Read the equation
This indicator equals one when the fixed detector says the observed history meets the registered declaration criterion. Reproducibility requires the detector, thresholds, and rules for repeated events to be specified. A first-person sentence by itself does not establish that the criterion is grounded in a measured property.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| D_t | Declaration indicator |
| O_le_t | Available observations through t |
How it works
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Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
Here tD is a candidate declaration time. A system can have bt>0 because it correctly tracks a changing reference while maintaining δt=0. This distinction prevents ordinary development or accurate adaptation from being classified as falsity solely because it differs from an earlier state.
A declaration is represented by an independently specified detector:
Dt=1{DO≤t meets a registered criterion}.
O≤t is the information available to the detector by time t. The detector cannot inspect later behavior and then retrospectively choose the statement that best predicts it. A nonverbal declaration is permitted in principle; an exact state operation, interface, or invariant would still need to define it. The acquired artifacts contain no such detector output.
2.3 Divergence and finite persistence
A measurable version of persistent discrepancy is:Exact original notation
{D}_{t}=1{D\left({O}_{\le t}\right) meets a registered criterion}.Related builds
Sources & provenance
{D}_{t}=1{D\left({O}_{\le t}\right) meets a registered criterion}.
{D}_{t}=1{D\left({O}_{\le t}\right) meets a registered criterion}.
{D}_{t}=1{D\left({O}_{\le t}\right) meets a registered criterion}.
{D}_{t}=1{D\left({O}_{\le t}\right) meets a registered criterion}.