TCDC: Target–Condition Dual Closure and Chen-Type Pressure
TCDC-18 · The harmonic level and the critical exponent
Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)
Aggregate Semiprime-Marginal Convolution and Level Lift: the Harmonic Distribution Level, the 0.641107 Critical Exponent, the 3/5 and 5/8 Benchmark Deficits, the Shell Portfolio Law and a Convolution-Provider Audit
Shows that an aggregate shell provider enters the linear-upper benchmark only through a weighted harmonic level θ_H (κ_SP = 2e^γ/(3θ_H)), derives the critical exponent θ_c = 0.641107 (above 5/8, below 2/3) and quantifies, under ideal neutral/mixed benchmarks, the coupled discount still needed at each level: 5.19% at 3/5, 2.99% at 66/107 and 1.95% at 5/8; no legal full-shell provider exists.
The single-layer 3/5, 66/107 and 5/8 linear-upper benchmarks are all insufficient without coupling, and no portfolio consisting only of shell levels ≤ 5/8 can cross without coupling. Verdict: NO UNIFORM LEVEL-LIFT CLOSURE YET; GOLDBACH STILL OPEN.
The status line says 5/8 'only needs' a coupled discount of about 1.954% and the conclusion speaks of a 'quantitatively small coupling regime': that figure is a floor under an ideal neutral lower bound, an ideal mixed upper bound and a heuristic rank-one benchmark, and must not be read as 'the problem is close'.