Read the equation
If d is a true metric, distance zero means the two compared representations are equal in the chosen measurement space. It does not require the entire underlying states to be identical when the extraction maps lose information. For a pseudometric, even distinct representations can have zero distance.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| delta_t | Current-reference discrepancy |
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
Define current-reference discrepancy and origin displacement separately:
δt=dzt,rt, bt=dzt,rtD.
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.Exact original notation
{\delta }_{t}=0