feat(api): a solve or a sweep asked for outputs={'slack'} reads how far each constraint is from binding

[FBumann]

Prompt: Then, we can continue with slack

…the second item of a plan whose text was: "Slack: nearly free. It's right-hand side minus row activity, and you already read activity."

Note

The following content was generated by AI.

outputs={'slack'} makes a solve or a sweep carry each constraint's distance to binding. It is non-negative wherever the row holds, however the row is written, and readable wherever the activity is.

What it is

• The value: rhs − lhs for <=, lhs − rhs for >=, and −|rhs − lhs| for ==, which holds only at zero. A binding row reads 0. A violated one, such as an incumbent inside the solver's tolerance, reads below 0 by how much.
• Why not plain rhs − activity, which the plan named and Gurobi's Slack is: that sign depends on which side the model writes a term on. x >= 1 and 1 <= x would read opposite signs. The distance to binding reads the same for both, and its sign answers "does the row hold?" on every comparator. For a <= row the two agree.
• How it is computed: from the activity the solver returns and the built model's right-hand sides (readback.slacks, one numpy pass over the rows). So it exists wherever the activity does, a mixed-integer incumbent included. No sink changes.
• An output under feat(api): every answer holds an optional output only when outputs= asks for it, and a sweep can hold the activity too #1865's rule, stacked on feat(api): a solve or a sweep asked for outputs={'reduced_cost'} reads each variable's reduced cost, with the same sign on every solver #1856: Result.slack, Sweep.slack, kind='slack' on the bridges, slack/<name>.parquet in a save, a spill and an archive, and a catalog row per constraint. No LAYOUT bump. After the stack's review simplification, the engine side is one case in Engine._output.

Verification

Gates: ruff check ., ruff format --check ., pyrefly check, the full suite (pytest -n auto, with HiGHS, Gurobi and Xpress installed), and zensical build --strict with the docs group installed.

After merging the simplified #1856, the branch was gated at f8489f2 with ruff check ., ruff format --check ., pyrefly check (0 errors), and the full suite with the dev group, Gurobi and Xpress installed: 5168 passed, 566 skipped, 1 xfailed. The docs build was not re-run.

tests/test_slack.py covers the following:

• A hand-derived optimum on every sink, with each row written three ways: variables on the left, variables on the right, constants moved across. All give the same slacks.
• An equality off its right-hand side, on either side, reading −0.5.
• A mixed-integer incumbent, which has a slack.
• A save that loads back.
• The refusal when not asked for.
• A sweep held, spilled and archived.

Mutation table: python -m tools.mutate for the first row, the rest by hand with its three precautions (a clean tree, git checkout -- to restore, __pycache__ dropped on both sides). Full suite each time.

guard	result
the slack is laid out per constraint (engine.py:324-330, re-taken at 8129926)	caught
<= reads rhs − lhs (by hand: → lhs − rhs)	caught (10 failed)
>= reads lhs − rhs (by hand: → rhs − lhs)	caught (10 failed)
== reads −|rhs − lhs| (by hand: → rhs − lhs)	caught (1 failed, the purpose-built residual test)

Tree clean after each run.

Deliberately not done

• No cross-check against each solver's native slack. The activity it is computed from is already the solver's own number, checked by test_activity.py, and the natives disagree on sign: Gurobi gives rhs − lhs on every comparator.
• No dual_ray output, which is still live-only. That is next, if wanted.

🤖 Generated with Claude Code

https://claude.ai/code/session_01GLBvwp6NU7YjszFz5QMRf1
https://claude.ai/code/session_01UFX6qbCYnXKTVkucgxEqfS

[codspeed]

Merging this PR will degrade performance by 5.47%

⚠️ Different runtime environments detected

Some benchmarks with significant performance changes were compared across different runtime environments,
which may affect the accuracy of the results.

Open the report in CodSpeed to investigate

❌ 1 regressed benchmark
✅ 66 untouched benchmarks
⏩ 307 skipped benchmarks¹

Warning

Please fix the performance issues or acknowledge them on CodSpeed.

Performance Changes

	Benchmark	BASE	HEAD	Efficiency
❌	test_window[commitment-s-specsolve-highs-one]	1.5 MB	1.6 MB	-5.47%

Tip

Investigate this regression by commenting @codspeedbot fix this regression on this PR, or directly use the CodSpeed MCP with your agent.

---

_{Comparing claude/festive-carson-8x46sq-slack (5b54514) with claude/festive-carson-8x46sq (2ce4c0e)}

Footnotes

1. 307 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩

[read-the-docs-community]

Documentation build overview

📚 specsolve | 🛠️ Build #35014822 | 📁 Comparing 5b54514 against latest (4a6a998)

  🔍 Preview build  

9 files changed · ± 9 modified

± Modified

• tables/index.html
• about/architecture/index.html
• about/changelog/index.html
• howto/archiving/index.html
• howto/debug/index.html
• reference/api/index.html
• reference/glossary/index.html
• reference/internals/index.html
• reference/sweeps/index.html