theta_coupling_stiffness
plain-language theorem explainer
The inequality supplies a quadratic lower bound on the reduced phase potential J̃(λ, δ) in terms of the product λ · dist_Z(δ). Researchers deriving the Global Co-Identity Constraint from the J-cost forcing chain cite it to control coupling stiffness near alignment. The proof is a direct one-line application of the Jtilde_stiffness_lb lemma.
Claim. $ (λ · dist_Z(δ))^2 / 2 ≤ J̃(λ, δ) $
background
The GCIC derivation module starts from the Recognition Science forcing chain (T5 J-uniqueness through T8 D=3) and extracts the Global Co-Identity Constraint with zero empirical axioms. J̃ is the reduced phase potential obtained from the J-cost functional after imposing ratio rigidity and compact phase Θ ∈ ℝ/ℤ. dist_Z(δ) is the defect distance on the phase variable δ, taken from the simplicial ledger and ledger-factorization structures upstream.
proof idea
The proof is a one-line wrapper that applies the lemma Jtilde_stiffness_lb to the parameters lam and δ.
why it matters
The bound closes the stiffness step between phase alignment minimization and the collective-cost theorems in the same module. It inherits directly from the J-cost structure in PhiForcingDerived and the ledger factorization in DAlembert, thereby linking T5 J-uniqueness to the GCIC statement. No open scaffolding remains at this node.
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