Read the equation
O≤t denotes all observations available up to and including time t. A prospective detector may use this history but cannot use observations that arrive later. This restriction helps separate real-time detection from a retrospective explanation using the full record.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| O_le_t | Observation history through time t |
How it works
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Assumptions & limits
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Original context
Read the surrounding source passage
Dt=1{D(O≤t)=1}, tD=inf{t:Dt=1}.
(2.3)
The indicator 1 equals one when its condition holds and zero otherwise. The detector D uses the observable record O≤t available by time t. Its positive class and decision rule must be fixed before confirmatory outcomes are examined. A declaration may be a nonverbal state event rather than a sentence. The definition does not require human language, a familiar model name, or a claim that the machine is conscious. If no declaration is observed, its time remains unobserved rather than receiving a convenient numerical value.
Marker status and causal status are separate. A declaration might reveal an emerging organization without causing it. The stronger claim is that the declaration reenters processing and contributes to subsequent change. Prediction can support the marker claim. An intervention on the feedback channel is needed to assess the causal extension.
2.3. Independent onset, persistence, and detection delay
For tolerance ϵ≥0 and a window of W consecutive updates, let TW contain every candidate starting time for which the required measurements are available. Eligibility is determined without reference to declaration time. DefineExact original notation
{O}_{\le t}