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QUESTION-241: In the coupled meaning–influence model linearized at its symmetric state, when is the symmetric state unstable, and does scoring endorsement independently of the interpretation remove the instability?

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Properties5
StatusAnswered
Tagsself-governance, complex-systems
Linedistributed-agency
RefinesQUESTION-100 — Beyond the linearization at symmetry, when does coupling interpretation-dependent retrieval to performance-dependent endorsement produce stable expertise, and when does it produce self-reinforcing interpretive capture?
Answered byCLAIM-330 — In the coupled meaning–influence model linearized at its symmetric state, with each field stable alone and nonnegative couplings, the coupling destabilizes symmetry exactly when βγ > (1 − α)(1 − δ): only the loop can do it, and the direction that grows mixes meaning and authority

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Answer

CLAIM-330 (Active, demonstrated), from the construction in CASE-099. For J = [[α, β], [γ, δ]] with nonnegative entries and α, δ < 1:

  • When. The leading eigenvalue exceeds 1 exactly when βγ > (1 − α)(1 − δ).
  • Only the loop. If either coupling is zero the eigenvalues are α and δ, so capture that starts at symmetry needs both arrows: authority shaping interpretation, and interpretation shaping endorsement.
  • Independent scoring. Scoring operators independently of the dominant interpretation (Regime B, γ ≈ 0) removes the coupling-driven instability, whatever the memory of endorsement.
  • What grows. The leading eigenvector, (β, λ+ − α), is positive in both components: a joint lean of meaning and authority.

CLAIM-340 adds that committing predictions before the evidence is not by itself Regime B. That is QUESTION-239.

What it leaves to QUESTION-100

The answer holds for the linearization at symmetry. CLAIM-330 does not say that CASE-092’s full model has this linearization, since the sign and size of γ in Regime A are assumptions about an unbuilt model. It says nothing about the bounded nonlinear system’s attractors or hysteresis, about whether capture costs fidelity, or about role-indexed endorsement.

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