A tier is a Closed view of the micro-state below: Closed v T ≔ ∃ h, v ∘ T = h ∘ v.
Failure has a normal form: a view fails closure if and only if there exist micro-states it cannot distinguish that the motion sends to distinguishable coarse readings (a witness pair).
The quantum-classical bridge is the retract: classical basis states embed diagonally, and Born readout is closed under classical operations. Coherence is the exact boundary where the classical tier ends:
diag_not_closed_under_coherence proves why superposition requires stratified quantum carriers.
A signed aggregate amplifies per-term perturbations by condition number κ = 1 / coherence.
During thermalization, signed momentum charts exhibit coherence decay (e.g. 0.998 → 0.125), while non-negative charts remain exactly 1.0.
Structure retention under decay rate λ and dose q converges to fixed point
G∞ = q / ((1 - λ) + q·λ). Maintaining autonomous composite holons against kinetic noise requires active work flow W*.