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Operator Theory · vibeeval | DecimalAI

scienceby vibeeval

Operator Theory

vibeeval/operator-theory

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for operator theory in functional analysis

SkillScore95Maintained

Automatic

Research pack

Last verified 8/3/2026

What it changes

Passed 20 of 21 test cases with the skill, and 15 of 21 without it.

Without skill73%

With skill95%

Checks it passed that the model alone missed

Includes the --at oo flag in the command invocation
Prefixes commands with uv run python -m runtime.harness
Specifies sympy_compute.py simplify on the difference of inner products

and 2 more in the full report

5 fixed16 passed either way1 still failing0 broke

Pass-rate lift: +23 pp
Tokens: +14%
Agent turns: 0%
Response time: -35%

Model gemini-3.6-flashMeasured 8/3/2026v121 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-operator-theory/SKILL.md https://app.decimal.ai/s/vibeeval-operator-theory/SKILL.md

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

decimalai skills add vibeeval-operator-theory

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

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

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

When running sympy_compute.py to evaluate the limit of ||T - T_n|| for compact operator approximation, what argument flag specifies the limit destination point infinity?

What was checked, without and with the skill
Checked	Without skill	With skill
Includes the --at oo flag in the command invocation	Missed	Passed

case-18 · 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.md69 linessingle file

Operator Theory

When to Use

Use this skill when working on operator-theory problems in functional analysis.

Decision Tree

Bounded operator verification
- ||Tx|| <= M||x|| for some M
- Operator norm: ||T|| = sup{||Tx|| : ||x|| = 1}
- z3_solve.py prove "operator_bounded"
Adjoint operator
- <Tx, y> = <x, Ty> defines T
- For matrices: T* = conjugate transpose
- sympy_compute.py simplify "<Tx, y> - <x, T*y>"
Spectral Theory
- Spectrum: sigma(T) = {lambda : T - lambda*I not invertible}
- Self-adjoint: spectrum is real
- z3_solve.py prove "self_adjoint_real_spectrum"
Compact operators
- T compact if T(bounded set) has compact closure
- Approximable by finite-rank operators
- sympy_compute.py limit "||T - T_n||" --var n
Spectral Theorem
- Self-adjoint compact: T = sum(lambda_n * P_n)
- eigenvalues -> 0, eigenvectors form orthonormal basis

Tool Commands

Z3_Bounded_Operator

uv run python -m runtime.harness scripts/z3_solve.py prove "norm(Tx) <= M*norm(x)"

Track record

Benchmark

20 / 21

test cases passed, vs 15 / 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/operator-theory/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

Operator Theory

When to Use

Decision Tree

Tool Commands

Z3_Bounded_Operator

Track record

Benchmark

Adoption

SkillSafety

Source

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