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Yuuki Yamagishi

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#small language model Open access Sep 2026

What Makes It Judder Is Not the Size of the Friction but the Gap Between Two ── With static 30 N, kinetic 20 N and a spring of 1000 N/m, each slip jumps 20.0000 mm ── make the two equal and the amplitude is exactly 0 ── stiffen the spring tenfold and it only falls to a tenth; it does not go ── [Paper 439]

Heavy friction is expected to make motion jerky. This paper shows that the cause is not the size but the gap──make the two frictions equal and the motion is smooth however large they are. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the distinction between static...

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

The Metal That Reacts Most Readily Is the One That Does Not Corrode ── Aluminium sits at -1.66 V, baser than iron, yet its film is 4 nm, 1/125 of iron's 500 nm ── the ordering is reversed ── what separates them is not the potential but whether the film can cover what lies beneath ── [Paper 441]

A metal that reacts more readily is expected to corrode sooner. This paper shows that the ordering is reversed──the basest metal is protected by the thinnest film. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──standard electrode potentials, passivity and the Pilli...

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

Whether Being Advantageous Matters Is Decided by the Size of the Population ── A mutation with a selection coefficient of 0.01 fixes 19.8013 times as often as a neutral one at N=500, but only 1.2012 times as often at N=10 ── what decides is not s but Ns ── and at s=0 the probability is exactly the neutral value ── [Paper 478]

An advantageous mutation is said to spread. This paper shows that what decides whether the advantage matters is not its size but its product with the population size──where Ns is small, being advantageous does no good. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed─...

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

The Water Load Grows as the Square, and the Dam Only as the First Power ── Ten times the depth multiplies the resultant thrust by 100 and the overturning moment by 1000 ── yet the required width only doubles ── 18.6339 m at H=50, 37.2678 at H=100, with b/H constant at 0.3727 ── [Paper 454]

A deeper dam is thought to need a disproportionately thicker body. This paper shows that although the force grows as the square and the moment as the cube, the required width grows only as the first power──because the resisting side grows as the cube too. No new theorem or law is claimed. Scope of this paper (scope not...

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

The Same Proportional Increase Buys Less at the Top ── Raising the compression ratio by 1.3333 gains +0.0531 in efficiency starting from 6 but only +0.0359 starting from 16 ── the ratio is 1.480429, matching the closed form (r_2/r_1)^gamma-1 exactly ── an efficiency of 0.70 needs a ratio of 20.2860 ── [Paper 468]

Raising the compression ratio raises efficiency──so it is said. This paper shows that the same proportional increase buys 1.480429 times less at the top──and that the ratio has a closed form. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the theoretical efficiency...

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

Halving the Size Beats Changing the Material Forty Times Over ── Spheres of radius 5 mm and 20 cm have cooling time constants of 348.8333 and 13953.3333 seconds, a ratio of exactly 40.000000000 ── changing the material from water to metal at one size gives only 1.3081 ── what sets the cooling is not specific heat but the surface-to-volume ratio ── [Paper 465]

How fast a thing cools is thought to be set by its material. This paper shows that size acts 40 times harder──changing from water to metal gives only 1.3081. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──Newton’s law of cooling, the lumped capacitance method and t...

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

What the Waiting Is For Is Diffusion, Not Reaction ── One millimetre takes 2.7778 hours and a hundred takes 3.17 years ── ten times the distance costs 100 times the time ── and ten kelvin multiplies the reaction by 4.0553 while multiplying the diffusion by only 1.5220 ── [Paper 445]

Ageing is taken to be slow because the reaction is slow. This paper shows that sometimes what one waits for is transport──and that transport barely speeds up when heated. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the diffusion equation, the square law for diff...

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

Raising the Lift Coefficient by Sixty Per Cent Lowers the Stall Speed by Twenty ── Taking the maximum lift coefficient from 1.5 to 2.5, a factor of 1.6667, takes the stall speed only from 99.3694 to 76.9712 km/h, a factor of 0.7746 ── because it acts through a square root ── and 0.4518 at 25 degrees is worse than 1.2990 at 10 ── [Paper 458]

Fit a high-lift device and you fly correspondingly slower──so it is thought. This paper shows that the lift coefficient acts on the stall speed only through a square root──a factor of 1.6667 buys a drop of 22.5 per cent. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claime...

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

Whether Being Advantageous Matters Is Decided by the Size of the Population ── A mutation with a selection coefficient of 0.01 fixes 19.8013 times as often as a neutral one at N=500, but only 1.2012 times as often at N=10 ── what decides is not s but Ns ── and at s=0 the probability is exactly the neutral value ── [Paper 478]

An advantageous mutation is said to spread. This paper shows that what decides whether the advantage matters is not its size but its product with the population size──where Ns is small, being advantageous does no good. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed─...

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

Both Improved 7.2446-Fold and the Ratio Never Moved ── Improving at two per cent a year, capability rises 7.2446-fold over a century while the ratio stays at exactly 1.000000000 ── let one side stop and the odds move from 0.5 to 0.878803 ── one runs not to overtake but not to fall ── [Paper 438]

Improving is expected to bring advantage. This paper shows that if the other improves as much, nothing changes──and that stopping nonetheless costs a great deal. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Red Queen hypothesis, coevolution and relative fitne...

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

Mixing the Unmixable Multiplies the Boundary by a Thousand ── Dividing 1 mL of oil from 1 mm drops into 1 mum drops takes the interface from 0.0030 to 3.0000 m^2 ── a surfactant cuts the energy to 1/6 but not to zero ── nothing mixed; separation merely became slow ── [Paper 444]

Shake oil and water hard enough and they look mixed. This paper shows that they have not mixed──the finer the division the more boundary there is and the higher the energy. Separation has merely become slow. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──interfacia...

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

Going Faster Makes the Wind Stronger, Which Is Why a Sailing Craft Can Outrun the Wind ── dead downwind the apparent wind reaches 0 the instant the boat matches the wind ── across the wind, a boat doing 50 m/s feels 50.9902 m/s ── same wind, same sail: one is capped and the other is not ── [Paper 390]

A sail is pushed by the wind, so a boat cannot outrun the wind──so it seems. This paper shows that changing only the heading removes the cap──neither the wind nor the sail is altered at all. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──apparent wind, propulsion b...

Yuuki Yamagishi · 0 citations

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