RFIsher

RFIsher determines how much residual digital television (DTV) power each 6 MHz channel can carry before it biases a 21 cm baryon acoustic oscillation (BAO) measurement by more than its own uncertainty.

For each channel, RFIsher runs one RadioFisher forecast at the channel's own redshift. The forecast uses CHIME as described in the CHIME Overview, the inter-cylinder baselines that CHIME's analyses use, the specified cosmology, and one retained year of data. The two fitted BAO dilations give the one number the CHIME Overview reports, the volume-averaged distance D_V (ln α_V = 2/3 ln α⊥ + 1/3 ln α∥), and the forecast gives its clean uncertainty σ. A coherent DTV residual of unit strength is then added through RadioFisher's residual hook, and the forecast returns the bias it causes in D_V. Since the bias is proportional to the residual's strength a, each channel reduces to one response (bias ÷ σ per unit strength) and one tolerance:

a_tol = 1 / |response_dv|

That is, a residual weaker than a_tol has a first-order assigned bias below its σ.

The table of these numbers is RFIsher's main output. Since the table does not depend on the detector's calibration, a new threshold, era, or mask never needs a new table. A new table is needed only for a new cosmology, telescope, residual model, or retained-time anchor.

The optional finite BAO-only likelihood check tests the local bias approximation against an explicitly defined nonlinear model. Failed fits and numerical checks are recorded with the successful ones, and the published table is left fixed. The check does not calibrate the physical residual or the sampling coverage.

Use

Start in a new directory with Git and Python 3.10 or newer. These steps need no telescope data, credentials, GPU, or TeX installation.

git clone https://github.com/WVURAIL/RFIsher.git
cd RFIsher
python3 -m venv .venv
. .venv/bin/activate
python -m pip install -e ".[test]"

The install selects the recorded RadioFisher revision. Keep that pin to reproduce the table, and develop RadioFisher's latest source in another environment. First, read the shipped table:

python - <<'PY'
import rfisher
table = rfisher.read_table()
row = next(r for r in table["channels"] if r["channel"] == 19)
print(f"Channel 19: response = {row['response_dv']:.0f}, a_tol = {row['a_tol']:.3g}")
a = 8.4e-8  # example residual strength, for illustration only
bias_over_sigma = a * abs(row["response_dv"])
print(f"First-order bias / sigma = {bias_over_sigma:.3g}")
PY

This prints approximately response = 8344, a_tol = 0.00012 and First-order bias / sigma = 0.000701. Next, rebuild one channel and check it:

rfisher table --channels 19 --workers 1 --out out/first-run
rfisher figures --table out/first-run/channel_table.json --out out/first-run/figures
python -m pytest tests/test_table.py -q

The forecast writes channel_table.json and channel_table.csv. With --table, the figure command reads this new table, and without it the shipped table. Lastly, the tests compare the rebuilt channel with the shipped result to the numerical tolerances given under Tests.

The full calculation is run with:

rfisher table --out out/all --workers 12
rfisher figures --table out/all/channel_table.json --out out/all/figures
rfisher overview --out out/overview --workers 12

--workers sets the number of processes. The paper/code contract traces each quantity to its code, and PilotProxy's first-run walkthrough continues from this response table to the paper's conditional thresholds.

The CHIME Overview forecast

rfisher overview reproduces the CHIME Overview forecast as its scripts compute it. RadioFisher's own fisher() is called for each redshift bin, with A, bσ8, fσ8, and the two dilations free in each bin and the damping variance s_NL shared by all bins. The dilations then give D_V. On the Overview's 15 bins, the clean one-year errors of 0.47% to 1.03% are reproduced to 0.0003 percentage points. The same forecast with 6 MHz bins over the DTV range gives 1.18% to 1.52% per channel. Each 6 MHz bin is about a quarter as deep, so its error is about twice as large.

The reproduction counts every baseline (RadioFisher's as-built density), as the Overview's forecast does, so it matches the published numbers. Only the inter-cylinder baselines are used for the tolerance table. CHIME's analyses drop the intra-cylinder pairs, which carry noise cross-talk and a strong response to diffuse Galactic emission (CHIME Collaboration 2025, arXiv:2511.19620), and the stack-to-proxy amplitude ratio used with the table is measured between cylinders. Without the intra-cylinder baselines, the table's clean σ(D_V) is 17% to 34% larger than on all baselines. On all baselines, the table agrees with the reproduction to 1.5% on every channel. The table integrates more finely than the reproduction and fits s_NL per channel.

