Ready to supercharge your AI agents?

Install any skill in seconds. Free to start, no credit card required.

Get Started Free →

Compactness · vibeeval | DecimalAI

scienceby vibeeval

Compactness

vibeeval/compactness

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for compactness in topology

SkillScore91Maintained

Automatic

Tutoring & Education pack

Last verified 8/3/2026

What it changes

Passed 19 of 21 test cases with the skill, and 13 of 21 without it.

Without skill64%

With skill91%

Checks it passed that the model alone missed

Includes scripts/sympy_compute.py limit with --at oo.
Specifies scripts/z3_solve.py prove "bounded_and_closed".
Specifies scripts/sympy_compute.py limit "a_n" --var n --at oo.

and 2 more in the full report

6 fixed14 passed either way2 still failing0 broke

Pass-rate lift: +27 pp
Tokens: +19%
Agent turns: 0%
Response time: -25%

Model gemini-3.6-flashMeasured 8/3/2026v120 of 22 cases passed with skill · 21 comparable

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-compactness/SKILL.md https://app.decimal.ai/s/vibeeval-compactness/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-compactness, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-compactness/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-compactness

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-compactness/SKILL.md https://app.decimal.ai/s/vibeeval-compactness/SKILL.md

Raw file: /s/vibeeval-compactness/SKILL.md ↗ · machine-readable summary at /s/vibeeval-compactness.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 6 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 6

Prompt

To test sequential compactness for $b_n = 1 - \frac{1}{n}$, I need to evaluate the limit at infinity using the project's SymPy harness. What command line string performs this calculation?

What was checked, without and with the skill
Checked	Without skill	With skill
Includes scripts/sympy_compute.py limit with --at oo.	Missed	Passed

case-16 · gemini-3.6-flash · 8/3/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md60 linessingle file

Compactness

When to Use

Use this skill when working on compactness problems in topology.

Decision Tree

Is X compact?
- If X subset R^n: Is X closed AND bounded? (Heine-Borel)
- If X is metric: Does every sequence have convergent subsequence?
- General: Does every open cover have finite subcover?
- z3_solve.py prove "bounded_and_closed"
Compactness Tests
- Heine-Borel (R^n): closed + bounded = compact
- Sequential: every sequence has convergent subsequence
- sympy_compute.py limit "a_n" --var n to check convergence
Product Spaces
- Tychonoff: product of compact spaces is compact
- Finite products preserve compactness directly
Consequences of Compactness
- Continuous image of compact is compact
- Continuous real function on compact attains max/min
- sympy_compute.py maximum "f(x)" --var x --domain "[a,b]"

Tool Commands

Z3_Bounded_Closed

uv run python -m runtime.harness scripts/z3_solve.py prove "bounded_and_closed"

Sympy_Limit

uv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at oo

Track record

Benchmark

19 / 21

test cases passed, vs 13 / 21 without

Adoption

Users: 0
Times used: 0

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/topology/compactness/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

More skills from the same source and nearby in the registry, with their headline benchmark lift.

Ready to supercharge your AI agents?

See it in action

What's inside

Compactness

When to Use

Decision Tree

Tool Commands

Z3_Bounded_Closed

Sympy_Limit

Track record

Benchmark

Adoption

SkillSafety

Source

Related skills