# Fixed Grid String Lab 0.1.0 results

## Result

The engine now distinguishes a fixed coordinate lattice from the stronger
claim that every observable is a direct integer multiple of one increment.
For the latter, it implements an exact failure rule: a candidate tick fails if
any declared measurement interval contains no integer multiple.

Using two rounded NIST Lyman-alpha wavelengths and half the last printed digit
as a reporting-resolution interval:

- `1e-18 s`, `1e-21 s`, and `1e-22 s` fail.
- CODATA's `5.391247e-44 s` Planck-time candidate passes trivially because it is
  vastly below the data resolution; this is not identification or evidence.
- The printed decimal wavelengths possess an exact rational reporting tick of
  `(1e-15 m)/c` by construction, proving that apparent common divisibility can
  be a reporting artifact.

The written theorem is stronger: for any finite measurements with positive
tolerances, every `delta <= 2 min(epsilon_i)` passes by nearest-integer
rounding. Thus finite-precision values alone cannot identify an arbitrarily
small universal tick.

## Discrete string engine

Four integer coordinate fields `(x,y,z,w)` evolve at integer ticks by an exact
reversible discrete wave equation. Across the frozen 128-tick run:

- 32,256 scalar forward-wave checks passed.
- 32,256 scalar reverse-wave checks passed.
- 16,384 scalar periodicity checks passed.
- An independent implementation reproduced 32,256 forward and 32,256 reverse
  checks and all five tick decisions.
- Two distinct full states were constructed with exactly the same 3D
  projection.
- All 13 unit tests passed.

## Limitation

This is written mathematics and finite exact computation. It does not establish
a physical spacetime lattice, a fundamental fifth-dimensional particle,
hydrogen dynamics, or a tick that generates all observable values. A coordinate
lattice also does not require arbitrary field amplitudes or energy eigenvalues
to be integer multiples of its coordinate spacing.

## Next test

Define one electromagnetic, gauge-consistent discrete hydrogen Hamiltonian on
a declared `(dx, dt)`, demonstrate convergence as the grid is refined, freeze
its parameters, and predict several hydrogen transitions before comparison to
new data.