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Equation 44 · Part 1 · How Fast Can a Horizon Learn Which Path You Took?

Symbol T_rm receipt

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

What this part means

TrT_rm receipt is part of the quantity the equation computes from the expression on the right.

Its job in the formula

TrT_rm receipt is part of the quantity the equation computes from the expression on the right.

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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