# Lab

The workhorse behind the research pages. Every sequence ships with its
generators, b-file, and run log; every census with the script that
produced it. Prose without the scripts is a claim, not a result.
Scripts are budgeted to about a minute of wall clock; deep ranges go
to `fast.c` or a stated smaller scale, never to an hour of python.

## Sequences

One directory per sequence under `sequences/`: `terms.py` (the
primary generator), `terms2.py` (an independent second generator
written from the definition), `bfile.txt`, and `RUN.txt` with the
commands, comparisons, and PASS/FAIL lines. Some entries add a
`fast.c` for deep ranges. The verified summary of every entry is the
[sequence ledger](../sequences.md).

## Censuses

`census/coprime/` is the coprime census: `general.py` and its four
result files. `census/fillclasses/` is the fill-polynomial census:
`census.py`, its csv outputs, and `verify_fillclasses.py`.

## Base 3

`base3/` holds the scripts behind the bases page: `makefig.py`
regenerates its figure, `precision.py` recomputes the constants at high
precision, `sieves.py` runs the structural checks, and `claims.md` is
the per-claim audit.

## Visibility

`visibility/` covers three arithmetic claims about designs: `visible.py`
for the density of origin-visible lattice points inside a base-`q`
design, `gaussian.py` for the Gaussian zeta of a 2D design and its 4D
quaternion analogue, and `pascal.py` for the base-2 carpet as the odd
entries of Pascal's triangle. A second pass adds `connectivity.py`, which
races self-similar designs against exactly matched random cell sets on
components and boundary, `baseq.py`, which counts base-`q` designs under
the dihedral wreath group and identifies the result in OEIS, and
`dirichlet.py`, which sums one design's fill-ratio fluctuation to
`pi^4/192`. A third pass re-runs those same three claims through
independently written generators - `matched.py`, `wreath.py` and
`lambda4.py` - which share no code with the second pass and reach larger
grids, two more bases and a second `pi` routine. `RUN.txt` carries the
derivations, the commands, and the PASS/FAIL lines.

## Porous

`porous/` measures Darcy conductance through a mixed-base carpet sponge:
`flow.py` builds the pore network by Kronecker product and solves it
matrix-free, `check.py` rebuilds it from the digit rule and solves it
directly. The finding is that scale ordering changes permeability at
fixed porosity.

## Millennium

`millennium/` recomputes the three measurements a survey of the Clay
problems leans on: `franel.py` for the Franel-Landau discrepancy of the
stack's Farey nodes, `lattice.py` for the log-periodic box counts that
place every design in the lattice class, and `gap.py` with `gap2.py`
for the code-23 Laplacian band gap by two independent routes. A second
pass adds `stack.py`, which re-derives the Farey identity step by step
and rebuilds the discrepancy meter from a different generator, and
`star.py`, which pins the upper edge of the band gap by exact integer
arithmetic instead of an eigensolver.

## Levels

`levels/` asks whether mrly fractal Laplacians repel their eigenvalues
like a random matrix or cluster them like an integrable system:
`graphs.py` builds the cell graphs, the diagonal slice graph and the two
controls, and `spacings.py` unfolds the spectra two ways and
Kolmogorov-Smirnov tests them against both laws.

## Lattice

`lattice/` works out the complex dimensions of a one-base design three
ways: `poles.py` locates them as roots of the Moran equation, `boxcount.py`
measures the log-periodic oscillation they force in the box count, and
`tube.py` computes the Minkowski content in closed form and shows it never
settles. `RUN.txt` carries the derivation, the commands, the PASS/FAIL
lines, and the two places the blanket "no mrly design is Minkowski
measurable" statement has to be qualified.

## Complex dimensions

`complex_dimensions/` is a second, independent pass at the subject of
`lattice/`, reached from a differently worded restatement of the same
result. `spectrum.py` prints the derivation, checks closure under
composition cell by cell, computes the tube in exact rationals, proves
the box-count identity `N(1/(nE)) = k N(1/E)` in exact integers, and
measures the frequency on two observables over two windows. It agrees
with `lattice/` on every structural conclusion, disagrees on one
measured number, and records both.