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We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In particular, we prove the best known lower bound for TSP with bounded metrics for the metric bound equal to 4.arXiv:1201.5821v2 fatcat:jq2orj3ky5cmzi4xvclg4p5wkq