# Methods

## Research question

Does the sign of a descriptive residual contrast between the published full
and component-removed CH4 spectral curves remain stable when adjacent JWST
channels are regrouped across every declared bin width and bin origin, in both
transmission and emission?

This is deliberately narrower than asking whether methane is detected. Bell et
al. (2023) answer that retrieval question; this repository audits the visible
spectral morphology supplied with that paper.

## Source reconstruction

`scripts/prepare_spectral_data.py` downloads or accepts Bell et al. Source Data
Fig. 3, requires the byte SHA-256 recorded in `data/spectra/provenance.json`,
and reads all 113 observed channels. The six transmission and six emission
model-contour columns are linearly interpolated from their 250-point grids to
the observed channel centres. Workbook percentages are divided by 100. No
observed channel is removed or averaged in the canonical native CSV.

## Frozen design grid

`configs/methane_morphology_audit_v1.json` declares adjacent-channel factors
1, 2, 4, 5, 8, and 10. For each factor, every integer bin origin from zero to
factor minus one is evaluated; incomplete edge groups are excluded. The sum of
origins is 30 designs per geometry and 60 reported rows overall.

Within each design, observations and curves are inverse-variance averaged with
the observed one-sigma errors. One additive data-minus-curve offset is fitted
separately for the full and no-CH4 curve. The diagnostic is

`chi-square(no-CH4 component removed) - chi-square(full curve)`.

A positive value means the full published curve leaves less weighted residual
structure for that binning design. Every complete bin is also deleted once;
the smallest resulting contrast is retained.

## Decision rule

The descriptive sign-robustness rule passes only when the contrast is positive
in all 30 designs for both geometries. There is no sigma conversion and no
post-hoc “detection” threshold.

## Why this is not a likelihood-ratio test

The source paper describes the no-CH4 curves as spectral post-processing of
posterior samples with the absorber removed. They are not maximum-likelihood
fits from a separately optimized methane-free retrieval. The same observations
also informed the posterior curves. Consequently the residual contrast has no
independent null distribution or Wilks-theorem interpretation.

## TESS analysis

The existing TESS analysis remains a separate diagnostic: a local linear null
is compared with a circular, fixed-limb-darkening transit whose midpoint,
radius ratio, impact parameter, baseline, and slope are bounded and fitted.
Formal errors are scaled by reduced chi-square and a residual time-averaging
beta factor. Only Sector 54 is available as a SPOC time series in the target's
MAST cone result, so the output is a one-sector noise audit, not a multi-sector
consistency measurement.