Hypotheses

Active

ID	Prediction	Refuted if	Experiment	Standing
HYP-001	Terminal position is recoverable from delay to $\delta = c\,\sigma_\tau \cdot \mathrm{HDOP}$ , and the estimator attains that bound	Empirical RMS error exceeds the Cramér–Rao bound by more than 10% at any swept $\sigma_\tau$	E2	supported
HYP-002	Under simultaneous multi-satellite observation with clock bias estimated, a uniform transmit-time offset produces zero horizontal displacement	Any aim point at any epoch produces displacement distinguishable from floating-point noise	E3	supported
HYP-003	$M$ identities relayed through one terminal collapse into one resolution cell and are detected once $M$ exceeds the per-cell quota	Detection is not total for relays materially larger than the quota	E4	supported, with a floor

Each hypothesis is stated in full on its own page. This table exists so that a reader of the project can see the whole set at once, and so that a hypothesis with no experiment is visible.

Only HYP-001 currently has its own registry page; HYP-002 and HYP-003 are stated here and need promoting to registry/hypotheses.yaml with their own identifiers.

HYP-002 in full, because it is the load-bearing one

Formulated as GNSS, the unknowns are $[p_E, p_N, b]$ with $b$ the clock bias as a range, and satellite $k$ contributes a geometry row $\mathbf{H}_k = [-\hat u_{k,E},\ -\hat u_{k,N},\ 1]$ .

Prediction

$\Delta\hat{\boldsymbol\theta} = a\,(\mathbf{H}^\top\mathbf{H})^{-1}\mathbf{H}^\top\mathbf{1} = a\,\mathbf{e}_3$

A single-beam adversary emits one transmit epoch, so every satellite observes the same offset $a$ . Since the third column of $\mathbf{H}$ is exactly $\mathbf{1}$ , that perturbation lands entirely in the clock coordinate and the position components are identically zero.

The prediction is therefore not “small displacement” but “zero displacement”, which is a stronger claim and an easier one to refute: a single counterexample at any epoch kills it.

Standing, with the caveat on HYP-003

HYP-003 is supported above a floor. Detection is total from $M = 5$ at quota $q = 2$ , and from $M = 3$ at $q = 1$ . Below that the relay is comparable in size to the quota itself and density estimation has too little to work with: at $M = 3, q = 2$ detection is 67%. The prediction as originally written did not anticipate a floor, and the floor is reported rather than absorbed into the claim.

Predictions made and not tested

A prediction that was written down and never tested is recorded here rather than removed. It is often the most useful thing in the project for whoever picks the work up next.

ID	Prediction	Why not tested
—	Folding Doppler into the estimator tightens $\delta$ , since it constrains the same unknowns independently of delay	Estimator is delay-only. Doppler is modelled in the code but unused. Worth testing because $\delta$ is the binding quantity for false positives
—	Independently timed multi-beam transmission leaves an anomalous relative-phase signature detectable from a common aperture	Would require a phased-array transmit model the project does not have. Stated as future work rather than claimed
—	The bound holds for terminals in motion (maritime, aeronautical)	Fixed terminals assumed throughout. Mobility changes the estimation problem and was scoped out deliberately