docs: results — reading, plotting, and persisting a solution

[ocots]

Summary

Stacked on #866 (docs/solve, not yet merged) — base branch is docs/solve, not main, since PR 7 depends on PR 6 per the work board. Rebase onto main once #866 (and #865) merge.

Writes the three "Results" pages (docs/src/results/), replacing the PR-2 stubs: solution.md, plot.md, save-load.md (new page — this API was undocumented anywhere on the site before). This section is deliberately placed before Flows (PR 8): a Flow-produced trajectory is read and plotted with the exact same generics as a solve-returned Solution, so PR 8 can say "same as Results" instead of repeating this content.

• solution.md: the spec's own accessor list includes is_empty(sol), which doesn't exist — is_empty only accepts a TimeGridModel, confirmed live via MethodError. Used the real accessor, is_empty_time_grid(sol), instead. Dropped the "Solution struct" section (API-reference material) and the inline export_ocp_solution/import_ocp_solution note, now save-load.md's job.
• plot.md: ported the attic almost entirely (spec: "thorough and current"), with two real fixes found by executing every example for real:
  • CTModels.jl#392 (the VBox-plotting bug found in docs: modelling — describe an optimal control problem #865, hit once more in docs: solve — direct methods, choosing and configuring them #866) turns out to affect nearly every bare plot(sol) call in this specific attic file — triggered by an empty/default description regardless of styles or layout=. Fixed throughout with explicit :state/:costate/:control selectors or layout=:group, with one clear note near the top instead of repeating the caveat at every occurrence.
  • The flow-plotting section's saveat=fine_grid no longer works as a call-time keyword ((::OptimalControlFlow)(tspan, x0, p0; ...) only accepts variable/unsafe/augment now) — it moved to a construction-time option on Flow(...) itself, and needs a companion dense=false to avoid a SciML-level dense/saveat conflict. Rewrote the subsection around the working form, verified live (117 points vs. 19 on the default grid).
  • Trimmed the plotattr()/Plots.attributes() <details> blocks — generic Plots.jl mechanics, not OptimalControl API.
• save-load.md (new): every claim verified live — exact JLD2 round-trip, JSON3 round-trip (bit-exact in this run, phrased as "not guaranteed" in general since JSON floats aren't always exact), the real ExtensionError/IncorrectArgument messages, and that a reloaded solution works as an init= warm start identically to a fresh one. Also filed CTModels.jl#399 (feature request, not a bug): filename is documented as a base name with the extension always auto-appended, so filename="sol.jld2" writes sol.jld2.jld2 — confirmed reproducible, documented explicitly on the page with a warning rather than silently worked around.

Test plan

• julia --project=docs docs/make.jl — full rebuild, two iterations to clean: 0 undefined-binding/no-docs/duplicate-docs warnings, all three pages' @example blocks execute, 0 unresolved @refs from them.
• npx vitepress build on the Documenter output — site builds; spot-checked cross-links into docs: modelling — describe an optimal control problem #865's modelling-inspect and docs: solve — direct methods, choosing and configuring them #866's solve-initial-guess anchors resolve in the built HTML.
• test/suite/shape/test_shape_contract.jl — 27/27 passed (backs the scalar-control-shape claim on solution.md).
• typos — clean.
• docs/reports/07-results.md acceptance criteria re-checked against the real build (6/6 ticked, two extra findings recorded beyond the checklist).

🤖 Generated with Claude Code