Large Language Models (LLMs) often struggle with temporally grounded reasoning because their static parametric memory is misaligned with the dynamic evolution of real-world knowledge. Although RAG and Parameter-Efficient Fine-Tuning (PEFT) provide practical ways to enhance LLMs, they remain insufficient for temporal reasoning. Existing retrieval methods typically prioritize semantic relevance while overlooking temporal validity, event order, and evolutionary dependencies, resulting in evidence that is relevant in isolation but temporally fragmented. Meanwhile, conventional PEFT methods usually employ fixed and input-agnostic low-rank updates, making it difficult to capture time-dependent entity semantics and relation drift. To address these limitations, we propose Temporal Evidence-Parameter Co-Alignment (TEPCA), a framework for LLM reasoning over TKGs. TEPCA aligns LLM reasoning with temporal knowledge at both the evidence and parameter levels. At the evidence level, it introduces time-constrained Dynamic Relevance-Guided Path (DRGP) pruning to preserve globally coherent temporal paths, together with Mutual-Information (MI)-based pruning to retain query-informative local facts under temporal constraints. At the parameter level, it integrates Dynamic-Gated LoRA (DG-LoRA), a timestamp-conditioned low-rank adaptation mechanism that dynamically modulates the effective adaptation subspace according to temporal context. This design enables LLMs to better capture fine-grained entity evolution and time-dependent relation semantics while preserving parameter efficiency. Experimental results on two TKG benchmarks demonstrate that TEPCA achieves state-of-the-art performance. Additional evaluations of DG-LoRA on eight commonsense QA datasets further verify its general input-adaptive capacity, scalability across LLM backbones, and interpretability.

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