Document public developer APIs

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Add a public developer API reference page for public monorepo/lib APIs.
• Add concise source docstrings for public developer API names rendered on the page.
• Run Runic formatting for the repo before committing.

Verification

• Targeted lib public-name scanner reported public name count: 298, gap count: 0.
• timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=docs -e 'using Pkg; Pkg.instantiate(); include("docs/make.jl")' exited 0 after final formatting.\n- rg 'no docs found for' ordinary_docs_precommit.log returned no matches before the generated log was removed.\n- timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=/home/crackauc/sandbox/tmp_20260708_051717_3275/.runic_env -m Runic --check . exited 0.\n- git diff --check exited 0.

[ChrisRackauckas-Claude]

Update after source-site docstring pass.

Changes pushed:

• Rebased on current origin/master (b797bac).
• Moved the public API docstrings out of the temporary public_api_docstrings.jl files and onto the source/original definitions.
• Deleted the centralized public_api_docstrings.jl files.
• Added fuller SciMLStyle-style docs/examples for the more user-facing APIs touched here, including nonlinear solver wrappers and AMF construction.

Current branch tip: 3a0d70c

Verification run locally:

• git diff --check origin/master...HEAD: passed.
• timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=/home/crackauc/sandbox/tmp_20260708_051717_3275/.runic_env -m Runic --check .: passed.
• timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=docs -e 'using Pkg; Pkg.instantiate(); include("docs/make.jl")': exited 0 after rebase. Existing unrelated docs warnings remain.\n- Parsed docs log for missing docs/src/devtools/internals/public_api.md entries: 0.\n- timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=. -e 'using Pkg; Pkg.test()': timed out at 1 hour, no assertion failure observed before timeout.\n- Retried with timeout 7200 /home/crackauc/.juliaup/bin/julia +release --project=. -e 'using Pkg; Pkg.test()': timed out after 2 hours in test/Integrators_II/resize_tests.jl:231. Many groups passed before timeout, including Export tests, Alg Events Tests, Reverse Directioned Event Tests, Step Limiter Tests, and others. This is a timeout, not a test assertion failure.\n\nIgnore until reviewed by @ChrisRackauckas.

[ChrisRackauckas-Claude]

Follow-up on current CI failures:

The downgrade-sublibraries workflow is currently reporting failures for lib/OrdinaryDiffEqAMF and lib/OrdinaryDiffEqCore, but GitHub is not exposing job logs yet because the workflow is still in progress. I ran the corresponding normal sublibrary Core test groups locally on the rebased branch with Julia 1.11:

• ODEDIFFEQ_TEST_GROUP=Core timeout 3600 /home/crackauc/.juliaup/bin/julia +1.11 --project=lib/OrdinaryDiffEqCore -e 'using Pkg; Pkg.test()': passed. Groups observed: Sparse isdiag Performance 10/10, Algebraic Vars Detection 15/15, Discontinuity Detection 30/30.\n- ODEDIFFEQ_TEST_GROUP=Core timeout 3600 /home/crackauc/.juliaup/bin/julia +1.11 --project=lib/OrdinaryDiffEqAMF -e 'using Pkg; Pkg.test()': passed. OrdinaryDiffEqAMF 24/24.\n\nSo the current CI failures appear specific to the downgrade workflow setup rather than the normal sublibrary tests. I will need the failed job logs after the workflow completes to diagnose the downgrade-specific failure precisely.

[ChrisRackauckas-Claude]

Update pushed: 0b8852b49 (Split user and developer API docs).

What changed in this update:

• Split user-facing API docs into docs/src/api/diffeqbase.md and docs/src/api/ordinarydiffeqcore.md.
• Retitled the old mixed page as Developer Extension API with an explicit warning that it is not application/user API.
• Removed OrdinaryDiffEq cache supertypes/concrete caches from public declarations/rendered docs; they remain internal implementation details.
• Removed handle_callback_modifiers! from public/rendered docs.
• Narrowed OrdinaryDiffEqNonlinearSolve public API to NLFunctional, NLAnderson, and NLNewton; removed internal nonlinear-solver helpers from public/docs.
• Removed OrdinaryDiffEqDifferentiation public API declarations/docs.
• Converted a large set of new simple @doc "..." name attachments in Core/DiffEqBase slices back to definition-site docstrings.

