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Author

Yuuki Yamagishi

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321 papers indexed here

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#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
#large language models Open access Sep 2026

What Chooses the First Principal Component Is Not the Data but the Units ── The same sample points at 55.6503 degrees in cm, 89.7345 in m, and 4.1934 in mm ── Not one value was changed; they were multiplied ── Standardising settles it at 45.0000 degrees, but standardising is itself a choice ── [Paper 375]

Principal component analysis is described as extracting the main direction in the data. This paper asks whether the data alone fix that direction──the answer is that they do not: the units do. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new...

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

An Achromat Meets at Two Wavelengths Only ── A single lens shifts focus by 1.558361 mm with colour (1.5584 per cent of its focal length) ── Two glasses cut that to 0.044604 mm, a factor of 34.9374, but not to zero ── The cause of the residue can be named by one number: the difference in partial dispersion ── [Paper 377]

An achromatic lens is called a lens with the chromatic aberration removed. This paper asks how far it is removed──the answer is at two wavelengths only, with a third colour remaining. 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 c...

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

In a Gravity Assist the Probe Speeds Up, and in the Planet's Frame Its Speed Never Changed ── Against Jupiter's orbital speed of 13.07 km/s, the gain seen from the Sun is at most 26.14 km/s ── Jupiter thereby loses 2.4310x10^-20 m/s of orbital speed ── The probe's change in speed is 1.0753x10^24 times Jupiter's ── [Paper 381]

A gravity assist is described as accelerating on a planet’s gravity. This paper asks in which frame the acceleration happened──the answer is that from the Sun it accelerated and from the planet its speed never changed. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathe...

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

What Chooses the First Principal Component Is Not the Data but the Units ── The same sample points at 55.6503 degrees in cm, 89.7345 in m, and 4.1934 in mm ── Not one value was changed; they were multiplied ── Standardising settles it at 45.0000 degrees, but standardising is itself a choice ── [Paper 375]

Principal component analysis is described as extracting the main direction in the data. This paper asks whether the data alone fix that direction──the answer is that they do not: the units do. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new...

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

"Moore's Law Is Ending" Has Been Said for Years, but What Ended Was the Other Law ── Under Dennard scaling, halving the dimensions leaves power per area at exactly 1.0000 ── Once the voltage stops falling it becomes 4.0000 ── The count still doubles every two years, reaching 1024 in twenty, and now the power does too ── [Paper 374]

“Moore’s law is ending” has been said for a long time. This paper asks what ended──the answer is that what ended was not the law of counting but the law of power. 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──Moore’s law,...

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

A Premium Is Not the Expected Loss ── And What Sets the Loading Is Not the Accuracy of the Probability but the Number of Policies ── With one policy, keeping the ruin probability at 1 per cent takes a loading of 23.1469 times the expected loss ── With a million policies it falls to 0.0231 ── The expected loss has not moved by a single unit ── [Paper 383]

It is tempting to think a premium is the probability of loss times its size. This paper asks whether that suffices──the answer is that it does not, and what sets the shortfall is the number of policies. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem...

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

How Much You Remember Is Decided by How You Test ── One memory, one day later: 71.70 per cent by free recall and 91.07 per cent by savings in relearning ── The gap widens with time, reaching 3.2698 after a month ── And an exponential forgetting curve predicts 10^-13 at a month, breaking down ── [Paper 378]

A forgetting curve shows memory falling with time. This paper asks what quantity is falling──the answer is a different quantity for each way of testing, giving three answers one day later. 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
#large language models Open access Sep 2026

The Brain Uses "2 Per Cent of the Mass and 20 Per Cent of the Energy" Because What It Is Compared With Is Resting ── The brain's specific power is 14.2857 W/kg against a whole-body average of 1.4286, a ratio of 10 ── But skeletal muscle in exercise runs at 100 W/kg, seven times the brain ── The factor of 10 comes from the smallness of the denominator, not the largeness of the brain ── [Paper 382]

The brain is said to use 2 per cent of the body’s mass and 20 per cent of its energy. This paper asks where that factor of 10 comes from──the answer is not that the brain is high but that the denominator is low. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical...

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

A Premium Is Not the Expected Loss ── And What Sets the Loading Is Not the Accuracy of the Probability but the Number of Policies ── With one policy, keeping the ruin probability at 1 per cent takes a loading of 23.1469 times the expected loss ── With a million policies it falls to 0.0231 ── The expected loss has not moved by a single unit ── [Paper 383]

It is tempting to think a premium is the probability of loss times its size. This paper asks whether that suffices──the answer is that it does not, and what sets the shortfall is the number of policies. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem...

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

"Free-Space Loss" Is Not a Loss: The Vacuum Absorbs Nothing ── 92.4478 dB at 1 km and 1 GHz; doubling the distance and doubling the frequency both add the same 6.0206 dB ── the frequency term comes not from space but from the receiving antenna, whose effective area scales as lambda^2 ── at 10 GHz that area is exactly 1/100 ── [Paper 384]

Radio waves are said to suffer a “loss” as the distance grows. This paper asks what is being lost──and the answer is that nothing is lost; what looks like loss is a fact about the receiver. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Friis transmission formu...

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

A Comet's Tail Is Not One Tail but Two, Pulled by Different Forces ── Radiation Pressure Balances Gravity at a Grain Radius of 0.2296 μm ── The Ion Tail Leans Only 5.7106 Degrees in the Solar Wind, While the Dust Tail Fans Out by Grain Size ── [Paper 339]

A comet trails its tail away from the Sun. This paper asks whether that tail is one thing──the answer is that there are two, and the forces pulling them are different. 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──the rati...

Yuuki Yamagishi · 0 citations

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