TCDC: Target–Condition Dual Closure and Chen-Type Pressure
TCDC-17 · The bad-mass simplex
Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)
The Bad-Mass Simplex and the Semiprime-Marginal Upper Constant: Even at the Best Distribution Level the Standard Fixed-Row Linear Upper Has a Semiprime Marginal Multiplier of About 2.0439
Normalizes the identity into a bad-mass simplex (M_PP/S = 1 − a − b) and shows, inside the heuristic rank-one benchmark, that the best fixed-row standard linear semiprime upper bound has multiplier about 2.0439 (cost 0.8367), so with an ideal mixed upper bound the bad mass is 1.0785 > 1 and at least 7.85% coupled recovery or an aggregate/switching provider is needed.
Clean geometry (the bad-mass simplex) plus a no-go conditional on the heuristic rank-one benchmark; a finite exact audit for 3 ≤ m ≤ 5000 matches the tables of the paper row by row. Verdict: NO UNIFORM SIMPLEX GAP YET; GOLDBACH STILL OPEN.
The paper itself says that no extrapolation to m → ∞ is legal; 2.0439, 1.0785 and 7.85% hold only inside that benchmark. This paper and TCDC-15 and 16 are three coordinate systems for one identity (T13 of TCDC-17 proves the change of variables).