Equation 49 · The Entry a Relabeling Cannot Write
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Symbol D_Lambda
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That identity is the construction’s first load-bearing check, and it is exactly the failure this approach would need to survive to be worth building in the first place: a relabeling — a change of coordinates, a change of basis, a renaming of which combination of amplitudes gets called “the excited state” — must never, by itself, generate a nonzero ledger reading. If some proposed accounting scheme returned a nonzero defect purely from renaming states, without discarding a single degree of freedom, it would be reporting an artifact of notation as if it were physics, and the diagnosis this article exists to enable would be worthless from the first page. Requiring to vanish…
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That identity is the construction’s first load-bearing check, and it is exactly the failure this approach would need to survive to be worth building in the first place: a relabeling — a change of coordinates, a change of basis, a renaming of which combination of amplitudes gets called “the excited state” — must never, by itself, generate a nonzero ledger reading. If some proposed accounting scheme returned a nonzero defect purely from renaming states, without discarding a single degree of freedom, it would be reporting an artifact of notation as if it were physics, and the diagnosis this article exists to enable would be worthless from the first page. Requiring to vanish identically under passive relabeling, and confirming that it does, is the covariance check every candidate in this literature has to survive before its behavior under a genuine coarse-graining is worth trusting at all.
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