Manuscript VII-F-ST@1 · VII-F-ST.tex · proposition · 9eee7a44

Proposition: No universal clock return and no finite CCR

Finite destructive clock and an exact evaluation table › Calibration is not singular acquisition · lines 1369–1388 · proof included or linked

VII-F-ST@1#prop:clocklimits

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The channel $M_{C}$ has no left inverse on its full input space. Finite matrices cannot satisfy $[T_{C}, H_{C}] = i ℏ I_{C}$ for $ℏ \neq = 0$ . Clock records do not uniquely determine a geometric dictionary.

Proof. The distinct clock states

(∣ τ_{0} ⟩ + ∣ τ_{1} ⟩) / 2, (∣ τ_{0} ⟩ - ∣ τ_{1} ⟩) / 2

with the same payload have identical destructive outputs. Taking the trace of a commutator proves the second assertion. For the third, keep the finite channel fixed and change the declared time labels or local rod-frame dictionary. Its record law is unchanged.

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unlabeled · line 1379
$(∣ τ_{0} ⟩ + ∣ τ_{1} ⟩) / 2, (∣ τ_{0} ⟩ - ∣ τ_{1} ⟩) / 2$

Proposition: No universal clock return and no finite CCR

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