Simulated annealing (SA) and fixed-temperature Markov-chain Monte Carlo (MCMC) run the same Metropolis-Hastings kernel over a tempered objective, but the variants appear as separate monolithic drivers, so improving one ingredient requires rewriting and re-verifying a whole solver. The shared kernel becomes a typed algebra of five components (objective, cooling schedule, neighborhood, move kernel, and acceptance rule) whose four local composition laws the construction checks; a single Sampler<f64> step then runs any point of the algebra. A surrogate proposal, a fitted generalized-Langevin thermostat, a quasi-Monte Carlo polish, or a noise-aware acceptance rule is implemented once and becomes available to every classical, fast, generalized, Hamiltonian, or parallel-tempered driver that shares the interface. The same typing carries the correctness artifacts: SymPy-checked reductions of Generalized SA to its Boltzmann, fast, and Metropolis limits (the reductions surfaced a sign error that had stood in the visiting-distribution literature for three decades); a TLA+ specification model-checked for four safety and two liveness properties; and a three-channel finite-precision audit showing that fixing one channel of the acceptance path does not let float16 reproduce float64 basin selection. The implementation is the open-source Rust-and-Python package anneal, with an Array-API/DLPack device boundary and a portfolio optimizer whose only argument is a budget. On the CUTEst collection under a shared work-unit budget it reaches the best observed basin on more problems than a budget-matched CMA-ES restart heuristic, while carrying the almost-sure convergence and regret guarantees that heuristic lacks. Every reported number and figure regenerates from the reproducibility package with its pinned environment.

翻译：模拟退火（SA）与固定温度马尔可夫链蒙特卡洛（MCMC）通过同一Metropolis-Hastings核在调节目标函数上运行，但各变体表现为独立的整体驱动模块，因此改进某一组成部分需重写并重新验证整个求解器。该共享核构成五个分量（目标函数、冷却调度、邻域、移动核与接受准则）的类型化代数——其四条局部组合律由构造过程检验；单一`Sampler<f64>`步骤即可运行该代数中的任意点。代理提议分布、拟合广义朗之万恒温器、拟蒙特卡洛抛光或噪声感知接受准则一旦实现，即可供所有共享接口的经典、快速、广义、哈密顿或并行回火驱动模块使用。相同类型系统承载了正确性验证成果：通过SymPy检验的广义SA向玻尔兹曼、快速及Metropolis极限的约简（这些约简揭示了一个在访问分布文献中存续三十年的符号错误）；经TLA+规范模型检验的四个安全性属性与两个活性属性；以及三通道有限精度审计——该审计表明，固定接受路径中的一个通道无法让float16复现float64的盆地选择结果。其实现为开源Rust与Python软件包`anneal`，采用Array-API/DLPack设备边界，并包含一个以预算为唯一参数的组合优化器。在CUTEst测试集上，以共享工作单元预算对比时，该优化器在更多问题上达到观察最优盆地，优于预算匹配的CMA-ES重启启发式算法，同时承载了启发式方法所缺乏的几乎必然收敛性与遗憾保证。所有报告数值与图表均可通过固定环境的可复现包重新生成。