AI 中文总结
研究计划任务与执行行动间分数信用分配问题，构建准线性费雪市场，通过市场工具得出相关定理，扩展市场考虑任务进度折扣，解决算法收敛问题，提出基准发现问题，用熵正则化泛化及规则解决，报告参数并讨论局限，关联相关算法。
AI 中文摘要
个人和组织规划系统中，计划（任务的努力预算）与实际完成情况（记录行动的持续时间和描述）的记录逐渐分离。现有系统用排他性的全有或全无链接来衔接，导致真正相关但未链接的努力被搁置，活跃目标出现虚假停滞。我们将其构建为准线性费雪市场，计划任务是预算受限的买家，执行行动是可分割商品，融合的文本/结构/时间信号设定每个买家的估值。通过两个市场工具得出守恒、硬预算上限和可证明的垃圾过滤定理。扩展市场时考虑任务接近计划时的凹完成效用折扣进度，通过满足阈值固定点解决算法收敛问题，并通过实验验证。提出去循环化、多种子基准，发现市场的尖锐零熵均衡对亲和力噪声更敏感，通过单参数熵正则化泛化及噪声自适应规则解决。报告完整的可重复性参数，坦率讨论局限性，并将结果与多触点归因、最优传输和在线费雪市场算法相关联。
英文摘要
Personal and organizational planning systems maintain two records that drift apart: what was planned (a task's effort budget) and what was done (a logged action's duration and description). Existing systems bridge them with an exclusive, all-or-nothing link that strands genuinely related but unlinked effort and reports false stalls on active goals. We formulate the bridge as a quasi-linear Fisher market: planned tasks are budget-constrained buyers, performed actions are divisible goods, and a fused text/structural/temporal signal sets each buyer's valuation. Two market instruments - a seller reserve price and a buyer cash option - yield conservation, a hard budget cap, and a provable junk filter as theorems. We extend the market with a concave completion utility discounting progress as a task nears its plan; standard convergence theory for the market's algorithm does not transfer here, resolved by a satiation-threshold fixed point with existence (Brouwer) and local uniqueness under an explicit diagonal-dominance condition, validated empirically on random and adversarial instances. A de-circularized, multi-seed benchmark - observed affinity corrupted independently of the scored ground truth - surfaces a genuine weak spot: the market's sharp, zero-entropy equilibrium is more sensitive to affinity noise than entropy-regularized optimal transport's permanently smoothed one. We resolve this with a one-parameter entropy-regularized generalization unifying the two, plus a noise-adaptive rule for its regularization strength. We report full reproducibility parameters, discuss limitations candidly, and relate the result to multi-touch attribution, optimal transport, and online Fisher-market algorithms.
Comments35 pages, 3 figures. Companion technical report with extended treatment of dynamic/forward-looking markets and reinforcement-learning extensions available separately
