# Fixed Grid String Lab claim ledger

## FG-1 — Exact lattice wave

- **Claim:** The implemented four-coordinate integer field obeys the declared
  Courant-1 discrete wave equation and is reversible one tick at a time.
- **Type:** Written algebra plus finite exact computation.
- **Assumptions:** Periodic string sites, integer initial profiles, the fixed
  recurrence in `discrete_string.py`.
- **Does not establish:** A physical spacetime lattice, a fifth-dimensional
  particle, hydrogen dynamics, Lorentz invariance, or a continuum limit.

## FG-2 — Projection ambiguity

- **Claim:** Distinct full `(x,y,z,w)` states can produce identical projected
  `(x,y,z)` occupancy.
- **Type:** Constructive mathematical counterexample and finite computation.
- **Consequence:** A single 3D image cannot identify hidden-coordinate motion
  without additional observables or a restricted generator class.

## FG-3 — Candidate tick rejection

- **Claim:** A specified positive tick is rejected by the strong direct-multiple
  hypothesis if a declared measurement interval contains no integer multiple.
- **Type:** Definition and exact-decimal finite computation.
- **Current data:** Two rounded NIST Lyman-alpha wavelengths converted to vacuum
  light-travel times. Their half-last-digit ranges are reporting-resolution
  intervals, not asserted full experimental uncertainty.

## FG-4 — Finite-precision non-identification

- **Claim:** Given finitely many observations with positive tolerances
  `epsilon_i`, every `delta <= 2 min(epsilon_i)` fits by nearest-integer
  rounding.
- **Type:** Written proof.
- **Consequence:** Finite-precision values alone cannot identify an arbitrarily
  small universal tick. A lower bound, complexity restriction, or predictive
  law is necessary.

## FG-5 — Reporting-grid counterexample

- **Claim:** Decimal reporting can create an exact apparent tick unrelated to
  nature. The printed nanometre wavelengths are exact multiples of
  `(10^-15 m)/c` after conversion to times.
- **Type:** Exact-decimal finite computation.
- **Consequence:** Discovering a common divisor of rounded data is not evidence
  for a natural spacetime tick.

## Preserved boundaries

- Complete deterministic closure for a fixed transition family is idempotent.
- Integer-tick point capture does not enforce continuous non-crossing.
- Angular impulse has no extra time factor.
- Finite observed prefixes do not identify arbitrary generators.
- The `2K` recurrence continuation guarantee still assumes a noiseless
  homogeneous constant-coefficient recurrence of order at most `K` from the
  initial state.
- No result here establishes seven physical dimensions, P=NP, or a theological
  cause.