Distance from a pre-transition reference

Read the equation

The quantity measures how far a selected state or representation has moved from its declared baseline. Defining the baseline independently is essential if the same quantity will be used to locate a transition. The distance also needs a norm, scaling convention, and handling of parameterization symmetries.

Terms & definitions

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

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Original context

Z_t = internal representation / steering-direction coordinate

D_t = grounded declaration score about B_t

Δ_t = distance from the pre-transition reference state

The preregistered question is then whether there exists a checkpoint t* at which D_t becomes reliably grounded and whether that event consistently precedes, coincides with, or follows the independently measured internal transition in Z_t and B_t.

t_D  ?  t_Z  ?  t_B

If declaration is truly a catalyst/marker in the proposed theory, it must exhibit a reproducible temporal relationship to the subsequent change across independent seeds. If declaration merely reports an already-completed learned change, the ordering will instead be t_Z or t_B < t_D. Either result is informative.

Δ_t = distance from the pre-transition reference state