[Metadata] Reference objectives per scheme, computed by a script

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@ocots 已经在做这个了。

开始于 2026年11月5日。

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描述

Agents: read the guide for agents in #310 first. Specification: this description, #306 and its comments.

Sub-issue of #306, part 1 of 5. Independent.

Scope

  • :reference_objective in the metadata: one entry per scheme at the default grid of the problem (value, source = :computed, grid_size, the configurations that converged and their objectives, their agreement, package versions); optionally an analytic value of the continuous problem with its source, shown as information only.
  • Computed entries are generated by scripts/reference_objectives.jl into one file per problem (ext/MetaData/references/<p>.toml), never edited by hand. Reference = best objective among the configurations of TestConfigs.CONFIGS that converged (tolerance 1e-8); a disagreement between configurations (local minima) is written and printed, not hidden.
  • Convergence report (#360): gap of each solve to the entry of its grid and scheme; no entry, no gap.
  • Consistency tests: type of the field; every :valid problem has a reference; comparison rule (a problem valid in one modeling only needs a reference).

Done when

  • Every problem has a computed trapezoid reference; the PR shows the agreement table.
  • A cron run shows the gap column filled.
  • READMEs say how to (re)compute the references.

Refs #306, #310

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  3. Fork 仓库，在一个分支上完成修改。
  4. 提交 Pull Request，并在描述里引用这个 Issue 编号。

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