Meaning
A finite AQFT probe seed organizes the finite data needed to ask algebraic quantum-field-theory questions.
AQFT means algebraic quantum field theory. This seed records regions, local algebras and inclusions, separation and generation statuses, finite dynamics, vacuum data, detector readout, Gauss–Ward information, and a slot for future cross-fiber transport. It makes these questions explicit at the finite stage.
Example (illustrative)
For two admitted regions O₁⊆O₂, the seed records the map A(O₁)→A(O₂) and its certification status. It separately records whether separated regions have commuting observables after physical reduction.
Scope and limits
A finite seed is not a net over all spacetime regions. It does not by itself prove covariance, the spectrum condition, Haag duality, or continuum reconstruction.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 8.8.