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

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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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TreceiptT_{\rm receipt}

Symbol T_rm receipt

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

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δ\delta

Symbol delta

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

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IirrI_{\rm irr}

Symbol I_rm irr

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

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Published contexts (1)

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

Equation 44 · Evolutionary Physics

How Fast Can a Horizon Learn Which Path You Took?

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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.

Meanings in this article

  • tct_c: the become irrevocable at an intermediate cutoff.
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