closedFramework_alone_insufficient_for_bridge
plain-language theorem explainer
A closed observable framework with positive observables and transition map fails to force either a constant inter-level ratio or the additive recurrence on initial iterates. Workers closing the T5 to T6 gap cite this to show why zero-parameter and locality axioms must be added. The proof is a direct one-line appeal to the combined obstruction theorem in the realization layer.
Claim. There exists a closed observable framework $F$ (state space $S$, transition $T:S→S$, positive observable $r:S→ℝ$) and base state such that the ratio $r(T^{k+2} base)/r(T^{k+1} base)$ is not constant in $k$, and $r(T^2 base) ≠ r(T^1 base) + r(base)$.
background
The module derives the Fibonacci recurrence from primitive ledger axioms to close the T5→T6 gap: T5 fixes the cost functional J as Jcost while T6 forces φ by self-similarity. ClosedObservableFramework supplies a structure with positive observable r, transition T, and closure (no external input, countable states, no continuous moduli). The upstream obstruction theorem closedFramework_does_not_force_realizedHierarchy_fields supplies the concrete existence claim that both the constant-ratio and additive-recurrence fields can fail inside this structure.
proof idea
The proof is a one-line wrapper that applies the obstruction theorem closedFramework_does_not_force_realizedHierarchy_fields from HierarchyRealizationObstruction.
why it matters
The result shows why the primitive closed framework alone cannot reach the hierarchy fields needed for the internal T5-T6 bridge; it therefore motivates the zero-parameter forcing, locality, and minimality steps that derive L_{k+2}=L_{k+1}+L_k and hence σ=φ. It sits immediately before the module's main bridge theorems (bridge_T5_T6, hierarchy_dynamics_forces_phi) and underscores that J-uniqueness plus self-similarity require the additional multilevel composition structure.
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