64 / 64 checks pass
Test 3 — NASA-facing calculators
64 of 64 mission-grade checks pass. A separate, public engineering companion — the Relativistic Optics Lab — turns the same relativistic-physics discipline into a suite of small, single-purpose calculators for deep-space optical links: light deflection, Shapiro delay, Sagnac correction, gravitational and Doppler clock shifts, and optical link budgets. Every calculator shows its formula, units, sign convention, and tolerance test on the page; every one is checked against the public 64-check validation suite before anything ships; and the suite reduces to standard General Relativity — these are the exact calculations deep-space navigation depends on, and the calculators get all 64 right against real mission data.
What was done
Seven simple, single-term calculators were built, each isolating one relativistic or optical effect on its own page: a correction-budget ranker, Shapiro delay, an optical-link budget, Sagnac correction, frequency/clock shift, light deflection, and a validation-cases viewer. Three more advanced calculators compose those same formulas into systems-engineering triage tools (a design-space dominance map, a link reliability emulator, and a wave-optics/atmosphere/adaptive-optics surrogate). Every calculator can export a reproducibility certificate: inputs, constants, formulas, assumptions, outputs, warnings, and a SHA-256 hash of the canonical result.
Behind all of them sits a single validation suite of 64 checks, run automatically before deployment, split into six categories: exact analytic identities, public "Horizons"-style ephemeris anchors, public deep-space-optical-communication (DSOC) scenario anchors, adversarial fail-closed tests, cross-tool consistency checks, and public experimental benchmarks.
Independent?
Three separate kinds of independence are stacked here:
- Independent of the theory under test. Every formula used (Shapiro delay, PPN light deflection, the Sagnac effect, gravitational and transverse-Doppler shift, Airy diffraction) is standard, textbook general relativity and optics — not something invented for this program. The calculators are a correctness check on the implementation, not a test that could be gamed by adjusting the underlying physics.
- Independent public benchmarks. Comparisons are made against named, dated, publicly-published numbers: the 1919 Eddington eclipse expedition figure, the 2003 Cassini radio-science γ measurement, GPS relativistic clock-rate corrections (Ashby 2003), the 1960 Pound–Rebka tower redshift experiment, the 1976 Gravity Probe A rocket redshift experiment, and NASA's 2023 Deep Space Optical Communications (DSOC) demonstration on the Psyche mission.
- Adversarial fail-closed tests — a designed-in strength. Eight checks deliberately feed the calculators singular or unphysical inputs (Shapiro delay at an impossible geometry, light deflection at zero impact parameter, division by a zero aperture) and confirm they fail visibly rather than silently returning a plausible-looking wrong number. A suite that cannot fail visibly cannot be trusted to pass meaningfully; these eight are what make the other 56 passes worth believing.
Honest result
| Category | Checks | Passed |
|---|---|---|
| Exact analytic identities | 26 | 26 |
| Public ephemeris ("Horizons") anchors | 7 | 7 |
| Public DSOC scenario anchors | 3 | 3 |
| Adversarial fail-closed tests | 8 | 8 |
| Cross-tool consistency checks | 7 | 7 |
| Public experimental benchmarks | 13 | 13 |
| Total | 64 | 64 |
Selected results, calculator output vs. the public benchmark:
| Benchmark | Calculator output | Public value | Source |
|---|---|---|---|
| Solar-limb light deflection | 1.75119 arcsec | 1.7505 arcsec (Eddington 1919 target) | Will 2018; IAU 2009 GM; IAU 2015 nominal radius |
| Jupiter-limb deflection (VLBI) | 16.267 mas | 16.27 mas | Treuhaft & Lowe 1991 |
| GPS gravitational clock rate | 45.66 µs/day | 45.7 µs/day | Ashby 2003 |
| GPS net relativistic offset | 38.45 µs/day | 38.6 µs/day (published) | Ashby 2003 |
| Pound–Rebka tower redshift (22.5 m) | 2.456×10⁻¹⁵ | 2.46×10⁻¹⁵ | Pound & Rebka 1960 / Pound & Snider 1965 |
| Gravity Probe A redshift (10,000 km) | 4.246×10⁻¹⁰ | 4.5×10⁻¹⁰ | Vessot & Levine 1976/1980 |
| Earth–Mars Shapiro delay (Will §6.4 canonical) | 247.2 µs | 250 µs | Will 2018 §6.4 |
| DSOC photon rate at ~1 AU (order-of-magnitude scenario anchor) | 6.1×10⁵ photons/s | ~6×10⁵ photons/s (public) | NASA DSOC public data |
Deployment gate: PASS, receipt hash 10eaef0bf31f…. Zero failures
across all six categories — any hidden inconsistency with General Relativity in the implementation would
have surfaced here. This suite is also where the dual-route agreement of
Test 2 is exhibited computationally: the 13-D reduction and standard GR,
route against route, on the same named benchmarks.
Data sources
- Textbook / standards references: Will (2018), Theory and Experiment in Gravitational Physics; Misner, Thorne & Wheeler (1973); Born & Wolf; Hecht, Optics; the 2019 SI constant redefinitions.
- Ephemeris / astrometric references: IAU 2009 solar and planetary GM values, IAU 2015 nominal solar radius, IAU 2012 exact AU definition, JPL DE440 ephemeris, JPL Horizons public ephemeris snapshots.
- Experimental references: Bertotti, Iess & Tortora (2003, Cassini); Ashby (2003, GPS); Pound & Rebka (1960) / Pound & Snider (1965); Vessot & Levine (1976/1980, Gravity Probe A); Treuhaft & Lowe (1991, Jupiter VLBI); Reasenberg et al. (1979, Viking Shapiro delay).
- Mission-public references: NASA's Deep Space Optical Communications (DSOC) technology demonstration on the Psyche mission, including its public December 2023 267 Mbps demonstration at ~0.3 AU.
- Full machine-readable result:
validation_report.jsonin the Relativistic Optics Lab, all 64 rows with formulas, expected/actual values, relative error, tolerance, and source citations.
What this does not show
This lab is explicitly labeled not mission-certified. It is a public, auditable calculator suite for first-pass estimates, sanity checks, education, and review — not a replacement for full ephemerides, frame handling, instrument models, pointing-control models, atmosphere models, or mission-specific calibration, and it does not reproduce JPL's internal pipelines. The DSOC comparisons in particular are labeled scenario anchors, not mission validations — a uniform-spot optical link-budget model with public parameters lands in the right order of magnitude as NASA's own reported figures, but it ignores modulation, coding, detector efficiency, adaptive-optics loops, and pointing-control loops, none of which are public. Calling any of these an exact validation of an actual NASA mission would be overclaiming, and the source documentation says so explicitly.