Meaning
A substantive physical comparison is the actual continuation information retained after justified changes of certification and auxiliary presentation are removed.
GAT VIII distinguishes these comparisons, P_phys, by their role. They carry the physical passage between reconstruction data, including the retained structures and defects. Certificate and enhancement reductions must preserve their composition and declared higher comparisons.
Example (illustrative)
A passage that changes scale while retaining a marked physical sector and recording a seam residual contains substantive comparison information. Replacing the proof of that same passage does not remove the scale change or the residual.
Scope and limits
The three comparison classes are distinguished by function, not asserted to be disjoint sets. Intrinsic reduction is not permission to forget physical continuation data.
Source
GAT VIII — Indexed Admissible Distributors and Selected Cofinal Čech Transport in Semisimple Yang–Mills Theory. GAT VIII, Section 4–5.