Read the equation
This version compares zₜ with the current reference rₜ and separately with r at declaration time. The fixed-reference distance can remain large even when the current representation accurately tracks the current reference. The later manuscript revises the event-time design, so this earlier baseline definition should retain its own date and version.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| delta_t | Current-reference distance |
| b_t | Distance from declaration-time reference |
| t_D | Declaration time |
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
Let rt=ρSt be an independently measured reference relevant to a task. Let zt=HSt be an internally maintained estimate or report. Both must be mapped into a common comparison space before a distance is meaningful. A physical robot and a sentence describing that robot are different types of objects; their raw inequality is not evidence of an error. A hand-position estimate and a measured hand position, by contrast, can be compared in the same coordinates.
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}.Exact original notation
{\delta }_{t}=d\left({z}_{t},{r}_{t}\right), {b}_{t}=d\left({z}_{t},{r}_{{t}_{D}}\right).Related builds
Sources & provenance
{\delta }_{t}=d\left({z}_{t},{r}_{t}\right), {b}_{t}=d\left({z}_{t},{r}_{{t}_{D}}\right).
{\delta }_{t}=d\left({z}_{t},{r}_{t}\right), {b}_{t}=d\left({z}_{t},{r}_{{t}_{D}}\right).
{\delta }_{t}=d\left({z}_{t},{r}_{t}\right), {b}_{t}=d\left({z}_{t},{r}_{{t}_{D}}\right).
{\delta }_{t}=d\left({z}_{t},{r}_{t}\right), {b}_{t}=d\left({z}_{t},{r}_{{t}_{D}}\right).