard Deviations and the Top Falls 1.76 ── Everyone equally able, both measurements independent, and the bottom decile moves +1.756597 while the top decile moves -1.759617 ── One treatment looks opposite depending on which group was chosen ── [Paper 371]

It is said that drilling the weak improves them and praising the strong spoils them. This paper asks whether that is the effect of the treatment──the answer is that it happens at the same size with no treatment at all. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathe...

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

Two Algebraically Equal Forms Return Answers Differing by 15 Digits ── The smaller root of a quadratic comes out with 0.59 correct digits from the naive form and 16 from the rationalised one ── The cause is that sqrt(b^2-4c) agrees with b to 15.83 digits ── Subtract two near-equals and exactly the agreeing digits vanish ── [Paper 368]

It is tempting to think that mathematically identical formulae return identical answers. This paper asks whether that holds in finite precision──the answer is that it does not, and the gap reaches 15 digits. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical the...

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

The "Depth" of Depth of Field Is a Convention, Not a Measurement ── With the same 50 mm lens at the same f/2.8, the hyperfocal distance is 29.8119 m and also 207.6912 m ── What changed is not the equipment but the circle of confusion, which is an agreement ── One set of equipment holds four answers ── [Paper 358]

Depth of field is printed in tables and looks like a property of the lens. This paper asks where that number comes from──the answer is that it comes not from the equipment but from an agreement about when blur becomes visible. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No n...

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

Adding Noise Can Improve Detection ── But "More Is Better" Is Not the Rule ── Zero noise gives detection rate 0, sigma=0.50 gives correlation 0.687458, sigma=4 gives 0.127152 ── The optimum is not at either end but in the middle ── [Paper 353]

One is taught that noise is to be reduced. This paper asks whether reducing it always improves matters──the answer is that in a system with a threshold it does not. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──stochastic...

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

The "Depth" of Depth of Field Is a Convention, Not a Measurement ── With the same 50 mm lens at the same f/2.8, the hyperfocal distance is 29.8119 m and also 207.6912 m ── What changed is not the equipment but the circle of confusion, which is an agreement ── One set of equipment holds four answers ── [Paper 358]

Depth of field is printed in tables and looks like a property of the lens. This paper asks where that number comes from──the answer is that it comes not from the equipment but from an agreement about when blur becomes visible. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No n...

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

Two Algebraically Equal Forms Return Answers Differing by 15 Digits ── The smaller root of a quadratic comes out with 0.59 correct digits from the naive form and 16 from the rationalised one ── The cause is that sqrt(b^2-4c) agrees with b to 15.83 digits ── Subtract two near-equals and exactly the agreeing digits vanish ── [Paper 368]

It is tempting to think that mathematically identical formulae return identical answers. This paper asks whether that holds in finite precision──the answer is that it does not, and the gap reaches 15 digits. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical the...

Yuuki Yamagishi · 0 citations
#explainable ai Open access Sep 2026

The Usual Explanation of the Brazil-Nut Effect Fails on the Size of the Gap ── The gap between three 20 mm spheres admits only 3.0940 mm ── For "small grains fall through the gaps" to work, the diameter ratio must be at least 6.4641, while the effect is seen at about 4 ── It is the explanation that fails, on geometry ── [Paper 365]

Shake a mixture and the large grains come to the top. This paper asks whether the usual explanation survives the geometry──the answer is that it does not: the gap is too small. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed─...

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

The Limit on Running Speed Is Not How Fast the Legs Move but How Hard the Ground Is Pushed ── As speed rises only the contact time shortens, and the duty factor falls from 0.6667 to 0.3714 ── Supporting the same body weight then takes a mean vertical force rising from 1.5 to 2.6923 times body weight ── The aerial time barely changes ── [Paper 380]

It is tempting to think one cannot run faster because the legs cannot turn over quickly enough. This paper asks which quantity reaches its limit first──the answer is the force applied to the ground. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and...

Yuuki Yamagishi · 0 citations

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