← TCDC: Target–Condition Dual Closure and Chen-Type Pressure / TCDC-01 · The failure transport polytope

TCDC: Target–Condition Dual Closure and Chen-Type Pressure TCDC-01 · The failure transport polytope Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)

The Prime-Square Target and the Failure Fixed-Surface Construction: the Root-Bounded Prime Terminal Domain, the Goldbach Failure Transport Polytope, Capacity Deficits and Cut Certificates

For a fixed 2m, recasts Goldbach failure as a finite symmetric integer transport feasibility problem on cube-root-rough survivor states (the exact identity M_PP = n_P − n_SP + M_SS; coarse, mixed-capacity and subset-cut deficit certificates; an LP relaxation), so any positive deficit certificate gives M_PP > 0, but no uniform positive deficit is shown.

The exact reduction that all later papers cite. The paper: 'what this round establishes is not a Goldbach proof'; it ends with NO UNIFORM POSITIVE DEFICIT YET; GOLDBACH STILL OPEN. 'Prime-square' means the root-bounded divisibility test r² ≤ x, not squares of primes; 'closure' in this series names the target of an emptiness certificate for the failure surface, not an achieved result.

Connections · Connections

PreviousTCDC-00 · The methodology · The Target–Condition Dual Closure Methodology: First Reverse-Solve the Conditions Under Which a Target Holds, Then Separately Establish Existence, Branches, Basins and Structural Closure

NextTCDC-04 · The Chen-type architecture and the cube-root barrier · High-Suffix P₂ Pressure and Chen-Type Weighting: the Pressure Scale Corrected to m/log³ m, the Exact Prime/Semiprime Split and the Cube-Root Linear-Sieve Barrier

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.

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