Mumbai, Jan. 29 -- Gold extended its record-breaking rally beyond $5,600 per ounce in electronic trade on Thursday, carving out fresh highs as persistent US dollar weakness and elevated economic and geopolitical risks reinforced haven demand. The metal has already advanced more than 30% in the opening month of the year, building on last year's explosive gains of over 60%, underpinned by fiscal concerns, aggressive central-bank buying, and steady ETF inflows. Momentum accelerated as the dollar index slipped below 96 and hovered near four-year lows, with markets parsing mixed signals from US policymakers over currency policy and the Federal Reserve's independence. Heightened geopolitical tensions, particularly fresh US warnings over Iran, fur...