continuity

Problem-solving strategies for continuity in real analysis

422 stars

Best use case

continuity is best used when you need a repeatable AI agent workflow instead of a one-off prompt.

Problem-solving strategies for continuity in real analysis

Teams using continuity should expect a more consistent output, faster repeated execution, less prompt rewriting.

When to use this skill

  • You want a reusable workflow that can be run more than once with consistent structure.

When not to use this skill

  • You only need a quick one-off answer and do not need a reusable workflow.
  • You cannot install or maintain the underlying files, dependencies, or repository context.

Installation

Claude Code / Cursor / Codex

$curl -o ~/.claude/skills/continuity/SKILL.md --create-dirs "https://raw.githubusercontent.com/vibeeval/vibecosystem/main/skills/math/real-analysis/continuity/SKILL.md"

Manual Installation

  1. Download SKILL.md from GitHub
  2. Place it in .claude/skills/continuity/SKILL.md inside your project
  3. Restart your AI agent — it will auto-discover the skill

How continuity Compares

Feature / AgentcontinuityStandard Approach
Platform SupportNot specifiedLimited / Varies
Context Awareness High Baseline
Installation ComplexityUnknownN/A

Frequently Asked Questions

What does this skill do?

Problem-solving strategies for continuity in real analysis

Where can I find the source code?

You can find the source code on GitHub using the link provided at the top of the page.

SKILL.md Source

# Continuity

## When to Use

Use this skill when working on continuity problems in real analysis.

## Decision Tree


1. **Check Definition**
   - f(a) exists (function defined at point)
   - lim_{x->a} f(x) exists
   - lim_{x->a} f(x) = f(a)

2. **Use SymPy for Limit Check**
   - `sympy_compute.py limit "f(x)" --var x --at a`
   - Compare with f(a)

3. **Piecewise Functions**
   - Check left and right limits separately
   - `sympy_compute.py limit "f(x)" --var x --at a --dir left`

4. **Verify with Z3**
   - `z3_solve.py prove "limit_exists implies continuous"`


## Tool Commands

### Sympy_Limit
```bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a
```

### Sympy_Limit_Left
```bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a --dir left
```

### Z3_Prove
```bash
uv run python -m runtime.harness scripts/z3_solve.py prove "continuous_at_a"
```

## Cognitive Tools Reference

See `.claude/skills/math-mode/SKILL.md` for full tool documentation.

Related Skills

continuity_ledger

422
from vibeeval/vibecosystem

Create or update continuity ledger for state preservation across clears

workflow-router

422
from vibeeval/vibecosystem

Goal-based workflow orchestration - routes tasks to specialist agents based on user goals

wiring

422
from vibeeval/vibecosystem

Wiring Verification

websocket-patterns

422
from vibeeval/vibecosystem

Connection management, room patterns, reconnection strategies, message buffering, and binary protocol design.

visual-verdict

422
from vibeeval/vibecosystem

Screenshot comparison QA for frontend development. Takes a screenshot of the current implementation, scores it across multiple visual dimensions, and returns a structured PASS/REVISE/FAIL verdict with concrete fixes. Use when implementing UI from a design reference or verifying visual correctness.

verification-loop

422
from vibeeval/vibecosystem

Comprehensive verification system covering build, types, lint, tests, security, and diff review before a PR.

vector-db-patterns

422
from vibeeval/vibecosystem

Embedding strategies, ANN algorithms, hybrid search, RAG chunking strategies, and reranking for semantic search and retrieval.

variant-analysis

422
from vibeeval/vibecosystem

Find similar vulnerabilities across a codebase after discovering one instance. Uses pattern matching, AST search, Semgrep/CodeQL queries, and manual tracing to propagate findings. Adapted from Trail of Bits. Use after finding a bug to check if the same pattern exists elsewhere.

validate-agent

422
from vibeeval/vibecosystem

Validation agent that validates plan tech choices against current best practices

tracing-patterns

422
from vibeeval/vibecosystem

OpenTelemetry setup, span context propagation, sampling strategies, Jaeger queries

tour

422
from vibeeval/vibecosystem

Friendly onboarding tour of Claude Code capabilities for users asking what it can do.

tldr-stats

422
from vibeeval/vibecosystem

Show full session token usage, costs, TLDR savings, and hook activity