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Equation 32 · Part 2 · The Entry a Relabeling Cannot Write

Symbol H_c

Λ†(Hc)=Hf\Lambda^\dagger(H_c) = H_f
HcH_c

What this part means

wrong, does not touch the total energy of any closed system, and does not by itself explain where a nonzero reading comes from.

Its job in the formula

HcH_c is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

It does not propose that HfH_f or HcH_c is wrong, does not touch the total energy of any closed system, and does not by itself explain where a nonzero reading comes from; it only names, precisely and checkably, how large the disagreement is between two fully specified descriptions.

The passage around this formula

is a real number in units of energy for every fine state ρ\rho : how much the coarse description, evaluated through HcH_c pulled back along Λ\Lambda , disagrees with the fine description’s own HfH_f , for that specific state. Because expectation values determine a Hermitian operator uniquely — two Hermitian operators with the same trace against every density matrix are the same operator — the strongest statement…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.