Why it is a question
A6 §2: “Suppose the interaction structure varies with a parameter θ: A = A(θ). A collective may become sharply distinguishable when an eigengap opens, and cease to be robustly identifiable when that gap closes. This is not automatically a dynamical bifurcation. It is a structural or identifiability transition.” It asked when the two coincide, and: “Their divergence may be just as revealing as their coincidence. A coalition might undergo a major change in behavior while preserving its internal organization. Conversely, a structural boundary could change while observed collective behavior remains almost identical.”
The two are different events in one spectrum. CLAIM-157’s boundary is a gap in the interaction matrix, strong couplings inside the block and weak ones across its edge, clearing the Occam factor (δ/ε > τ), and the form “lasts as long as that block persists”. CLAIM-164 says what the gap makes definite: the block’s subspace, and a single direction only when its own gap is wide. A bifurcation is an eigenvalue crossing the stability boundary, as in CLAIM-330, where the leading eigenvalue of the meaning–authority map crosses +1 at βγ = (1 − α)(1 − δ). A gap can open far from any crossing, and a crossing can happen inside a block whose gap does not move.
The record already holds one dissociation. THEORY-265, as CLAIM-157 reads it: in a modular coordination game “the block verdict is the same before and after entrainment. What changes is timing”. That is a change of dynamical regime with the boundary unchanged. The other direction, a boundary that forms or dissolves with behaviour unchanged, has no case.
QUESTION-079 is the neighbouring question for an agent’s regimes: discrete switches between metastable states or continuous reorganization, and what then counts as a transition. If reorganization is continuous, a boundary may change with no bifurcation at all.
What would count as an answer
A parametrized family A(θ) with three regions, built or found: one where the block’s gap closes at the parameter value where a regime loses stability, one where the regime changes with the gap intact, and one where the gap closes with the regime and its observable behaviour intact. For each, a statement of which of regime identity, organizational individuality and observable function changed. A6’s caution applies to any answer: “attractor-basin membership is not numerical identity. Different individuals can occupy the same attractor, and one individual can cross between attractors.”