The forecast inputs have two cosmologies. For the table, the specified cosmology cmbspa2026 is used (SPT-3G, ACT, and Planck CMB with DESI DR2 BAO, from Omori et al. 2026, arXiv:2608.31136v1, Table 8). For the reproduction, the Overview's Planck 2018 is used, so that the reproduction can be checked against the published forecast. Only the cosmological parameters and the P(k) table change between the two, and the HI models, damping scale, and CHIME are the Overview's in both. In the specified cosmology, the 6 MHz errors are 7% to 8% smaller (1.09% to 1.40% per channel).

rfisher overview --out out/overview --cosmology planck2018 --compare cmbspa2026

The residual strength

The detector maps the retained shelf proxy to the table's strength with

a = (gamma x_hi)^2 N G

where x_hi is the upper end of the retained per-input shelf proxy, gamma is the measured, calibrated redundant-stack amplitude divided by the archive proxy, N = 16384 is the frame length, and G is an assumed effective temporal gain for an unmeasured cross-moment. gamma is an amplitude ratio, and no intrinsic coherent fraction is inferred from it. No coherence time or cross-day bound has been measured, so G is assumed.

To first order, the ratio of bias to σ is a * abs(response_dv). Since the fitted dilation is alpha_V = D_V_fid / D_V, the signed distance shift is delta ln D_V / sigma_dv = -a * response_dv. The table field bias_dv_per_unit_a (schema v2) stores the ln(alpha_V) projection, which has the opposite sign.

The table is normalized to 8760 retained hours. For the paper's primary calendar time, the Overview's ideal year is assumed, so retaining a fraction kappa of the data requires 1 / kappa years for this reference exposure. An operating-duty penalty is treated as an additional scenario. A forecast for a fixed calendar duration of Y years uses ttot = 8760 * Y * kappa hours and must be recomputed at that exposure.

The threshold rule is in PilotProxy. Its finite-amplitude and channel-specific transfer budgets are external inputs to the rule, and a_tol holds none of them. nonlinear.py and the validation tools check the expected-likelihood model. These checks do not cover the physical transfer or the cross-day DTV covariance (see the paper/code contract).

The model

The fixed forecast inputs are set in inputs.py. The cosmology is the specified cmbspa2026 (SPT-3G, ACT, and Planck CMB with DESI DR2 BAO), and its linear P(k) table is checked against the cosmology before use. CHIME is modeled as in the CHIME Overview, with 4 cylinders × 256 feeds, T_sys = 55 K, 31000 deg², and 0.39 MHz channels. Only the inter-cylinder baselines are used, and their density is built from the array layout (baselines.py, data/nx_CHIME_inter.dat). Built from all pairs, the same code reproduces RadioFisher's as-built density exactly. The exposure is 8760 h of retained data.

The fit (tolerance.py) has six free parameters: A, s_NL = σ_NL², α⊥, α∥, fσ8, and bσ8. The rest are held at the fiducial. As in the CHIME Overview, the dilations give D_V, and the first-order bias is compared with the clean σ of D_V. Where the biases of the two dilations have opposite signs, they partly cancel in D_V. The response changes sign between channels 31 and 32, so the tolerances of those two channels are the loosest. The matrix coordinate s_NL is the damping variance in Mpc squared, and the configuration value sigma_nl is the damping length in Mpc.

The residual (residual.py) is an assumed flat 6 MHz template of residual power. This template puts the same visibility on every baseline that measures a Fourier cell, and its support is the horizon wedge. No wedge modes are excised, and no delay filter is applied. Relative to the noise power, the residual is dP / C_N = a × N_ν × N_meas(k⊥) × f_w(k⊥) for |k∥| ≤ m k⊥ + π/L and zero elsewhere.

The quadrature (forecast.py) is Gauss–Legendre in k and μ, split at every kink of the integrand. Evaluation is batched by radial segment, which keeps the k-dependent angular boundaries of each segment and bounds the memory use. The same node generator is used by the finite check. Doubling either order changes the tolerance by less than 3 × 10⁻⁷.

