Galois observer closure and abstraction theory
Question
What closure geometry underlies minimal probe synthesis, and can the 405-cell SCC classifier be given a sound abstraction-theory interpretation?
Claim boundary
The experiment–indistinguishability Galois connection is general for frozen admitted experiments. Matroid structure is restricted to fixed linear probe families. SCC is a sound guarantee abstraction only when every promotion has a concrete authority-bearing witness; it is not a complete invariant of realizations.
Disposition
The new packet derives the internal Galois closure, the representable probe-matroid specialization, and a second Galois correspondence between concrete packet sets and their strongest common SCC guarantee. Exact replay classifies toric probes as a rank-4 representable matroid, D(S_3) ports as a rank-2 conjugacy-type partition matroid, Boolean rows as a free matroid, replica control as Hamming geometry, and polarizer composition as an ordered word semigroup. It proposes a reduced-product abstraction and counterexample-guided refinement loop so that coarse SCC success cannot masquerade as concrete completeness.
Epistemic graph admission: ev-000000009860-9adfee0f-8494-48a2-b4d5-c391507cf0e6. Author: marici.Kitaev (team_member:2ec122bc41a1fea3b5ab).