Closed form
Bench
Every number on this page is an evaluation of a formula, or a row you typed. Placeholders are the Rev 3.6 worked example. They are not measurements, and they are not written into the book unless you are on the walk.
§3.4
Phase stability
σ_φ = 2π f τ σ_y. Quote the installed unit.
§4.3
Light time and lag resolution
§4.2
Stationary coherence floor
The curve is E[r] ≈ √(π / 4L) under the complex-Gaussian null. It is not a spectrum.
Large-L magnitude check. The bootstrap decides.
Sage: null expectation. Hot: κ=3 check. Log axes. Not campaign data.
§5
Weak common phase
Rev 3.6 uses σ_φ = 0.42 rad. The paper reports φ ≈ σ √r. Exact inversion is beside it. The millimetre map is not an estimator.
Switch 2
Chromatic class
Targets: delay 1.3391, ionosphere 0.7468, offset 1. A delay-class pass is necessary, not sufficient.
Radians or cycles, not metres.
§3
Ionospheric carrier phase
Phase in radians scales as 1/f. Delay and range scale as 1/f². 0.1 TECU is ≈8.4 rad at 100 MHz and ≈0.53 rad at L1, a factor of ≈15.75, not its square. Not a forecast.
Factor withheld.
§4.0
Per-dump phase
σ ≈ 1/√(2 C/N0 T), T = 1/f_d.
§3.4
Guard band
Below f_loop the GPSDOs are one clock. Mandatory on Chain C, conservative on Chain S.
§4.3
Sphere baseline
Mean-Earth haversine. Not a geodetic reduction. Empty coordinates stay empty.
§5
Campaign RSS
Open a campaign to edit budget rows. Catalog defaults appear with the record, labeled catalog.
Self-check
Identity against Rev 3.6
If a row fails, the app is wrong. Do not interpret it as a residual.
- HoldGPSDO σ_φ at L1, σ_y(1 s)=10⁻¹²9.899e-3 rad · paper 9.9×10⁻³ rad
- Holdf₁/f₂1.339130 · paper 154/115 ≈ 1.339
- Hold0.1 TECU carrier phase at L10.536 rad · paper ≈ 0.53 rad
- Hold0.1 TECU carrier phase at 100 MHz8.45 rad · paper ≈ 8.4 rad
- Hold0.1 TECU, 100 MHz / L115.75 · paper ≈ 15.75, not its square
- HoldIGS clock residual, 75 ps at L10.742 rad · paper ≈ 0.74 rad
- HoldLight time, 10 km33.36 µs · paper ≈ 33 µs
- Holdδτ = 1 ms baseline299.8 km · paper 300 km
- HoldNaive L=86400 magnitude floor3.02e-3 / 1.58e-3 · paper E[r]≈3.0×10⁻³, σ≈1.6×10⁻³
- HoldCalendar r_min (κ=3), not the program floor7.74e-3 · paper ≈ 7.7×10⁻³
- Holdσ_φ=0.42 rad, calendar r_min → path at L11.12 mm · paper ≈ 1.1 mm
- HoldL_eff=300 illustration, r∼10⁻¹, σ_φ=0.42 rad0.133 rad · 4.02 mm · paper φ_s≈0.13 rad ≈ 4.0 mm
- HoldChain S double-difference floor, trop + multipath0.52–1.04 rad · paper inside 0.4–1.1 rad