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Author

Yuuki Yamagishi

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#small language model Open access Aug 2026

"Capacity" Is a Number Attainable Only at Infinite Length ── At Blocklength 100 Only 41.68% of the Capacity Is Usable, and Reaching 99.99% Takes 3.4x10^9 ── C Is a Supremum, Not a Maximum ── [Paper 304]

Shannon’s coding theorem says that below the channel capacity C the error can be made arbitrarily small. This paper asks whether C itself is attainable──the answer is not at any finite blocklength. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and n...

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

One Number Sets the Limit of Forecasting ── Each Extra Day Costs 1.5874 Times the Initial Accuracy ── Observe 10 Times More Precisely and You Gain Only 4.98 Days ── [Paper 289]

That a weather forecast cannot reach beyond a certain horizon is due neither to missing equations nor to slow computers. This paper asks what sets the limit──the answer is one number, the error doubling time tau_d. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathemati...

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

What Changed the Exponent of a Chain Was Self-Avoidance Alone, and above Four Dimensions That Cost Disappears ── An Error of 2.11% in the Exponent Becomes 29.33% in the Length at N=10^9 ── And 2+2=4 Empties Avoidance of Its Meaning ── [Paper 279]

The spread of a polymer chain is fixed by a power of the number of units N. For a Gaussian chain it is N^1/2, and for a self-avoiding chain N^0.588. This paper asks where that difference comes from and where it disappears──the answer is the count 2+2=4. No new mathematical theorem and no new law is claimed. Scope of th...

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

To Determine an Object You Need Every Other One ── What the Yoneda Lemma Requires and What Is Lost When the Probe Is Weakened: Counted over the 156 Graphs on Six Vertices ── [Paper 244]

The Yoneda lemma says that an object is completely determined by its relations to every other object. This paper asks about that word every: where does the separating power fall when the probe is weakened? And the loss turned out not to be governed by the strength of the probe. No new mathematical theorem and no new la...

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

To Determine an Object You Need Every Other One ── What the Yoneda Lemma Requires and What Is Lost When the Probe Is Weakened: Counted over the 156 Graphs on Six Vertices ── [Paper 244]

The Yoneda lemma says that an object is completely determined by its relations to every other object. This paper asks about that word every: where does the separating power fall when the probe is weakened? And the loss turned out not to be governed by the strength of the probe. No new mathematical theorem and no new la...

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

To Determine an Object You Need Every Other One ── What the Yoneda Lemma Requires and What Is Lost When the Probe Is Weakened: Counted over the 156 Graphs on Six Vertices ── [Paper 244]

The Yoneda lemma says that an object is completely determined by its relations to every other object. This paper asks about that word every: where does the separating power fall when the probe is weakened? And the loss turned out not to be governed by the strength of the probe. No new mathematical theorem and no new la...

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

Time Is One-Dimensional Because Prediction Demands It, Not Because a Law Says So ── The Same Procedure, With Only the Signature Changed, Gives Amplifications of 0.012 and 3.5 × 10^32 ── [Paper 253]

Why is time one-dimensional? The answer offered here is that no law decrees it; the requirement that one be able to predict allows nothing else. The equations of a universe with two times can be written, and their solutions exist. What breaks is prediction. No new mathematical theorem and no new law is claimed. Scope o...

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

Time Is One-Dimensional Because Prediction Demands It, Not Because a Law Says So ── The Same Procedure, With Only the Signature Changed, Gives Amplifications of 0.012 and 3.5 × 10^32 ── [Paper 253]

Why is time one-dimensional? The answer offered here is that no law decrees it; the requirement that one be able to predict allows nothing else. The equations of a universe with two times can be written, and their solutions exist. What breaks is prediction. No new mathematical theorem and no new law is claimed. Scope o...

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

The Four Pi That Catches Molecules Is the Four Pi That Spreads a Field ── Steady Diffusion Is Laplace's Equation: the Flux Through Every Enclosing Sphere Is 12.566370614359, and in Two Dimensions No Steady Absorber Exists ── [Paper 249]

When four pi turns up in a biological setting, is it a coincidence of numbers or the same root? This paper treats exactly one case: the four pi in the rate at which a cell captures molecules is the same solid angle as in Gauss's law. Not by analogy, but because it is the same equation. No new mathematical theorem and n...

Yuuki Yamagishi · 0 citations

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