This randomized trial reveals coherence dynamics govern decision-making in structural optionality, indicating significant applicability across domains.
Structural optionality is defined as the form of capital whose value derives from measured substrate-level deformation rather than from stochastic volatility or market-implied uncertainty. This paper establishes the theoretical and formal foundations of structural optionality through the Scale-Free Coherence Framework (SCFL) and its primary instrument, the Standard Coherence Fidelity Layer (SCFL). The central claim is precise: SCFL is an upstream measurement framework that characterizes the coherence dynamics governing transitions between stochastic regimes, which Real Options Theory (ROT) assumes as exogenous inputs to optimal decision-making under uncertainty. ROT tells you how to value optionality. SCFL tells you when optionality exists. The paper formalizes the Precursor Window W_P = (T₀, T₁) as the maximal interval in which substrate degradation is active (dC/dt < 0), outcome-level stationarity holds (dO/dt ≈ 0), and coherence half-life compression is present (τ½(t) < τ½_baseline). This three-condition definition ties T₀ identification directly to τ½ behavior rather than qualitative early movement, and is empirically grounded in the ERCOT April 7–8, 2026 prospective validation event (τ½ = 3.36 hours, R² = 0.964, ΔT ≈ 7 hours). A formal crosswalk maps classical ROT constructs to SCFL analogues: the coherence field C(t) replaces the stochastic underlying asset; coherence deformation operators Δ1 and Δ2 replace volatility σ; the precursor window ΔT replaces time-to-expiration; and the recoverability corridor D(C(t)) > 0 replaces the exercise boundary. SCFL does not generate stochastic processes — it constrains the admissible regime space ΩC(t) in which those processes operate, detecting regime transitions in C(t) prior to distributional change in S(t). The Non-Reducibility Theorem establishes that if W_P ≠ ∅, then C(t) ∉ span{F(O(s))}s≤t for any measurable functional F — making SCFL irreducible to Early Warning Signal theory, network robustness frameworks, or dynamical systems models. The Domain-Invariance Axiom establishes that the existence of W_P is preserved under any invertible measurable embedding, grounding SCFL’s cross-domain applicability across infrastructure, finance, healthcare, supply chains, and government systems. Synthetic validation across three testbed system classes (flow-network, queue-based logistics, agent-based institutional) confirms domain-invariant precursor detection. The paper includes a full mathematical appendix (coherence field construction, operator definitions, stability analysis, Rupture-Corridor Lemma) and a literature positioning appendix (Non-Reducibility Theorem with corollaries against EWS, network robustness, and dynamical systems theory). This paper is part of the Upstream Coherence Measurement Stratum (UCMS) canon (128 confirmed Zenodo publications).
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Ronald Brogdon (2026) studied this question.
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