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Language-guided UAV navigation has largely focused on long-horizon route planning, leaving short-range, object-relative flight maneuvers underexplored. To address this gap, we formulate Flying-on-a-Word (Flow), a task requiring a UAV to convert concise natural-language instruction, egocentric visual observation, and current state dynamics into continuous flight actions. Flow encompasses both primitive motion commands and complex object-interactive behaviors, assessing motion intent comprehension and spatial context grounding. To enable policy learning and closed-loop evaluation, we introduce UAV-Flow, a comprehensive dataset comprising 30,692 expert-piloted real-world trajectories across eight distinct motion categories, alongside 10,109 simulation trajectories in the UAV-Flow-Sim environment equipped with task-specific completion criteria. Furthermore, we develop FlowVLA, which undergoes imitation pretraining on mixed real-sim demonstrations and online post-training via Tail-Aware GRPO (TGRPO). By leveraging group reward distributions, TGRPO effectively reinforces high-reward action sequences. Evaluated on 273 held-out UAV-Flow-Sim episodes, pretrained FlowVLA achieves a mean success rate of 75.58%, outperforming the strongest baseline by 6.72 percentage points, which TGRPO post-training further elevates to 93.16% with superior sample efficiency. Physical UAV experiments demonstrate robust execution of object-relative commands in both indoor and outdoor real-world scenes. Together, Flow establishes a novel benchmark and learning framework for language-conditioned flight maneuvers.

Existing adaptive-reasoning methods shorten the explicit reasoning a model writes, or skip it by switching modes; either way the answer is still written out token by token. \emph{Rather than deciding how much to think}, we explore a different paradigm, \emph{zero-or-$T$ thinking}: a single model either answers from the implicit thinking inside one forward pass, generating no token, or performs full autoregressive reasoning at a cost of $T$ tokens when that is worth paying. We realise it in a \emph{hybrid decision model} (HDM), where one frozen backbone serves both modes and a lightweight \emph{self-routing block} chooses between them. The block estimates the \emph{value of thinking}, the utility the slow mode is expected to add over the fast one, from what that implicit thinking has already produced, and the slow mode runs only where that value exceeds a price $λ$ set per request. Where no per-decision label exists, as in episodic agentic tasks, we introduce \emph{Calibrated Decision Policy Optimisation} (CDPO), a reinforcement-learning recipe that trains the block from episode-level returns. We evaluate HDM on MMLU-Pro, AGIEval, GPQA-Diamond, JevBench, BANKING77 and MiniWoB. Specifically, on JevBench HDM-4B scores $0.857$ against Jev's $0.851$ ($+0.7\%$) at a median $0.179$\,s against $0.652$ ($-72.5\%$). On the agentic venue MiniWoB HDM-27B cuts token cost by $80.1\%$.

Financial backtests of large language models (LLMs) are meaningful only if the model did not already know the outcomes it is asked to predict. Practitioners guard against this by trusting a vendor's stated knowledge cutoff, by asking the model what it knows, or by instructing it to answer as of a past date. To verify whether any of these safeguards can be trusted, we introduce FinDendro, a benchmark of 2,226 dated U.S. facts from 1999 to 2026, covering monthly macroeconomic series, month-end stock prices and Federal Reserve decisions. Each fact yields four prompts: a value question, Recall and Predict questions that pair each candidate value with a claim of knowing or guessing without a declared date, and a Predict question with a historical declared date. Controls for persistence and dominant outcomes keep chance accuracy near 0.27. Results show that for most frontier models, self-reports understate knowledge. GPT-5 answers 76% of controlled facts correctly but claims to know 38%, and answers 61% of the facts it says it does not know. Knowledge claims can persist beyond the measured knowledge boundary, by up to seven quarters, and a declared date removes most of the claims of prior knowledge while leaving accuracy unchanged. Backtests inside a model's training window therefore cannot be certified leak-free by self-report, instruction or stated cutoff. These findings motivate behavioral measurement of temporal knowledge boundaries, and FinDendro provides a benchmark and procedure for selecting backtest periods based on demonstrated factual knowledge.