CRITICAL WINDOW: ACTUAL SAVED OUTPUT

Seed 20260908; 400 independent samples per displayed point.
PASS: U_5=62, R_5=196; 36 food gateways, of which 32 enlarge closure.
PASS: all 64 small-example matrices give equal history polynomials.
PASS: exact literal witnesses, failed-support example and food-only RAF.
PASS: append-then-split produces target 101 using four fresh reactions.
PASS: common-mark RAF monotonicity and nested static escape events.
PASS: static barrier: 53 barrier successes, 282 RAFs; zero implication violations in 400 samples.
PASS: exact positive-bound condition at a=1/2: k=458, L=4580.
Paper-backed lower bound: Theta(ln 2) >= 2^(-((4580-2)*2^(4580+1)+5)) > 0.
Paper-backed upper bound: Theta(ln 2) <= 1 - 2^(-36) < 1.

FINITE RAF FREQUENCIES (95% pointwise Wilson intervals)
n= 4, lambda=0.1: 317/400 = 0.7925 [0.7501, 0.8294]
n= 4, lambda=0.5: 400/400 = 1.0000 [0.9905, 1.0000]
n= 4, lambda=1: 400/400 = 1.0000 [0.9905, 1.0000]
n= 6, lambda=0.1: 103/400 = 0.2575 [0.2171, 0.3025]
n= 6, lambda=0.5: 400/400 = 1.0000 [0.9905, 1.0000]
n= 6, lambda=1: 400/400 = 1.0000 [0.9905, 1.0000]
n= 8, lambda=0.1: 24/400 = 0.0600 [0.0406, 0.0877]
n= 8, lambda=0.5: 400/400 = 1.0000 [0.9905, 1.0000]
n= 8, lambda=1: 400/400 = 1.0000 [0.9905, 1.0000]
n=10, lambda=0.1: 5/400 = 0.0125 [0.0054, 0.0289]
n=10, lambda=0.5: 400/400 = 1.0000 [0.9905, 1.0000]
n=10, lambda=1: 400/400 = 1.0000 [0.9905, 1.0000]

INDEPENDENT FINITE IMPLEMENTATION COMPARISON (n=6, lambda=0.2)
literal catalysis: 276/400, 95% interval [0.6430, 0.7333]
cardinality replacement: 257/400, 95% interval [0.5944, 0.6879]

Static escape frequencies estimate upper approximations to S(a), not S(a) itself.
The paper proves the infinite-size statements. This run did not compile Lean.