docs: the logo, the favicon, and the page that explains them (Phase K)

[ocots]

What

The site had no logo and no favicon — DocumenterVitepress warned about both on every build. This adds them, and a page that explains what the logo actually is: an optimal control problem.

The OptimalControl.jl logo is an energy-minimal low-thrust orbit transfer — a spacecraft spiralling from a low circular orbit out to a higher one under continuous weak thrust. Solved once and rotated by ±120°, the three trajectories' departure points land as the three dots of the Julia logo, winding onto the outer orbit around the central body.

Commits

1. Assets + deps — logo.png (1200×1200, copied verbatim from .extras/logos/logo-gagnant/) and favicon.ico (multi-resolution, derived). CairoMakie + Colors join docs/Project.toml, pinned 0.15 / 0.13 to match the CT*Makie extensions' own compat. docs/src/assets/{Manifest,Project}.toml regenerated in the same commit per the standing rule.

2. The page — examples/logo.md, one linear executed @example session:

   • the transfer OCP in @def (normalised two-body dynamics, three insertion conditions, ∫‖u‖² → min)
   • a warm-started solve + the insertion residuals
   • Makie.plot(sol) — the docs' first page to use the Makie plotting backend
   • the (x₁, x₂) spiral
   • the ±120° rotation into the finished figure, which matches the committed logo.png
   • a pointer to .extras/logos/logo-gagnant/ for the exact asset script

   No Transfer/Layout structs, no trait dispatch — the generator in .extras stays the reference render; the page is a worked example, not a script.

Decision recorded

CairoMakie in the docs env (decision B in .reports/campaign/K-logo.md): the page runs the real thing and generates the published asset, at the cost of ~a few hundred MB and ~4 min of CI precompile. This is the docs' first Makie usage — ahead of the dedicated Makie-doc phase, but self-contained and not in conflict.

Verification

Full julia --project=. docs/make.jl:

• exit 0
• 0 Cannot resolve @ref
• the two DocumenterVitepress: No logo.png / No favicon.ico warnings gone
• the in-page generated logo matches docs/src/assets/logo.png
• only build errors are the 4 unchanged Phase-D @extref upstream-backlog items

Add the run documentation label to build the site in CI.

🤖 Generated with Claude Code

[ocots]

Suite au retrait de favicon.ico avant merge : docs/src/examples/logo.md:171-172 dit encore que la figure est utilisée « downscaled, as its favicon », ce qui n'est plus vrai — le site garde le favicon DocumenterVitepress par défaut.

Correction en une ligne (retirer la clause « and, downscaled, as its favicon »), à traiter dans une petite PR de suivi ou à plier dans E6 (suppression de docs/attic/).

[ocots]

Corrigé directement sur main : 185a54f (clause « downscaled, as its favicon » retirée).