teal-sea / zeta-labstate of record · compiled 14 Aug 2026 · revision 9ebdea0 · source

Library · docs/doors/learn.md

Guide: see the machinery run

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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 seconds

The 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.py

The reading course

docs/00docs/18 are a course, in order. Short version of the path:

ReadFor
00-orientation.mdscope, and the house rule about what a computation can settle
0103continuation, θ and modularity, the functional equation
04-explicit-formula.mdthe zeros ↔ primes duality, measured
06-hilbert-polya-and-gue.mdwhy everyone reaches for an operator
08-why-it-is-hard.mdread this before believing any numerical evidence
12-how-hard-problems-die.mdthe 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.