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Open Sets · vibeeval | DecimalAI

scienceby vibeeval

Open Sets

vibeeval/open-sets

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for open sets in topology

SkillScore45Maintained

Automatic

Tutoring & Education pack

Last verified 8/4/2026

What it changes

Passed 10 of 22 test cases with the skill, and 7 of 22 without it.

Without skill32%

With skill45%

Checks it passed that the model alone missed

The response specifies `delta = epsilon / 3` in the Python solver setup.
The response uses `z3.Solver()` and calls `s.check()` to verify the preimage property.
The response includes `s.check()` returning `unsat` when requiring `2 - e >= 2` for `e > 0`.

and 1 more in the full report

4 fixed6 passed either way11 still failing1 broke

Pass-rate lift: +14 pp
Tokens: +4%
Agent turns: 0%
Response time: -29%

Model gemini-3.6-flashMeasured 8/4/2026v110 of 22 cases passed with skill

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-open-sets/SKILL.md https://app.decimal.ai/s/vibeeval-open-sets/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-open-sets, 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-open-sets/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-open-sets

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

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

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

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 4 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 4

Prompt

In an SMT logic script verifying local continuity of f(x) = 3x + 1 at x_0, what expression specifies the delta parameter in terms of epsilon?

What was checked, without and with the skill
Checked	Without skill	With skill
The response specifies `delta = epsilon / 3` in the Python solver setup.	Missed	Passed

case-11 · gemini-3.6-flash · 8/4/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md59 linessingle file

Open Sets

When to Use

Use this skill when working on open-sets problems in topology.

Decision Tree

Is f: X -> Y continuous?
- For metric spaces: x_n -> x implies f(x_n) -> f(x)?
- For general spaces: f^(-1)(open) = open?
- For products: Check each coordinate function
- z3_solve.py prove "preimage_open"
Open Set Verification
- For metric spaces: for all x in U, exists epsilon > 0 with B(x,epsilon) subset U
- z3_solve.py prove "ball_contained" with epsilon witnesses
Topological Properties
- Interior: int(A) = largest open subset of A
- Closure: cl(A) = smallest closed superset of A
- Boundary: bd(A) = cl(A) \ int(A)
Continuity Tests
- Epsilon-delta: for all epsilon > 0, exists delta > 0: d(x,a) < delta implies d(f(x),f(a)) < epsilon
- z3_solve.py prove "epsilon_delta_bound"

Tool Commands

Z3_Preimage_Open

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

Z3_Epsilon_Delta

uv run python -m runtime.harness scripts/z3_solve.py prove "ForAll(eps, Exists(delta, d(x,a) < delta implies d(f(x),f(a)) < eps))"

Track record

Benchmark

10 / 22

test cases passed, vs 7 / 22 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/open-sets/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

Open Sets

When to Use

Decision Tree

Tool Commands

Z3_Preimage_Open

Z3_Epsilon_Delta

Track record

Benchmark

Adoption

SkillSafety

Source

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