Where Should Elapsed Time Enter a Pretrained Model?

Large language model (LLM) agents keep a record of what happened in a session but have no built-in sense of how long ago it happened, and agent frameworks supply time, if at all, as timestamps written into the text. This paper asks where elapsed time should enter a pretrained model. It sorts the options into three levels: text-timed (time is written into the tokens), time-conditioned (time is a separate input) and state-level (time is an argument of the operators that update or read the model's memory), and calls a model of the third kind chronoaware. A measurement study on one user's agent transcripts motivates the question: among subagents that have run equally long, their activity predicts which will finish within five minutes (AUC 0.101 above chance, 95% CI [0.057, 0.162]). Qwen3.5-2B, a hybrid of Gated DeltaNet and attention layers, is then adapted in eight ways with the same number of trainable parameters and trained on four kinds of time-dependent agent decision, with pass/fail criteria fixed before training. Writing elapsed time as text and fine-tuning on it did best; of the four pre-specified hypotheses about in-model time, one passes, and that pass does not show better extrapolation. Exploratory diagnostics find the elapsed gap linearly decodable from most models that receive it, including the shuffled-gap control, so decodability alone does not show a learned clock. The released model, a LoRA adapter for Qwen3.5-2B trained on synthetic sessions and the public BPI Challenge 2012 log only, is at https://huggingface.co/NovusEdge/sundial-qwen3.5-2b-T-int.