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An independently specified detector is applied to the observations available up to time t. The indicator records whether its criterion is satisfied, and t_D is the first time this happens. If no qualifying event is observed, t_D is missing or censored; it should not silently be recorded as time zero.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| D_t | Binary declaration marker |
| O_le_t | Observation history through t |
| t_D | First qualifying declaration time |
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2.2. Declaration as a measurable marker
The equality x=x is not a detector. In a time dependent description, xt=xt is compatible with xt+1≠xt. I treat declaration as an operation or observation that must be identified under a separate rule:
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.Exact original notation
{D}_{t}=1{D({O}_{\le t})=1}, {t}_{D}=inf{t:{D}_{t}=1}.Related builds
Sources & provenance
{D}_{t}=1{D({O}_{\le t})=1}, {t}_{D}=inf{t:{D}_{t}=1}.
{D}_{t}=1{D({O}_{\le t})=1}, {t}_{D}=inf{t:{D}_{t}=1}.
{D}_{t}=1{D({O}_{\le t})=1}, {t}_{D}=inf{t:{D}_{t}=1}.
{D}_{t}=1{D({O}_{\le t})=1}, {t}_{D}=inf{t:{D}_{t}=1}.