Equation 111 · No Particle Without a Cosigner
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Symbol D_rm det
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subscript
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The kill criterion stated for this kind of construction is that the distance must not change under mere reparametrization, and must not be dominated by unmatched detector design masquerading as a trajectory effect. Both were tested directly rather than assumed: reparametrization invariance follows from building entirely out of proper time and proper-frame quantities, with no coordinate freedom left to exploit; and the coupling-type argument above shows explicitly, in closed form, that an unmatched instrument does move even on a single, fixed worldline — which is not a failure of the construction but confirmation that it flags exactly the artifact it was built to…
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The kill criterion stated for this kind of construction is that the distance must not change under mere reparametrization, and must not be dominated by unmatched detector design masquerading as a trajectory effect. Both were tested directly rather than assumed: reparametrization invariance follows from building entirely out of proper time and proper-frame quantities, with no coordinate freedom left to exploit; and the coupling-type argument above shows explicitly, in closed form, that an unmatched instrument does move even on a single, fixed worldline — which is not a failure of the construction but confirmation that it flags exactly the artifact it was built to catch. The genuine failure is the inertial-eternal degeneracy: a case where the object simply does not exist without an additional, non-trivial choice of switching profile that the idealization was meant to avoid needing. A construction that is honest about that gap is more useful than one that is silent about it.
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