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Banach Spaces · vibeeval | DecimalAI

scienceby vibeeval

Banach Spaces

vibeeval/banach-spaces

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for banach spaces in functional analysis

SkillScore73Maintained

Automatic

Research pack

Last verified 8/4/2026

What it changes

Passed 15 of 21 test cases with the skill, and 11 of 21 without it.

Without skill55%

With skill73%

Checks it passed that the model alone missed

Invokes z3_solve.py with extension_exists
Runs sympy_compute.py simplify on the norm expression
Executes z3_solve.py prove with graph_closed implies T_bounded

and 1 more in the full report

4 fixed12 passed either way6 still failing0 broke

Pass-rate lift: +18 pp
Tokens: +8%
Agent turns: 0%
Response time: -38%

Model gemini-3.6-flashMeasured 8/4/2026v116 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-banach-spaces/SKILL.md https://app.decimal.ai/s/vibeeval-banach-spaces/SKILL.md

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

decimalai skills add vibeeval-banach-spaces

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

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

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

I am evaluating a linear combination norm expression norm(alpha*x + beta*y). What tool command simplifies this norm expression?

What was checked, without and with the skill
Checked	Without skill	With skill
Runs sympy_compute.py simplify on the norm expression	Missed	Passed

case-06 · 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.md69 linessingle file

Banach Spaces

When to Use

Use this skill when working on banach-spaces problems in functional analysis.

Decision Tree

Verify Banach space
- Complete normed vector space
- Check: every Cauchy sequence converges
- z3_solve.py prove "completeness"
Hahn-Banach Theorem
- Extend bounded linear functionals
- Separate convex sets
- z3_solve.py prove "extension_exists"
Open Mapping Theorem
- Surjective bounded operator between Banach spaces is open
- Consequence: bounded inverse exists
- z3_solve.py prove "open_mapping"
Closed Graph Theorem
- T: X -> Y has closed graph implies T bounded
- Strategy: verify graph closure, conclude boundedness
- z3_solve.py prove "closed_graph_implies_bounded"
Uniform Boundedness Principle
- Pointwise bounded family of operators is uniformly bounded
- Application: prove operator families are bounded

Tool Commands

Z3_Completeness

uv run python -m runtime.harness scripts/z3_solve.py prove "cauchy_sequence implies convergent"

Track record

Benchmark

15 / 21

test cases passed, vs 11 / 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/functional-analysis/banach-spaces/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

Banach Spaces

When to Use

Decision Tree

Tool Commands

Z3_Completeness

Track record

Benchmark

Adoption

SkillSafety

Source

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