constructing-knowledge-space

A knowledge-space tool that derives all feasible combinations of mastered topics from prerequisite links. Knowledge Space Theory is a way to model which sets of knowledge a learner can reasonably have.

In plain words
What is it for?
It helps enumerate possible knowledge states, find inner and outer fringes—the topics already secured or ready to learn—and produce representative learning paths.
Why use it?
It makes a prerequisite map usable for understanding possible learner states and next steps.

Skill for Claude CodeCodex

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

agentmods
npx agentmods add skills/vanderbilt-data-science/knowledge-spaces/constructing-knowledge-space
Any agent
npx skills add vanderbilt-data-science/knowledge-spaces --skill constructing-knowledge-space
Clone the repo
git clone --depth 1 https://github.com/vanderbilt-data-science/knowledge-spaces

Made for: Claude Code, Codex.

Per session 92 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 2,375 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5 $0.00092 $0.02375
Opus 5 $0.00046 $0.01188
Sonnet 5 $0.00018 $0.00475
Haiku 4.5 $0.00009 $0.00237

Measured 2d ago against content hash b43c08b1eea8, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

constructing-knowledge-space scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 2d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

.claude/skills/constructing-knowledge-space/SKILL.md · 226 lines

How it starts

The opening of the file, as written. The whole thing — 226 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Constructing Knowledge Space

Role

You are a KST mathematician deriving the full knowledge space from the surmise relation -- computing all feasible knowledge states, their fringes, and representative learning paths. You work within the CbKST framework (Heller & Stefanutti, 2024), maintaining awareness of the duality between item-level and competence-level structures.

Input

$ARGUMENTS

The user provides a path to a knowledge graph file containing:

  • items[] -- the domain's knowledge items (required)
  • surmise_relations[] -- the validated prerequisite quasi-order (required)
  • competences[] -- latent competences (optional, CbKST)
  • competence_relations[] -- competence-level prerequisites (optional, CbKST)

Load the graph and verify it conforms to schemas/knowledge-graph.schema.json.

Computational Tools

Use scripts/kst_utils.py for all computation. Do not enumerate states, compute fringes, or generate paths manually.

python3 scripts/kst_utils.py validate <graph-path>              # Pre-check surmise relation
python3 scripts/kst_utils.py enumerate <graph-path> --save       # Enumerate states, compute fringes, save
python3 scripts/kst_utils.py enumerate <graph-path> --save --max 5000  # With state limit
python3 scripts/kst_utils.py paths <graph-path>                  # Generate learning paths
python3 scripts/kst_utils.py stats <graph-path>                  # Summary statistics

Methodology

1. Pre-Check

Verify the surmise relation before attempting enumeration:

python3 scripts/kst_utils.py validate <graph-path>

If validation reports failures (cycles, referential integrity issues), these must be resolved before proceeding. Return to /building-surmise-relations or /validating-knowledge-structure as needed.

2. Knowledge Space Derivation

A knowledge state is a subset K of items Q that is downward-closed under the surmise relation: if item b is in K and a -> b, then a must also be in K. The family of all such downsets forms the knowledge space. See shared-references/kst-foundations.md for formal definitions.

Read the full file on GitHub · 226 lines

Files

What ships with it

1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 2d ago First seen · 226 lines · 92 tokens per session scan A b43c08b1eea8

Subscribe to this mod's changes

constructing-knowledge-space is a skill published in the GitHub repository vanderbilt-data-science/knowledge-spaces (20 stars, last pushed 6mo ago), licensed MIT. It adds 92 tokens to every session and 2,375 once invoked, about $0.0005 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.

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