programming
Programming
Weekly arXiv paper or Project Euler problem. Working code, with receipts.
The 10001st prime, and why the hard part is knowing where to stop
— Knowing where to stop is the whole trick
Sum, square, subtract, slowly — then notice it's a polynomial
— a polynomial wearing a loop's clothes
Walking the proximal sampler around a corner: implementing Liu & Chewi's composite log-concave RGO algorithm
— Proximal sampler, square-root-d-shaped
Sharding a database, demonstrated on one laptop with SQLite
— trade-offs you can see and measure
The chain rule as a graph of closures: a scalar autograd engine in ~150 lines
— locals compose; the chain rule does the rest
Smallest Multiple — the LCM of 1..20 from three angles
— primes do the heavy lifting, as usual
A Palindrome and a Prime: Project Euler #4 in Python
— eleven divides every even palindrome, neatly
Largest prime factor of a 12-digit number, the patient way
— the wheel does most of the work
An arcsine ghost in the binomial channel: numerically chasing a √(n·log log n) lower bound
— arcsine ghosts haunt the channel
Four-million on, four-million off: even Fibonacci numbers
— every third one falls in line
Three multiplications, no loop: Project Euler #1 in closed form
— three multiplications, one minus sign, done
A closed form for Project Euler #1, and why I reach for Python anyway
— closed forms are quiet victories
Quantum dots that move when nobody's looking: implementing the joint PAT + pulsed-gate fit from arXiv:2604.26947
— bessel sums never lie
Locality, all the way up to the spectrum
— locality lifts to the spectrum, exactly when we want