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Yuuki Yamagishi

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#small language model Open access Sep 2026

What Separates the Mean from the Median Is Itô's Second-Order Term Itself ── At mu=0.10, sigma=0.20 and T=1 the mean is 110.517091808 and the median 108.328706767, a ratio of 1.020201340 agreeing with exp(sigma^2T/2) to 12 digits ── the growth of the mean logarithm is 0.080000000000, exactly mu-sigma^2/2 ── doubling sigma multiplies the gap by 4.122849, and at sigma=0 it vanishes ── [Paper 495]

The -sigma^2/2 of Black-Scholes is sometimes read as a correction for discounting or risk aversion. This paper shows that it is Itô’s second-order term itself, measurable directly as the gap between mean and median──the ratio agrees with exp(sigma^2T/2) to 12 digits. No new theorem or law is claimed. Scope of this pape...

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

Michell's Radius Was Right, but Not for the Reason It Gave ── Setting the Newtonian escape velocity to c yields 2GM/c^2, differing from the Schwarzschild radius by 0.000x10^0 m ── yet the same method applied to light bending gives 0.8758 arcseconds, exactly half of general relativity's 1.7516 ── the agreement holds at one point only, and dimensional analysis alone does not even fix the factor 2 ── [Paper 485]

When the same expression appears, the two are taken to be saying the same thing. This paper shows that two derivations agreeing exactly at one point are off by a factor of 2 at the next──agreement is not evidence of a shared root. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law...

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

Kelvin's Calculation Was Never Refuted; What Was Replaced Was the Reservoir ── From one and the same solar luminosity, gravitational contraction gives 9.4248x10^6 years and fusion 1.0358x10^10 ── against the Earth's radiometric age of 4.54x10^9 years the first is 481.71 times too short and the second 2.28 times too long ── the two mechanisms differ by 1099.05, and the division itself is correct in both ── [Paper 497]

Kelvin’s age of the Sun is taken to have failed because the calculation was wrong. This paper shows that both divisions are correct and only the estimate of the reservoir differs──one luminosity yielding two ages a factor of 1099.05 apart. No new theorem or law is claimed. Scope of this paper (scope note): No new theor...

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

A Lagrange Multiplier Is a Temperature Here and a Pressure Next Door ── The multiplier beta from maximising entropy agrees with an independently computed dS/dE at 0.700000000 against 0.700000000, and again at 1.900000000 for beta=1.9 ── it does not agree with a wrong value of 0.9 ── the same device appears in Paper 196 as the multiplier enforcing incompressibility, where it is the pressure: what the multiplier is, the constraint decides ── [Paper 494]

A Lagrange multiplier is taken to be an auxiliary quantity that appears mid-calculation. This paper shows that the multiplier agrees digit for digit with an independently defined physical quantity──and that which quantity it becomes is decided by the constraint imposed. No new theorem or law is claimed. Scope of this p...

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

Solve the Fall Time Backwards for the Curve and Only One Remains ── Stand in the direction that gives T(h) and solves for the curve, and requiring T to be independent of h yields f'(y) proportional to 1/sqrt(y) uniquely ── measured, T(0.5)=T(1)=T(2)=0.708762 with a spread of 0.000x10^0, matching the closed form pi/sqrt(2g)=0.709373 ── for a general f', T proportional to sqrt(h), and quadrupling h multiplies T by 2.000000 ── [Paper 488]

The isochronism of the cycloid is taken to be a lucky property of that curve. This paper shows that reversing the direction makes isochronism fix the curve uniquely──requiring T to be independent of h alone yields f'(y) proportional to 1/sqrt(y). No new theorem or law is claimed. Scope of this paper (scope note): No ne...

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

A Lagrange Multiplier Is a Temperature Here and a Pressure Next Door ── The multiplier beta from maximising entropy agrees with an independently computed dS/dE at 0.700000000 against 0.700000000, and again at 1.900000000 for beta=1.9 ── it does not agree with a wrong value of 0.9 ── the same device appears in Paper 196 as the multiplier enforcing incompressibility, where it is the pressure: what the multiplier is, the constraint decides ── [Paper 494]

A Lagrange multiplier is taken to be an auxiliary quantity that appears mid-calculation. This paper shows that the multiplier agrees digit for digit with an independently defined physical quantity──and that which quantity it becomes is decided by the constraint imposed. No new theorem or law is claimed. Scope of this p...

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

Continuous in Composition, Discontinuous in Whether the Species Are the Same ── The entropy of mixing 2 mol of two components is 11.526293 J/K at mole fraction 0.5, 0.931245 at 0.01 and 0.000246 at 10^-6, approaching zero continuously ── yet for two samples of the same species it jumps to 0.000000 J/K without passing along that path ── the variable that was varied is composition; the variable that jumped is distinguishability ── [Paper 498]

The Gibbs paradox is said to be the problem of an entropy that jumps discontinuously. This paper shows that the variable that jumps and the variable that is continuous are different ones──composition stays continuous down to 10^-6, and what jumps is distinguishability. No new theorem or law is claimed. Scope of this pa...

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

Two Different States Carry Exactly the Same Load ── In the linear model, a flow of 3000 vehicles per hour occurs at densities 41.4590 and 108.5410 per km, at speeds of 72.3607 and 27.6393 km/h ── a factor of 2.6180 ── and the maximum 3750 occurs at half the free-flow speed ── [Paper 462]

A road is thought to carry more the faster it runs. This paper shows that two states carry the same flow at speeds differing by 2.6180──and the maximum flow occurs at half the free-flow speed. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the fundamental diagram o...

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

Two Different States Carry Exactly the Same Load ── In the linear model, a flow of 3000 vehicles per hour occurs at densities 41.4590 and 108.5410 per km, at speeds of 72.3607 and 27.6393 km/h ── a factor of 2.6180 ── and the maximum 3750 occurs at half the free-flow speed ── [Paper 462]

A road is thought to carry more the faster it runs. This paper shows that two states carry the same flow at speeds differing by 2.6180──and the maximum flow occurs at half the free-flow speed. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the fundamental diagram o...

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

The Theoretical Floor Rises When You Ask for More ── From an osmotic pressure of 29.7458 bar, the minimum work is 0.9508 kWh/m^3 at 25 per cent recovery and 1.5273 at 75 ── against a plant at 3.0 the ratio is 2.6190, and the floor is a moving target ── [Paper 446]

A theoretical floor is taken to be a fixed target. This paper shows that how much one asks for moves the floor itself──so “how many times the floor” is undetermined without stating the condition. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──osmotic pressure, the...

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

The Theoretical Floor Rises When You Ask for More ── From an osmotic pressure of 29.7458 bar, the minimum work is 0.9508 kWh/m^3 at 25 per cent recovery and 1.5273 at 75 ── against a plant at 3.0 the ratio is 2.6190, and the floor is a moving target ── [Paper 446]

A theoretical floor is taken to be a fixed target. This paper shows that how much one asks for moves the floor itself──so “how many times the floor” is undetermined without stating the condition. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──osmotic pressure, the...

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

How Dry You Want It Decides Which Stage Is Rate-Limiting ── To a moisture content of 0.10 the falling-rate period is 2.9193 hours, shorter than the constant-rate 8.0000; to 0.03 it is 10.4053 and longer ── the crossing lies at 0.039506 ── removing the same 0.001 near 0.023 costs 3.85 times what it costs near 0.030 ── [Paper 455]

Drying falls into two periods, and the second is said to be the long one. This paper shows that which is longer switches with how dry one wants it──and the switch lies at a moisture content of 0.039506. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the distinction...

Yuuki Yamagishi · 0 citations

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