# ORIGINAL CLAIM — E4-H160

Preserved verbatim from the Expedition IV corpus. **This file is not edited.**

## Statement (Expedition IV, Volume A)

> **E4-H160 — Aperture–dispersion limit on the range resolution of wavelength-steered phased-array lidar**
>
> In a wavelength-steered optical phased array the beam angle is a function of optical frequency, so
> the chirp that buys range resolution also sweeps the beam across the scene. A target is illuminated
> only while the beam covers it, so the effective bandwidth saturates at
> `B_eff = c/(λD|dθ/dλ|)` and the range resolution floors at `δR = λD|dθ/dλ|/2`, independent of chirp
> bandwidth and sweep time.

## Derived claims as recorded in the refined dossier (D15)

- **(R1)** The ceiling is `δR = max(c/2B, λD|dθ/dλ|/2)`, with crossover `B* = c/(λD|dθ/dλ|)`.
  The number of usable range bins is `N = B_eff T`, independent of B: extra chirp bandwidth adds
  neither resolution nor bins.
- **(R2)** The floor grows linearly with aperture: a larger aperture makes range resolution *worse*.
- **(R3)** The effect is absent for an independently phase-steered array, because there the beam
  direction is not tied to the optical frequency.

## Corrections already recorded in the dossier (carried forward as questions, not accepted)

The dossier recorded two defects in the original, and this project treats them as claims to test, not
as conclusions:

1. The original's §9 said only a larger aperture improves range resolution, contradicting its own
   formula in which `B_eff ∝ 1/D`.
2. The §8 feasibility check was inconsistent about whether the floor is set by `Nλ/2` or by the
   beam-dwell bandwidth.

**Verified here:** (2) is resolved — `Nλ/2` is the correct O(1) form of the dwell-limited floor
(`δR/D = 0.171` in T1, constant across aperture), and (1) is a genuine self-contradiction in the
original, with the formula being right and the sentence wrong.

## What was proposed, minimally

If true, the claim says a designer cannot improve range resolution by increasing chirp bandwidth past
`B*`, and that making the aperture larger makes it worse. Both are testable statements about the
measurement, and both were tested here (one confirmed as a naive-resolution statement, one corrected).