Version 2 · reproducible methods note

Resolution helps.
Not linearly forever.

A controlled, 288-scenario test of the shortcut that Doppler information always scales linearly with spectrograph resolving power.

Interrogate the model Download all scenarios

Grid8 × 4 × 3 × 3R · width · depth · line count

Photon budget10⁹ e⁻fixed continuum electrons

Sampling check0 flips4 versus 8 pixels / resolution element

EvidenceSHA-256protocol and model bound to results

Finding 01

The same proxy fails at both ends for different reasons.

Narrow unresolved lines lose more information than the shortcut admits at low R. Broad resolved lines saturate while the shortcut keeps promising a 1/R improvement.

Worst declared scenario 2.924×

Exact uncertainty divided by proxy uncertainty at R=40,000, 1 km/s intrinsic FWHM, depth 0.2, and 80 lines.

Broad-line gain 5.86%

Median exact improvement from R=100k to 250k for 10 km/s lines. The proxy claims 60% in every width regime.

Narrow-line gain 66.89%

Median exact improvement over the same resolving-power interval for 1 km/s lines.

Line chart of exact-to-proxy uncertainty ratio against resolving power for four intrinsic line widths. Broad 10 kilometre per second lines cross the twofold optimism threshold at high resolving power; narrow lines are most discrepant at low resolving power. — **Figure 1.** Direct comparison at depth 0.45 and 40 lines. The dashed line is the rule frozen before computing the grid.

Interactive sensitivity explorer

Change one assumption. See where the shortcut breaks.

The browser and offline study call the same scientific implementation. Values are synthetic photon-noise lower bounds.

Uncertainty curve

Exact bound versus calibrated proxy

Computing…

Generalization map

Exact uncertainty ÷ proxy uncertainty

Current depth, count, and electron budget

proxy conservative near calibration ≥2× optimistic

Method in brief

A lower bound with its assumptions attached.

Read the full methods →

Construct

Place deterministic Gaussian absorption lines across a fixed 3,000 km/s interval.

Broaden

Convolve intrinsic and instrumental Gaussian widths while conserving equivalent width.

Count

Distribute a fixed continuum-electron budget over four pixels per resolution element.

Differentiate

Evaluate the analytical spectrum derivative and independent-Poisson Fisher information.

Challenge

Calibrate the old proxy once, then test every cell without retuning it.

Boundary of inference

This is not a spectrograph forecast.

It excludes detector noise, throughput, wavelength calibration, template mismatch, tellurics, photospheric velocities, cadence, orbital search, and correlated noise. No named instrument is predicted or ranked. No planet-detection limit is estimated.

Claim ledger Limitations Reproduce

Primary-source context

Reported values stay in their own estimands.

Design goals, formal errors, short-term precision, and long-baseline residuals are not treated as interchangeable validation points.

Before / after

From interactive claim to auditable evidence chain.

The 41→95 score records repository practices, not scientific merit, impact, or peer-review outcome.

Grouped horizontal bars across ten repository-practice dimensions, increasing from 41 before to 95 after out of 100. — **Figure 2.** Scores and dimension definitions are machine-readable in the maturity rubric.