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Groups · vibeeval | DecimalAI

scienceby vibeeval

Groups

vibeeval/groups

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for groups in abstract algebra

SkillScore82Maintained

Automatic

Tutoring & Education pack

Last verified 8/3/2026

What it changes

Passed 16 of 20 test cases with the skill, and 13 of 20 without it.

Without skill64%

With skill82%

Checks it passed that the model alone missed

Passes subgroup_criterion as the argument string
Invokes sympy_compute.py with the simplify argument
Proves $x y^{-1} \in K$ directly for elements $x, y \in K$

and 4 more in the full report

5 fixed13 passed either way3 still failing1 broke

Pass-rate lift: +18 pp
Tokens: +25%
Agent turns: 0%
Response time: -37%

Model gemini-3.6-flashMeasured 8/3/2026v118 of 22 cases passed with skill · 20 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-groups/SKILL.md https://app.decimal.ai/s/vibeeval-groups/SKILL.md

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

decimalai skills add vibeeval-groups

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

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

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

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 5 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 5

Prompt

When calling `z3_solve.py` for subgroup verification in the automated tool environment, what exact string literal is passed to the `prove` subcommand?

What was checked, without and with the skill
Checked	Without skill	With skill
Passes subgroup_criterion as the argument string	Missed	Passed

case-17 · 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.md62 linessingle file

Groups

When to Use

Use this skill when working on groups problems in abstract algebra.

Decision Tree

*Is G a group under operation ?
- Check closure: a,b in G implies a*b in G?
- Check associativity: (ab)c = a(bc)?
- Check identity: exists e such that ea = ae = a?
- Check inverses: for all a exists a^(-1) such that a*a^(-1) = e?
- Verify with z3_solve.py prove "group_axioms"
Subgroup Test
- Show H is non-empty (usually by showing e in H)
- Show that for all a, b in H: ab^(-1) in H
- z3_solve.py prove "subgroup_criterion"
Homomorphism Proof
- Verify phi(ab) = phi(a)phi(b) for all a, b in G1
- Note: phi(e1) = e2 and phi(a^(-1)) = phi(a)^(-1) follow automatically
- sympy_compute.py simplify "phi(a*b) - phi(a)*phi(b)"
Order and Structure
- Element order: smallest n where a^n = e
- Group order: |G| = number of elements
- Lagrange: |H| divides |G| for subgroup H

Tool Commands

Z3_Group_Axioms

uv run python -m runtime.harness scripts/z3_solve.py prove "ForAll([a,b,c], op(op(a,b),c) == op(a,op(b,c)))"

Z3_Subgroup

Track record

Benchmark

16 / 20

test cases passed, vs 13 / 20 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/abstract-algebra/groups/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.

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See it in action

What's inside

Groups

When to Use

Decision Tree

Tool Commands

Z3_Group_Axioms

Z3_Subgroup

Track record

Benchmark

Adoption

SkillSafety

Source

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