Future work

Active

Next steps

Ordered by value, not by ease.

#	Step	Why it matters	Effort
1	Fold Doppler into the estimator	Doppler constrains the same unknowns independently of delay, so it should tighten $\delta$ . Since $\delta$ binds the false-positive envelope, this directly widens the operating envelope — the method’s binding practical constraint	Low. Already modelled in `Satellite::doppler_from`, needs wiring into the solve and re-validation against the CRLB
2	Establish achievable arrival-time precision on real hardware	The whole operating envelope rests on 10 ns being achievable. That value comes from link-budget reasoning, not measurement, and it is the single most load-bearing unvalidated number in the project	Medium. Bench measurement, no operator cooperation needed
3	Characterise the small-relay detection floor	Detection is 67% at $M=3, q=2$ and total from $M=5$ . The boundary is where relay size approaches the quota, but its shape is not established, and small relays are the operationally interesting case	Low. Sweep the region finely; the harness already supports it
4	Extend from access identities to compute tenants	The orbital-edge literature assumes tenants are who they claim to be. An access-layer identity bound is a prerequisite for admission control on orbital compute, and that is the larger question this project serves	High. New threat model, likely a separate project
5	Implement a comparison baseline	“Compared to what?” has no strong answer today. An RSSI-based Sybil detector from the WSN literature would be a weak baseline but is better than none	Medium
6	Operational validation	Measurement against a real terminal and gateway would move the work from simulation to evidence	High. Needs operator cooperation or instrumented hardware
7	Multi-beam adversary detection	The one adversary class that defeats the bound. Independently timed beams still radiate from a common aperture, so their relative phase behaviour may be anomalous	High and speculative. Stated as an idea, not a plan

Tried and did not work

The most valuable section for anyone picking this up, and the one most often omitted. An approach abandoned without a recorded reason will be tried again.

Approach	Why it failed	Would it work with
Fixed-grid quantisation for relay detection	Fixes scatter with standard deviation of order $\delta$ , so a relay at an arbitrary offset straddles several grid cells. On 200 relayed identities the modal cell held only 45	Nothing. Replaced with density over a $2\delta$ neighbourhood, which is translation-invariant and has no boundary artefact. Do not return to grids
Selecting the six highest-elevation satellites	High satellites cluster near zenith and leave the geometry matrix ill-conditioned. Median HDOP 2.73 against 1.02 for diverse selection, and the tail is worse and less stable across datasets	Nothing. `select_diverse` is strictly better at the same cost
Modelling A1 (emulator) and A2 (replayer) adversaries	An adversary holding no terminal has no physical layer into which to inject observables. Simulating one would model a capability it does not have	Nothing. They are excluded by construction, and the paper says so in one sentence rather than evaluating a non-adversary
Walker-delta constellation as a stand-in for real elements	Not wrong, but superseded. A synthetic 1,584-satellite single shell shows 9 to 14 satellites visible against 56 to 82 for the real multi-shell constellation, so its resolution figures are not comparable	Only as a dependency-free fallback when no TLEs are available, which is what it is retained for
Waiting for a fresh supplemental element set	CelesTrak’s supplemental set is operator-uploaded and was unchanged over a 14-hour window	The general-perturbations endpoint, which refreshes every two hours and, being a different orbit-determination pipeline, is the stronger cross-check anyway
Scripted download of four open-access references	Cloudflare returns 403 to MDPI and PeerJ regardless of headers; PMC serves a JavaScript interstitial. Semantic Scholar, OpenAlex and Europe PMC offered no alternate host	A browser. Not a research finding, but it will cost the next person an hour if unrecorded

Open questions raised

Questions this project produced rather than answered. Promote any that survive scrutiny into research questions with their own number.

Why is the geometry so insensitive to constellation density? Visible count varies more than 3× across latitude while HDOP varies by 10%. Six well-separated links appear sufficient and even the sparsest site supplies six, but the flatness of that tail is not explained. If it generalises, it says something about how much constellation a geometric defence actually needs.
Is there a selection rule better than greedy max-min separation? The greedy rule was the first thing tried and beat the intuitive rule by 2.7×. Nothing establishes it is near-optimal, and HDOP with all 68 visible satellites is 0.32, so there is a factor of 3 unclaimed.
Can the multi-beam adversary be bounded rather than merely named? The spoofing result is exact for one transmit epoch. An adversary with $N$ beams defeats it. Whether there is a corresponding bound in $N$ — a cost that grows with the number of positions faked — is open and would close the last gap.
Does the same duality appear elsewhere? The estimator’s uncertainty and the adversary’s freedom to lie are the same quantity here, governed by the same matrix. Whether that duality is a general property of physical-layer identity bounds or an accident of this geometry is unexplored.