Meaning
A thin dynamical packet collects a closed excitation form, its operator, its exact ground, and a positive lower bound before invariant spectral identification.
The packet is (q,K,H_thin,P_Ω,κ,Π_thin). The form q is densely defined, closed, and nonnegative; K is its associated self-adjoint operator; H_thin=K^(1/2); Ran P_Ω=ker K; and K≥κ(I−P_Ω) with κ>0. The provenance entry identifies the physical construction to which these data belong.
Example (illustrative)
For K=diag(0,4,9), H_thin=diag(0,2,3), P_Ω=diag(1,0,0), and κ=4 give an elementary packet. Notice that the floor 4 belongs to K; the corresponding floor of its square root is 2.
Scope and limits
The packet precedes the identification with a covariant energy–momentum spectral system. It is not already an invariant mass-gap conclusion.
Source
GAT V — Invariant Spectral Transfer. GAT V, Definition 4.1.