Manuscript Hawk02-E@1 · Hawk02-E.tex · proposition · 4841592b

Proposition: Zero source energy can coexist with perfect residual storage

Information endpoint and gravitational endpoint › A full-residual energy criterion and its limitations · lines 2067–2081 · proof included or linked

Hawk02-E@1#prop:zero-energy

Vanishing source energy does not prove an information endpoint.

Proof. Take a source with vacuum $∣ 0 ⟩_{S}$ of energy zero, an inaccessible degenerate memory $E$ , and the isometry

V ∣ ψ ⟩ = ∣ 0 ⟩_{S} ∣ 0 ⟩_{R} ∣ ψ ⟩_{E} .

The source energy is zero, but $E$ stores the code.

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