The table

The table has 24 channels, all in the specified cosmology. These are the DTV allocations 14 to 36 and channel 37, which carries no DTV and is the control. σ is the clean one-year uncertainty of D_V in percent, and the response is signed.

Channel	MHz	z	σ(D_V)/D_V (%)	Response	a_tol
14	470–476	2.003	1.63	+2,947	3.39e-04	plate
15	476–482	1.965	1.65	+3,625	2.76e-04	plate
16	482–488	1.929	1.66	+4,232	2.36e-04	plate
17	488–494	1.893	1.65	+5,045	1.98e-04	plate
18	494–500	1.858	1.62	+6,371	1.57e-04	plate
19	500–506	1.824	1.58	+8,344	1.20e-04	plate
20	506–512	1.791	1.55	+10,810	9.25e-05	plate
21	512–518	1.758	1.52	+13,445	7.44e-05	plate
22	518–524	1.726	1.50	+15,850	6.31e-05	plate
23	524–530	1.695	1.48	+17,700	5.65e-05	plate
24	530–536	1.665	1.47	+18,602	5.38e-05	plate
25	536–542	1.635	1.46	+18,375	5.44e-05	plate
26	542–548	1.606	1.46	+16,976	5.89e-05	plate
27	548–554	1.578	1.45	+14,569	6.86e-05	plate
28	554–560	1.550	1.44	+11,502	8.69e-05	plate
29	560–566	1.523	1.43	+8,141	1.23e-04	plate
30	566–572	1.496	1.43	+4,739	2.11e-04	plate
31	572–578	1.470	1.44	+1,433	6.98e-04	plate
32	578–584	1.445	1.45	-1,609	6.22e-04	plate
33	584–590	1.420	1.47	-4,207	2.38e-04	plate
34	590–596	1.395	1.48	-6,339	1.58e-04	plate
35	596–602	1.371	1.48	-8,315	1.20e-04	plate
36	602–608	1.348	1.47	-10,621	9.42e-05	plate
37 (control)	608–614	1.325	1.47	-13,364	7.48e-05	plate

Each plate shows the residual in Fourier space at the tolerated strength and the bias of D_V against the residual's strength. Since the docs/figures/ gallery is checked in, every channel can be inspected without installing the software. No calculation reads these images. The channel gallery is regenerated with rfisher figures --out docs/figures, and the two Overview plots with rfisher overview --out docs/figures --cosmology planck2018 --compare cmbspa2026. Exploratory figures go in out/.

Files

File	Contents
src/rfisher/bands.py	the channels and their redshifts
src/rfisher/inputs.py, pk_cache.py	the fixed forecast inputs and the P(k) table check
src/rfisher/baselines.py, data/nx_CHIME_inter.dat	the inter-cylinder baseline density, built from the array layout
src/rfisher/residual.py	the coherent DTV residual
src/rfisher/forecast.py	one channel's Fisher matrix with the residual's bias row
src/rfisher/tolerance.py	σ and bias of D_V, response and tolerance
src/rfisher/overview.py	the CHIME Overview forecast, reproduced, and in 6 MHz channels
src/rfisher/table.py, figures.py, cli.py	the table, the figures, the command line
src/rfisher/data/channel_table.json, .csv	the shipped table, with provenance
tools/generate_call_graph.py	draws the call graph above

Tests

python -m pip install -e ".[test]"
python -m pytest -q

One test rebuilds channel 19 and compares it with the shipped table, σ to 1e-5 and the responses to 1e-4 of the larger dilation response. Other numpy and scipy builds change the result by a few parts in a million, and the partial cancellation in D_V magnifies this change. CI also rebuilds channels 14, 29, and 37 with RadioFisher at the pinned commit.

Figure colors

Plots and diagrams use the WVU colors of the Beamer template, and src/rfisher/wvu_palette.py is a standalone copy, updated with the template's tools/export_plot_palette.py. Blue is used for measurements, and old gold gives contrast for model curves and small labels. Further series use the WVU accents, with their own markers or line styles where needed, and grayscale masks keep their binary meaning. A journal's figure requirements take precedence over this palette. The palette has no effect on the calculations or the shipped table.