* Philippine peso dips after surprise rate cut * AI rally lifts emerging Asian stock markets * Thai equities rise on dovish central bank stance (Updates for afternoon trade) By Rishav Chatterjee Oct 9 (Reuters) – The Philippine peso weakened a shade while equities slid further after the central bank unexpectedly cut interest rates on Thursday, though stock markets elsewhere in emerging Asia rallied on renewed AI-related buying. The peso slid to 58.165 per dollar while the equity benchmark gauge, trading largely in the red through the day, slipped a few additional points after the Bangko Sentral ng Pilipinas (BSP) delivered a surprise quarter-point rate cut. This was the fourth consecutive easing by the central bank, which warned that the Philippine growth outlook had weakened, though infla

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