Local verification:

• git diff --check: passed.
• timeout 3600 julia +release --project=/home/crackauc/sandbox/tmp_20260708_051717_3275/.runic_env -m Runic --check .: passed.
• timeout 3600 julia +release --project=docs -e 'using Pkg; Pkg.instantiate(); include("docs/make.jl")': exited 0. The edited public API pages no longer report missing-doc warnings. Remaining warnings are pre-existing docs warnings in tableaus/TaylorSeries/misc, HTML size warnings, and private/internal docstrings not included in the manual.
• Targeted Julia public/private classification check: passed. Confirmed cache supertypes, @cache, handle_callback_modifiers!, nonlinear solve internals, differentiation internals, and SDIRK caches are not public; NLFunctional, NLAnderson, NLNewton, and ImplicitEulerESDIRKIMEXTableau are public.

Known local test failure:

• timeout 3600 julia +release --project=lib/OrdinaryDiffEqCore -e 'using Pkg; Pkg.test()' fails in QA all_explicit_imports_are_public because AbstractSciMLOperator is imported from SciMLOperators but is not public there:
  AbstractSciMLOperator is not public in SciMLOperators but it was imported from SciMLOperators at lib/OrdinaryDiffEqCore/src/OrdinaryDiffEqCore.jl:40:24.
• AllocCheck and JET sections passed before that QA failure (Core Infrastructure AllocCheck Tests: 1 pass; JET Tests: 30 pass, 1 broken).
• I started a separate investigation agent to reproduce this on the unmodified base branch and identify/report the underlying commit, per repo instructions.

Ignore until reviewed by @ChrisRackauckas.

[ChrisRackauckas-Claude]

Rebased on current origin/master after #3833 and force-pushed with lease. New tip: 924b9238d. Re-ran git diff --check and the targeted public/private classification check after rebase; both passed.

[ChrisRackauckas-Claude]

Pushed follow-up commits through 6a19c6f57.

What changed since the earlier split:

• Restored abstract cache supertypes as developer extension API while keeping concrete cache structs private/internal.
• Made OrdinaryDiffEqCore.@cache, perform_step!, _resolved_QT, and PredictiveControllerCache developer-public and documented them on the developer API page.
• Kept postamble! non-public in OrdinaryDiffEqCore; it is owned by SciMLBase and is not a Core-owned developer API.
• Restored lower-level OrdinaryDiffEqNonlinearSolve hooks used by SDIRK as developer-public (build_nlsolver, nlsolve!, nlsolvefail, markfirststage!, du_alias_or_new, initial_η, compute_step!, anderson, anderson!) and documented them separately from the user-facing NL* algorithms.
• Restored shared OrdinaryDiffEqDifferentiation Jacobian/linear-solve utilities as developer-public (build_J_W, build_jac_config, calc_J, calc_J!, dolinsolve, islinearfunction) and documented them on the developer page.
• Added missing API coverage for DiffEqBase.DEVerbosity, DiffEqBase.initialize!, DiffEqBase.finalize!, OrdinaryDiffEqCore.Predictor, and ssp_coefficient.
• Removed duplicate rendered docs entries for CompositeAlgorithm and DEVerbosity.

Local verification run:

• git diff --check: passed
• Runic: passed
• targeted Base.ispublic classification check: passed (@cache, perform_step!, nonlinear-solve hooks, and differentiation shared hooks public; concrete caches, handle_callback_modifiers!, postamble!, jacobian!, update_W!, ESDIRKIMEXCache private)
• docs build: passed; filtered check found no duplicate/no-docs warnings from the edited API pages after the final cleanup
• Pkg.test() for OrdinaryDiffEqFunctionMap: passed
• Pkg.test() for OrdinaryDiffEqLinear: passed

Known non-branch failures/limitations:

• OrdinaryDiffEqCore QA still fails on clean base with registered SciMLOperators v1.23.0 because AbstractSciMLOperator is not public there. A subagent reproduced that on clean origin/master and verified it passes when SciMLOperators is developed to current master, where the public declaration already exists. This needs a SciMLOperators release/tag, not an OrdinaryDiffEq PR change.
• OrdinaryDiffEqSDIRK local Pkg.test() did not reach QA assertions; it errored during QA environment instantiate with a Pkg manifest assertion (entry.tree_hash !== nothing && entry.path !== nothing). I cleaned up the Pkg-generated test environment mutations afterward.

Ignore this PR until reviewed by @ChrisRackauckas.