For you if you want real intuition and real numerics about ζ — to watch the theorems occur rather than read that they hold.
First command:
.venv/bin/python scripts/06_tour.py # the whole story, ~90 secondsThe one that makes the subject real
The primes are reconstructed from the zeros alone. Nothing else in the subject lands the same way:
.venv/bin/python scripts/03_primes_from_zeros.pyThe reading course
docs/00–docs/18 are a course, in order. Short version of the path:
| Read | For |
|---|---|
00-orientation.md | scope, and the house rule about what a computation can settle |
01–03 | continuation, θ and modularity, the functional equation |
04-explicit-formula.md | the zeros ↔ primes duality, measured |
06-hilbert-polya-and-gue.md | why everyone reaches for an operator |
08-why-it-is-hard.md | read this before believing any numerical evidence |
12-how-hard-problems-die.md | the failure catalogue |
The house habit
Every identity here is exposed as a measured defect, not asserted. ξ(s) = ξ(1−s) is not a comment; it is functional_equation_defect(s), and a test pins how small it is. Every number in a docstring is checked by tests/.
That habit is the reason the numbers can be trusted, and it is the thing worth stealing if you are building something similar.
What you will not find
Evidence for RH. docs/08 explains why: Littlewood's theorem guarantees a pattern can hold for every case anyone will ever compute and still be false. The house rule is that if a computation here appears to settle something open, the correct inference is a bug.
Next door: refute.md, for when you have a claim of your own.