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Agent skill

Channel Capacity

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for channel capacity in information theory

MITAuto-check: notes

Install Channel Capacity

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill channel-capacity -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 channel-capacity --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/information-theory/channel-capacity .claude/skills/channel-capacity && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
channel-capacity
GitHub stars
3.9k
Used in
1 other repo
Token cost
~579 tokens
SKILL.md length
200 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for channel capacity in information theory

  • Works in 5 steps: Mutual Information → Channel Model → Channel Capacity → …
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
  • Calls uv

What it does

Channel Capacity is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for channel capacity in information theory

Its SKILL.md is about 580 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.

Example prompts

  • “/channel-capacity”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

5 steps, taken from the first numbered list in SKILL.md.

  1. Mutual Information
  2. Channel Model
  3. Channel Capacity
  4. Common Channels
  5. Blahut-Arimoto Algorithm

What it can do on your machine

Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Bash
    • Read

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Shell commands in SKILL.md call:

    • uv

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Channel Capacity loads about 579 tokens when it runs. Until then it costs about 22 tokens; SKILL.md has 200 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~22
When it runs · the whole SKILL.md, loaded when a task matches
~579

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check: notes

The automated check noted patterns worth knowing about, such as sudo or a known installer.

  • NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
    allowed-tools: Bash, Read

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 200 words, ~579 tokens.

Download SKILL.mdSave it as .claude/skills/channel-capacity/SKILL.md (or your agent's skills folder).
name
channel-capacity
description
Problem-solving strategies for channel capacity in information theory
allowed-tools
Bash, Read

Channel Capacity

When to Use

Use this skill when working on channel-capacity problems in information theory.

Decision Tree

  1. Mutual Information

    • I(X;Y) = H(X) + H(Y) - H(X,Y)
    • I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X)
    • Symmetric: I(X;Y) = I(Y;X)
    • scipy.stats.entropy(p) + scipy.stats.entropy(q) - joint_entropy

  2. Channel Model

    • Input X, output Y, channel P(Y|X)
    • Channel matrix: rows = inputs, columns = outputs
    • Element (i,j) = P(Y=j | X=i)

  3. Channel Capacity

    • C = max_{p(x)} I(X;Y)
    • Maximize over input distribution
    • Achieved by capacity-achieving distribution

  4. Common Channels

    ChannelCapacity
    Binary Symmetric (BSC)1 - H(p) where p = crossover prob
    Binary Erasure (BEC)1 - epsilon where epsilon = erasure prob
    AWGN0.5 * log2(1 + SNR)

  5. Blahut-Arimoto Algorithm

    • Iterative algorithm to compute capacity
    • Alternates between optimizing p(x) and p(y|x)
    • Converges to capacity
    • z3_solve.py prove "capacity_upper_bound"

Tool Commands

Scipy_Mutual_Info
bash
uv run python -c "from scipy.stats import entropy; p = [0.5, 0.5]; q = [0.6, 0.4]; H_X = entropy(p, base=2); H_Y = entropy(q, base=2); print('H(X)=', H_X, 'H(Y)=', H_Y)"
Sympy_Bsc_Capacity
bash
uv run python -m runtime.harness scripts/sympy_compute.py simplify "1 + p*log(p, 2) + (1-p)*log(1-p, 2)"
Z3_Capacity_Bound
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "I(X;Y) <= H(X)"

Key Techniques

From indexed textbooks:

  • [Elements of Information Theory] Elements of Information Theory -- Thomas M_ Cover & Joy A_ Thomas -- 2_, Auflage, New York, NY, 2012 -- Wiley-Interscience -- 9780470303153 -- 2fcfe3e8a16b3aeefeaf9429fcf9a513 -- Anna’s Archive. Using a randomly generated code, Shannon showed that one can send information at any rate below the capacity C of the channel with an arbitrarily low probability of error. The idea of a randomly generated code is very unusual.

Cognitive Tools Reference

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

© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

Just SKILL.md in .claude/skills/math/information-theory/channel-capacity of parcadei/Continuous-Claude-v3.

Open the folder on GitHubat commit d07ff4b

Used in 1 other repository

We found 1 copy of this SKILL.md (exact, near-identical or edited) in other folders, from 1 other GitHub owner. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Channel Capacity next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Channel Capacity compared with similar skills
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Channel Capacity this skillparcadei/Continuous-Claude-v33.9k1 repos~579Automated safety check: NotesMIT
Gtm Strategyphuryn/pm-skills27k—~1kAutomated safety check: PassMIT
Good Strategy Bad Strategywondelai/skills2.4k—~4.8kAutomated safety check: PassMIT
Ieee Transactions On Information Theorybrycewang-stanford/Awesome-Journal-Skills1.2k—~1.8kAutomated safety check: PassMIT
Configure Channelopenclaw/openclaw392k—~946Automated safety check: PassMIT
Product Strategyphuryn/pm-skills27k—~1.2kAutomated safety check: PassMIT

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Questions about Channel Capacity

What does Channel Capacity do?

Problem-solving strategies for channel capacity in information theory. Channel Capacity is an agent skill from parcadei/Continuous-Claude-v3.

How do I install Channel Capacity in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill channel-capacity -a claude-code`. Or copy the skill folder (.claude/skills/math/information-theory/channel-capacity in parcadei/Continuous-Claude-v3) into .claude/skills/channel-capacity in your project. Claude Code loads it when a task matches its description.

How do I install Channel Capacity in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill channel-capacity -a codex`. Or copy the skill folder (.claude/skills/math/information-theory/channel-capacity in parcadei/Continuous-Claude-v3) into .agents/skills/channel-capacity in your project. Codex loads it when a task matches its description.

Can I use Channel Capacity in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill channel-capacity -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/channel-capacity, .gemini/skills/channel-capacity, .github/skills/channel-capacity and .opencode/skills/channel-capacity in your project.

What does Channel Capacity need to run?

Going by SKILL.md and its folder, Channel Capacity needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Channel Capacity access the network?

SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.

Is Channel Capacity safe to install?

Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.

What licence does Channel Capacity use?

Channel Capacity is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Channel Capacity use?

About 579 tokens (SKILL.md is roughly 2.3k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Channel Capacity?

Skills that share tags, products or a category with Channel Capacity: Gtm Strategy (phuryn/pm-skills, 27k stars), Good Strategy Bad Strategy (wondelai/skills, 2.4k stars), Ieee Transactions On Information Theory (brycewang-stanford/Awesome-Journal-Skills, 1.2k stars) and Configure Channel (openclaw/openclaw, 392k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Channel Capacity?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,943 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.

Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.