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TCDC-14 · The branch ratio and joint transfer
TCDC: Target–Condition Dual Closure and Chen-Type Pressure
TCDC-14 · The branch ratio and joint transfer
Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)
Bulk Mixed Deficiency and the Coarse-Balance Constant: the Cube-Root Buchstab Branch Constants, the Prime–Semiprime Bias and the Parity Barrier of Joint Transfer
Proves the one-variable cube-root rough ratio P₁ : P₂ = 1 : log 2 (p* = 0.5906, s* = 0.4094), states that transferring it to the joint Goldbach survivor (H01) would itself be an asymptotic, parity-sensitive theorem of Goldbach strength, and offers a heuristic rank-one Buchstab matrix benchmark plus a bulk prime-sink capacity route (multiplier ceiling 1/s* ≈ 2.4427).
The one-variable 1 : log 2 ratio is a classical asymptotic; the paper says plainly that transferring it to the joint survivor (H01) 'is itself an asymptotic theorem of Goldbach strength and cannot be treated as an ordinary sieve technicality'.
Verdict: NO JOINT BRANCH TRANSFER THEOREM; NO UNIFORM BULK CAPACITY GAP; GOLDBACH STILL OPEN. The rank-one Buchstab matrix is a heuristic benchmark inside which every later threshold of the series (TCDC-14 to 22) is priced.
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This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.