# Research

The mathematics of the mrly tree: a parity rule on a cube, substituted
into itself. These pages are the near-final findings. Every claim is
tagged Proved, Verified, or Conjecture, every sequence was regenerated
by two independent generators before it shipped, and every page
survived an adversarial verification pass. The scripts, b-files, and
run logs live in the [lab](lab/README.md).

## Pages

- [core](core.md) — what a design is, and the headline counts.
- [bijection](bijection.md) — designs are Boolean functions up to cube
  symmetry; the count is A000616. The strongest theorem.
- [pi](pi.md) — pi recovered from the density of coprime points in the
  stacked set.
- [primes](primes.md) — the stack's moire is a Farey resonance diagram;
  each scale n adds exactly `phi(n)` bright nodes.
- [coprime](coprime.md) — the coprimality spine: exact base-local
  factors on every design, and the census behind them.
- [euler](euler.md) — Euler characteristics of the parity solids: two
  closed forms, and a disproof corrected in public.
- [bases](bases.md) — what base 3 hides: an Eisenstein-lattice constant
  inside base-3 arithmetic.
- [cuts](cuts.md) — the six-gasket theorem: a diagonal cut through one
  parity solid is Sierpinski all the way down.
- [slices](slices.md) — the diagonal slice of the solid cube: the 6n
  census, centered-hexagonal vertices, and the splitting-prime rule.
- [connectivity](connectivity.md) — self-similar designs raced against
  matched random cell sets on components and boundary.
- [dimensions](dimensions.md) — complex dimensions: every design in
  the lattice class, and where Minkowski measurability fails.
- [complexity](complexity.md) — Boolean complexity of the catalog, and
  the Laplacian spectra of the walk graphs.
- [evidence](evidence.md) — the skeptic-facing summary of what is
  actually checked, weaker results included.
- [sequences](sequences.md) — the ledger: every sequence this project
  has produced, with terms, formulas, and verification status.
- [method](method.md) — how the results here are produced and checked,
  worked through on the odd-side fill polynomial.