# PREREGISTRATION — E4-H160

Written before the calculation was run (2026-11-01), and preserved unedited.

## Hypothesis under test

H1: The illumination-dwell limit sets a resolution floor `δR = c/(2B_eff)` that no processing can
beat — i.e. it is a *fundamental* bound, independent of the target.

## Competing models

| Model | Prediction |
|---|---|
| **M1 — fundamental bound** | Resolution floors at `c/(2B_eff)` for any target; extra bandwidth is useless |
| **M2 — information bound** | The floor is the CRB for the *illumination-weighted* spectrum; it saturates only while the target is envelope-limited |
| **M3 — no limit** | Any envelope can be deconvolved, so resolution always improves as `1/B` |

## Primary outcome

Delay-estimation precision (Cramér–Rao bound, and Monte-Carlo RMSE of a correlator) as a function of
chirp bandwidth `B`, for a point target and for an angularly extended target, at fixed array size,
fixed peak SNR, and fixed sample count.

## Secondary outcomes

- `B_eff` and the naive floor vs aperture (T1); the ratio `δR/D`.
- Whether the point-target bound flattens, worsens, or improves for `B > B_eff`.

## Controls

- Same array geometry, same SNR definition, same number of frequency samples across B.
- Target placed inside the unambiguous range `c/(2Δf)` at every B — checked after a first run aliased
  and was corrected before any result was recorded.
- An unweighted correlator (no envelope knowledge) run alongside the matched one, so a difference
  attributable to processing can be separated from a difference attributable to information.

## Decision rules (fixed in advance)

- **M2 supported** if the point-target CRB saturates within a factor 2 while the extended-target CRB
  keeps falling as `B` increases by an order of magnitude.
- **M1 supported** if both saturate together.
- **M3 supported** if the point-target CRB keeps falling as fast as the extended one.
- The claim "fundamental bound" is **rejected** if any target geometry or any estimator achieves a
  precision better than `c/(2B_eff)` by more than a factor 2.

## Falsification conditions

- If the apparent plateau moves when sample count or reconstruction grid changes, it is numerical.
- If the matched and unweighted correlators perform identically at all B, the envelope carries no
  information and M2 is unsupported.

## What would count as inconclusive

If the Monte-Carlo does not attain the bound within 50%, the absolute claim about attainable precision
is untested, and only the bound's *scaling* can be reported.

## Budget

Pilot: two tables (T1 geometry, T2 bound) and one Monte-Carlo (T3). No parameter sweep beyond
N ∈ {256…8192} and B ∈ {10…2000 GHz}. Stop after T3 regardless of outcome.

## Known risk recorded in advance

The original claim may simply be a restatement of a known FMCW/OPA trade-off. A search hit
("System trade-offs in a swept source FMCW LiDAR with dispersive OPA beam steering") suggests this.
If so, the project must report rediscovery, not novelty.