Meaning
A vacuum lineage identifies complete ground sectors across changing carriers through certified, coherently composable comparisons.
At each stage, the vacuum is represented by the complete ground sector appropriate to that stage’s physical carrier. A lineage records why these stage-dependent representatives belong to one continuing vacuum structure: the prescribed retention or transport data connect them, and successive comparisons agree in the required sense. The identity is carried by those comparisons, not by writing the same vacuum symbol at every stage.
Example (illustrative)
As a finite illustration, let one carrier have ground space span(e₁,e₂) and another have ground space span(f₁,f₂). An explicitly certified comparison taking e₁ to f₁ and e₂ to f₂ can retain the whole ground sector. Choosing only e₁ and f₁ would leave part of that sector unaccounted for.
Scope and limits
This remains the archive’s source-audited summary, not a newly asserted formal definition from the release-gated GAT IV master. Lineage does not mean that operators on different carriers are globally equal, or that the ground is one-dimensional.
Source
GAT IV — Vacuum Lineage and Spectral Identification. GAT IV canonical identity verified; exact master remains release-gated.