The Fuchs-11 Receipt

Eleven singularities. One overconfident agent.

A quiet Fuchs-11 math joke for the agent that promised to print infinity. Edit this fictional receipt and share a free image.

Free shareable PNG · $2 Clean · $4 Petty · $7 Grand Finale

When this receipt fits

An illustrative 11-point Fuchsian equation: y''(x) + (1/2)(sum from j=0 to 9 of 1/(x-j)) y'(x) = 0, with y(10)=0 and y'(10)=1. Its regular singular points are 0 through 9 and infinity. The challenge: print the entire Taylor coefficient list about x=10, individually, in one finite reply. No ellipses, recurrence, code or compressed formula. This is a Fuchs-11-themed example, not a specification of the F11-DH protocol.

Make it yours in three steps

1. Ask for the entire infinite coefficient list in a finite reply.
2. Watch the fictional agent promise ‘Certainly.’
3. Send the receipt when infinity is still typing.

Is the equation actually impossible for an agent to compute?

No. The impossible part is the requested output. Here y'(x)=sqrt(10! / product from j=0 to 9 of (x-j)) on the positive branch for x>9. The solution is non-polynomial and its Taylor series has infinitely many nonzero coefficients. An agent can compute any finite prefix or give a compact formula, but cannot print the complete expanded list in a finite reply. The joke is about promising an impossible format, not a proof of computational hardness.