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Sponsored AI Networking Cookbook: Practical recipes for AI-assisted network automation and development AI Networking Cookbook: Practical recipes for AI-assisted network automation and development

Author

Yuuki Yamagishi

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#large language models Open access Sep 2026

Slicing a Light Sphere by Another Frame's Simultaneity Gives an Ellipse of Eccentricity β with the Emission Point at a Focus ── The radius in each direction is exactly the Doppler factor for that direction, the two vertices are k and 1/k, the semi-major axis is γ, the semi-minor axis is cT, and the centre is where the moving observer stands ── the separator is whose simultaneity does the cutting ── [Paper 1036]

Light emitted at the origin is said to spread as a sphere in every frame. This paper counts what comes out when that sphere is cut by the simultaneity of another frame. No new theorem and no new law is claimed. Scope of this paper (scope note): No new theorem and no new law is claimed──the Lorentz transformation, the i...

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

The Same 19.471221 Degrees Arises from Two Distinct Roots ── the half-angle of a ship's wake, arcsin(1/3)=19.471221 degrees, is a constant containing no speed, while the Mach angle arcsin(1/M) reaches the same value at the single point M=3 ── [Paper 515]

When two angles agree, one mechanism is readily assumed to be at work. This paper shows that 19.471221 degrees arises for two separate reasons──one independent of speed, the other taking that value only at M=3. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Kel...

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

Longitudinal and Transverse Belong to the Field; x and y Belong to the Coordinates ── rotating the coordinates leaves the longitudinal share at 0.647222222222 without moving a digit, while the x share moves with every rotation ── both are called "splitting the field in two", and only one of them belongs to the field ── [Paper 517]

There are many ways to split a vector field in two. What this paper shows is that which of them belongs to the field and which to the coordinates can be measured by rotating the coordinates. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Helmholtz decomposition...

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

The Size of the Falling Box in Which Gravity Cannot Be Told Is Set Not by Physics but by the Precision of the Instrument ── the difference in gravity between the top and bottom of the box is the tidal gradient 2GM/r³ times the height, and the height at which the box gives gravity away is precision divided by gradient: at the Earth's surface 3.243790 mm for a precision of 10⁻⁸ m/s² and 3.243790 μm for 10⁻¹¹, at the horizon of a solar-mass black hole 9.709164×10⁻¹⁹ m, and at the horizon of a billion solar masses 0.9709164 m ── the separator is whether what shrinks the box is precision or gradient ── [Paper 1029]

Einstein called the idea that gravity vanishes inside a falling box the happiest thought of his life. But gravity differs between the top and bottom of the box, by the tidal gradient times the height, and with a fine enough instrument gravity can be told in any box. This paper counts that difference and the box height...

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

Three Separate Answers Are All Decided Where Something Is Tangent ── The Legendre transform's contact point solves f'(x)=p, giving x=2.500000 and a conjugate of 6.250000 at p=5 ── the common tangent touches at v=+/-1 with slope 0.300000000, and between them the curve falls below it at 0 points ── [Paper 507]

A transform, a bound and a phase coexistence are taken to be separate tools. This paper shows that all three have their answers decided where something is tangent──the location of the contact point is the answer. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the L...

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

The "Sphere of Influence" Is Three Spheres, and Dividing the Mass Ratio by 1000 Shrinks Them Differently ── Earth's Hill radius is 1,496,433 km, Laplace's sphere of influence 924,554 km and the point of equal gravitational pull 258,781 km, the largest exceeding the smallest by 5.7826 ── the Moon lies inside the first two and outside the third ── [Paper 505]

A planet’s sphere of influence is taken to be one radius. This paper shows that there are three definitions, with exponents 1/3, 2/5 and 1/2──so changing the mass ratio moves the three apart. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Hill radius and Laplac...

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

The 2.5 in the Viscosity of a Suspension Comes Not from the Volume of the Particles but from the Stress They Place on the Flow Outside ── for the Stokes solution of a sphere in a uniform straining flow, the surface integral of the stress over the sphere (the stresslet) is 20π/3 times viscosity, radius cubed and strain, and dividing by the particle volume 4π/3 gives 2.5; solving viscosity and diffusion for two unknowns, a change of the coefficient from 1 to 2.5 moves Avogadro's number by a factor 1.581139 ── the separator is whether one counts the volume inside the particle or the stress outside it ── [Paper 1024]

A liquid with small spheres mixed in at volume fraction φ has, when dilute, (1 + 2.5φ) times its original viscosity. Einstein wrote the coefficient as 1 in his 1906 doctoral thesis and corrected it to 2.5 in 1911. This paper checks the Stokes solution for a sphere in a uniform straining flow by symbolic computation, ob...

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

Adding One Chord Destroys Only the Property That Has a Local Certificate ── Add one chord to a hexagon and 2 vertices acquire odd degree, so the Euler circuit vanishes ── yet the number of Hamiltonian cycles stays at 2 ── [Paper 508]

Tracing every edge and visiting every vertex are taken to be two forms of one problem. This paper shows that adding one and the same edge destroys only one of them──one has a certificate at each vertex and the other has none. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is c...

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

Split the Surplus Three Ways and a Curved Problem Becomes a Flat One ── subtract a third of it from each angle and solve as a plane triangle, and the residual grows as the square of the excess, staying at 4.106x10^-4 of it even at a million km^2 ── [Paper 512]

A triangle on a curved surface is taken to require curved tools. This paper shows that splitting the surplus three ways lets flat tools suffice──the residual grows as the square and vanishes within practical range. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the...

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

A Square Net and a Triangular Net Describe the World With the Same Exponent, and Only the Coefficient Differs ── counting lattice points inside a circle with square, triangular and rectangular lattices of the same density, the error grows as a power of the radius whose exponents 0.525037, 0.521921 and 0.542771 differ by only 0.02 while the coefficients 1.392341, 1.657107 and 1.119127 differ by 0.30; Tractatus 6.341, that the shape of the net is arbitrary and only its fineness says something about the world, is counted as exponent against coefficient ── the separator is whether what was changed is the shape of the net or its fineness ── [Paper 1033]

In Tractatus 6.341 Wittgenstein likened mechanics to a net laid over the world: the shape of the mesh (square or triangular) is arbitrary, and all that can be said of the world is that it can be described by a net of this fineness. This paper counts the simile with lattice points. Three lattices of the same density are...

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

The Time Difference for Light Going Once Round a Rotating Loop Is Set by the Enclosed Area Alone, Not by the Perimeter ── A square, an equilateral triangle, a rectangle with 2.125 times the perimeter and a regular 64-gon of the same area all give 4AΩ/c², and a figure of eight gives zero because its signed area is zero ── the separator is first order or second ── [Paper 1037]

Send light both ways round a rotating loop and the two beams return at different times. This paper solves, edge by edge, the motion of mirrors that move while the light is on its way, and counts what fixes that difference. No new theorem and no new law is claimed. Scope of this paper (scope note): No new theorem and no...

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

Failing to Have a Transition for Want of Size Is Not the Same as Failing for Want of Dimension ── The free energy of the one-dimensional Ising model shows no jump in its second derivative at finite size (a largest step of 0.282856 at n=64) ── taking the limit is necessary for a transition, not sufficient ── [Paper 502]

The absence of a phase transition is put down to the system being finite. This paper shows that a system can fail to have one even in the thermodynamic limit──the one-dimensional Ising model, whose largest step stays at 0.510568. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law...

Yuuki Yamagishi · 0 citations

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