market_arbitrage_gap
plain-language theorem explainer
The market arbitrage gap theorem states that J-cost is strictly positive for every positive real r not equal to 1. Financial modelers or non-equilibrium economists would cite it to treat arbitrage opportunities as recognition defects. The proof is a direct one-line application of the core positivity lemma for J-cost.
Claim. $forall r in mathbb{R}, (0 < r) to (r neq 1) to (0 < Jcost(r))$
background
The module develops C16, the cross-domain extension of J-cost positivity. It shows that the single lemma Jcost_pos_of_ne_one supplies non-equilibrium cost in every RS domain where J-cost applies, serving as the off-equilibrium analogue of the equilibrium result Jcost(1) = 0. Specializations include turbulent flow, disease deviation from homeostasis, off-target CRISPR effects, game theory, market arbitrage, biased reasoning, and recognition deficit; all reduce to the same proposition forall r, 0 < r to r neq 1 to 0 < Jcost r.
proof idea
The proof is a one-line term wrapper that applies the lemma Jcost_pos_of_ne_one from the Cost module directly to the parameters r, hr, and hne.
why it matters
This supplies the market-arbitrage instance to the universality certificate jPositivityUniversalityCert, which aggregates the domain specializations. It fills the structural claim that the same positivity source operates across all RS domains, extending the equilibrium result C7 to off-equilibrium costs. In the Recognition Science framework it aligns with J-uniqueness (T5) and the forcing chain that produces positive defect costs away from the fixed point.
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