The laboratory
Every figure in these four documents comes out of one Python module, and here it is — a numbered menu of twenty-three pictures, each one reproducible from a seed.
The papers say their figures are reproducible. This is the thing that reproduces them: a single module, about sixteen hundred lines, where every picture in the expedition is a function you can call by number.
>>> from determinant_ladder import menu
>>> menu()
Or go straight at one:
>>> import determinant_ladder as dl
>>> dl.fig_rainbow_ports()
Figures are shown on screen and saved into ./figures/ beside the
module. It needs numpy, sympy, scipy and matplotlib, and nothing else.
What is in it
The menu is organised the way the main paper is — one primitive, and the directions you can climb away from it.
| Direction | Figures | |
|---|---|---|
| 0 | The map of the journey | 3 — the five-arrow compass, the hidden hypotheses, the Paper II teaser |
| 1 | Size of the matrix | 8 — formulas, geometry, Sarrus paths, the rainbow at n = 5, growth and the exact crossings |
| 2 | Richness of the entries | 4 — det as a field, the commutativity fork, the two vacuums, the two nothings |
| 3 | Dimension of the map | 6 — symbolic verification of the 2026 counterexample, the collision wells, the numerical hunt, escape and properness, the information ladder |
| 4 | Degree of the map | 3 — the degree axis, freedom against constraints, the curve d*(n) with the Wang guardrail |
Direction 3 is the one that touches the counterexample directly. Its first entry verifies the map symbolically rather than taking anyone’s word for it, which is where this expedition started.
The conventions it is written under
Every figure is a function fig_<name>() saving through one _finish()
helper, registered in a catalogue under its direction. Randomness is
seeded explicitly, so a figure drawn today is the figure drawn in August.
Numerical searches are labelled as hunts and probes, never as proofs —
the same rule the prose is written under, applied to titles and comments.