Quantify the Jao Gap at catalog scale: bootstrapped per-strip depth, global significance, and centroid vs metallicity in Gaia DR3

The Jao Gap is a narrow ($\sim 0.05$ mag) under-density in the lower main sequence near $M_G \approx 10.0$–$10.35$, sloping fainter with redder color across $2.3 \lesssim G_{BP}-G_{RP} \lesssim 2.7$, associated with the partially-to-fully-convective transition in M dwarfs. Its discovery characterization was largely by-eye: per-strip decrements were published without uncertainties, and its metallicity dependence only qualitatively. Task, entirely from frozen public Gaia releases with pinned queries and dataset hashes: (1) per-color-strip gap depth with bootstrap confidence intervals; (2) a global detection significance against a smooth no-gap null with look-elsewhere control across the search region; (3) the gap locus $M_G(G_{BP}-G_{RP})$ fit with propagated parallax and photometry uncertainties; (4) gap depth and locus as functions of metallicity (GSP-Spec [M/H] or a defensible photometric proxy), with propagated errors and a stated detection or non-detection of the trend at quantified confidence.

Acceptance. FULLY RESOLVES: an analysis on a frozen Gaia release with pinned query + dataset hash reporting (a) per-strip depths with 68/95% bootstrap CIs, (b) a global gap significance against a smooth null with explicit look-elsewhere control, (c) a gap-locus fit with propagated uncertainties, and (d) depth-vs-[M/H] with propagated errors and a quantified detection or non-detection of the metallicity trend. PARTIAL: any proper subset of (a)–(d), or a demonstration with evidence that a specific axis (e.g. the metallicity trend) is not measurable from public DR3 data at useful confidence, with the systematics budget that shows why. All numbers must be regenerable by one public script.