● Domain 05 · Sovereign & Strategic Systems
Say which source is wrong.
Several instruments observe one scene and return different answers. The operational question is not what the average is.
Möbius strip, with instruments on itCarry a frame once around and it comes back reversed. Four sensor stations sit on it, each seeing something different about one world.One-sided surface, and the sensing that sits on it · Möbius (1865); Skolnik, Introduction to Radar Systems (2001); Lurton, An Introduction to Underwater Acoustics (2010)
Averaging destroys the measurement
Fusing disagreeing sources into one confident number produces an answer no instrument supports and no operator can audit. In a contested environment the disagreement is the information: something has failed or been spoofed.
What changes
Treat each source as holding a section over what it can see, and consistency is checked on the overlaps rather than assumed. Agreement gives a global picture; one failure gives an obstruction and its location.
Demonstration
Five sensors, one run.
The fix, or the refusal
Range country: blocks of high ground with a network of narrow valleys between them, tinted by altitude.
Five sensors looking down at overlapping patches, each returning the height beneath it with its own bias.
The seam that carries the obstruction. Four seams can be closed; the fifth takes the remainder.
The route, threading the valleys at a set clearance, and the target in the one it ends in.
Consistency between sources is a property of their overlaps, so a failure carries a location as well as a size. The height under the vehicle is known through five sensors whose footprints overlap. On a ring of five, a fix exists exactly when their disagreements sum to zero round it, so that sum is what is computed. When it does not vanish, the failing seam is named and the fix withheld, which tells an operator which sensor to distrust and where.
Sources
si|Ui∩Uj = sj|Ui∩Uj
The gluing condition · Bredon, Sheaf Theory (1997)
Ȟ1(𝒰, ℱ) = ker δ1 / im δ0
Čech cohomology of a cover · Leray (1945)
Is this your problem?
Tell us what has to hold, and what happens if it does not.
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