Experiments

Active

Full records live under experiments. This page is the project’s index into them. All eight sub-experiments run from a single harness, ephemeris/examples/evaluate.rs, and complete in about two seconds once built.

Configuration common to all runs

Parameter	Value
Element set	10,734 Starlink elements, CelesTrak supplemental GP, median epoch 2026-08-29 21:17:42 UTC
Propagator	SGP4, TEME → ECEF → ENU
Observer	38.9°N, 77.0°W (Washington DC)
Elevation mask	25°
Epochs	96 at one-minute spacing, spanning a full orbital period
Link budget	6, selected for angular diversity
Seed	`20271002`

Runs

Experiment	Tests	Status	Result	Reported in
E1 Visibility and dilution of precision	Instrument characterisation	complete	56 to 82 visible, median 68; HDOP median 1.02 on six diverse links	CH05, PUB-001 §VI-A
E2 Resolution vs Cramér–Rao bound	HYP-001	complete	Ratio 0.97 to 1.02 across three decades	PUB-001 Table III
E3 Spoofing immunity across epochs	HYP-002	complete	384 attempts, worst displacement $1.51\times10^{-10}$ m	PUB-001 §VI-D
E4 Relay detection vs size and quota	HYP-003	complete	Total from $M=5$ at $q=2$ ; 67% at $M=3$	PUB-001 Figure 1
E5 False positives vs terminal density	Operating envelope	complete	Clean at 10 ns to 1000/km²; 28.3% at 100 ns and 100/km²	PUB-001 Table IV
E6 Degradation without Condition S	Boundary of HYP-002	complete	OCXO 228–411 m; TCXO 22.8–41.1 km	PUB-001 §IV-A
E7 Terminals required by residual adversary	Economic bound on A4	complete	$\lceil M/q \rceil$ ; 500 terminals for $10^3$ identities at $q=2$	PUB-001 §VI-H
E8 Robustness across ground sites	External validity	complete	Five sites, 1.4°N to 69.7°N; HDOP 1.01 to 1.10	PUB-001 Table V

Cross-set replication

The entire evaluation was repeated on an independently derived element set: CelesTrak’s own general-perturbations solution, 10,731 elements at a median epoch nine hours later, produced by a different orbit-determination pipeline.

Metric	Supplemental	GP
Visible, median	68	72
HDOP, six diverse	1.02	1.02
$\delta$ at 10 ns	3.1 m	3.1 m
Estimator / CRLB	0.97–1.02	0.94–1.02
Worst spoof displacement	$1.51\times10^{-10}$ m	$1.71\times10^{-10}$ m
Relay $M=5$ , $q=2$	100%	100%
False positives, 10 ns, 1000/km²	0%	0%

Every headline figure reproduced. One difference is worth recording: the top-elevation HDOP tail is worse on the GP set, 8.90 against 6.01, which strengthens the case for diverse link selection rather than weakening it.

Planned but not run

Experiment	Purpose	Why not run
Doppler-augmented estimation	Test whether folding Doppler in tightens $\delta$	Estimator is delay-only. Doppler is modelled in the code but not wired into the solve. Highest-value remaining run, since $\delta$ binds the false-positive envelope
Multi-beam adversary detection	Test whether independently timed beams leave an aperture-level signature	Requires a phased-array transmit model the project does not have
Mobile terminals	Test whether the bound survives maritime and aeronautical motion	Scoped out; fixed terminals assumed throughout
Second epoch of the supplemental set	Cross-epoch replication within one pipeline	CelesTrak’s supplemental set is operator-uploaded and was unchanged over a 14-hour window. Substituted the GP set, which varies both epoch and pipeline and is the stronger check

Run and excluded

A run that happened but is not reported is listed here with the reason. Silently dropping runs is the difference between a result and a selected result.

Experiment	Reason for exclusion
Full evaluation on the Walker-delta constellation	Superseded. Run while CelesTrak was unreachable, using a synthetic 1,584-satellite single shell. Every qualitative conclusion matched, but the single-shell model shows only 9 to 14 satellites against 56 to 82 for the real multi-shell constellation, so its resolution figures are not comparable. The code is retained as a dependency-free fallback
Detector runs using fixed-grid quantisation	Instrument was flawed, not the run. The grid fragmented relay clusters, placing 45 of 200 identities in the modal cell. Replaced with density-based detection and re-run; see methodology
Adversary classes A1 (emulator) and A2 (replayer)	Not implemented rather than excluded. An adversary holding no terminal has no physical layer into which to inject observables, so simulating one would model a capability it does not have