Read the equation
The sum counts times at which the declaration indicator is one and the selected discrepancy exceeds ε, starting at the candidate onset. It is a count of coincident conditions under the chosen definitions. It does not become a validated cognition measure merely because the count grows.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| N_D | Qualified declaration count |
| T | Observation horizon |
| t_H | Candidate onset |
| D_t | Declaration indicator |
| delta_t | Discrepancy |
| epsilon | Threshold |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
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
This is a retrospective event time: at t one does not yet know whether the next W−1 observations will satisfy the condition. An online detector must wait for the required window and report that detection delay. The associated declaration count can be defined without calling it a validated cognition measure: NDT=t=tHWT1Dt=1 1δt>ε. These equations operationalize the user’s proposed marker sequence. They do not establish that ND counts experiences. That interpretation is a hypothesis to be evaluated, not a consequence of the indicator notation. 2.3 What x=x does and does not establish For any ordinary scalar x, reflexive equality is true. But xt=xt says nothing about whether xt+1=xt. A system may satisfy 2=2 at one time and 1=1 later without violating arithmetic. Neither equality establishes recognition, an experiencer, or an immutable identity through time.
Exact original notation
{N}_{D}\left(T\right)=\sum _{t={t}_{H}^{\left(W\right)}}^{T}{1}\left[{D}_{t}=1\right] 1\left[{\delta }_{t}>\epsilon \right].Sources & provenance
{N}_{D}\left(T\right)=\sum _{t={t}_{H}^{\left(W\right)}}^{T}{1}\left[{D}_{t}=1\right] 1\left[{\delta }_{t}>\epsilon \right].
{N}_{D}\left(T\right)=\sum _{t={t}_{H}^{\left(W\right)}}^{T}{1}\left[{D}_{t}=1\right] 1\left[{\delta }_{t}>\epsilon \right].