A paper introduces Transition Information Density (TID) and Positional Identity to describe the information recoverable from structured intermediate states between training endpoints. The authors ground these constructs in grapheme-color synesthesia and a four-condition training experiment across different representational mediums.
- Probes trained on structured interpolation at defined Positional Identities exhibit substantially lower intrinsic dimensionality than controls in Phonetic/Linguistic (3.33 vs. 10.81) and Semantic Description (4.59 vs. 8.67) mediums.
- Visual and cross-modal mediums do not show this effect, establishing a modality boundary condition.
- A fixed-N=50 comparison confirms that Positional Identity structure, not sample count, drives the effect.
- Resolution N scales monotonically with representational richness.
The paper contributes a formal definition of TID and Positional Identity, a nine-metric shape characterization framework, and an experimental design isolating trajectory structure as distinct factors.