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Equation 44 · Part 3 · How Fast Can a Horizon Learn Which Path You Took?

Symbol t_c

Treceipt(δ)=inf⁡{tc:Iirr(tc)≥1−δ}.T_{\rm receipt}(\delta)= \inf\{t_c:I_{\rm irr}(t_c)\geq1-\delta\}.
tct_c

What this part means

the become irrevocable at an intermediate cutoff.

Its job in the formula

tct_c is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

It does not answer how much information has become irrevocable at an intermediate cutoff tct_c .

The passage around this formula

Finally, the proposed horizon receipt time is Treceipt(δ)=inf⁡{tc:Iirr(tc)≥1−δ}T_{\rm receipt}(\delta)= \inf\{t_c:I_{\rm irr}(t_c)\geq1-\delta\}. These are proposed definitions, not results from the 2025 optimization paper. They deliberately make admissible control part of the quantity. If A\mathcal A grants arbitrary global unitaries on the horizon, the record can become fictitiously erasable. If it permits only “do nothing,” receipt time collapses into an ordinary decay threshold. A physically useful answer must live between those caricatures.

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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

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