isomorphism-falsification

isomorphism-falsification is a skill for Claude Code, Codex from yogsoth-ai/stress-test. It costs 94 tokens per session (1,222 once invoked), scanned A, original, Apache-2.0.

A mathematical challenge method for claims that two or more structures are isomorphic, meaning they match through a reversible map that preserves the relevant relationships. It tests whether the proposed correspondence is genuinely precise or only a loose analogy.

In plain words
What is it for?
Use it to examine cross-language mathematical claims, test structure-preserving correspondences, and decide whether a result should be called an isomorphism, a weaker relationship, or an analogy.
Why use it?
Elegant connections between different mathematical descriptions can be misleading. This method forces the author to show the required map and exposes cases where the claim does not hold.

Skill for Claude CodeCodex

Written for no agent in particular: nothing here depends on one.

Good fit Use it to examine cross-language mathematical claims, test structure-preserving correspondences, and decide whether a result should be called an isomorphism, a weaker relationship, or an analogy.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/yogsoth-ai/stress-test/isomorphism-falsification
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.

Any agent
npx skills add yogsoth-ai/stress-test --skill isomorphism-falsification
Clone the repo
git clone --depth 1 https://github.com/yogsoth-ai/stress-test

Made for: Claude Code, Codex.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for isomorphism-falsification

README.md
[![agentmods](https://agentmods.dev/badge/skills/yogsoth-ai/stress-test/isomorphism-falsification/github.svg)](https://agentmods.dev/skills/yogsoth-ai/stress-test/isomorphism-falsification)
Your own site
<a href="https://agentmods.dev/skills/yogsoth-ai/stress-test/isomorphism-falsification"><img src="https://agentmods.dev/badge/skills/yogsoth-ai/stress-test/isomorphism-falsification/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for isomorphism-falsification

Your own site · 80×15
<a href="https://agentmods.dev/skills/yogsoth-ai/stress-test/isomorphism-falsification"><img src="https://agentmods.dev/badge/skills/yogsoth-ai/stress-test/isomorphism-falsification.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 94 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 1,222 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 1 finding. A grade says what 26 rules found in the file — not that it is safe.
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 5.1 $0.00094 $0.01222
Opus 5 $0.00047 $0.00611
Sonnet 5 $0.00019 $0.00244
Haiku 4.5 $0.00009 $0.00122

Measured 7d ago against content hash b028cfa666c3, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-10, from the pricing page.

Security

Grade A, and why

isomorphism-falsification scanned grade A with 1 finding 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 7d 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.

Makes network callslowCapability

Not a fault in itself. Listed so you know the mod talks to something, and to what.

For each language in which the artifact claims the same object lives, write down EXACTLY what that object is: its ambient space, what "zero/null/kernel/curl" means there, and what structure (group action, vector space, o
skills/isomorphism-falsification/SKILL.md · 52 lines

How it starts

The opening of the file, as written. The whole thing — 52 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Isomorphism Falsification

A dedicated attacker for the single most suspicious kind of claim an artifact can make: "X = Y = Z = W" asserted across multiple mathematical languages. "Isomorphism" is a precise mathematical word with a heavy burden of proof. "These things rhyme" is an analogy with almost none. The danger is that a pleasing analogy gets promoted to "isomorphism" because it FEELS unifying — pure elegance-trap. This strategy forces the claim to pay its burden or be demoted.

Why this needs its own strategy

Generic debate/red-team will poke at it, but they don't know the specific bar an isomorphism must clear. This strategy encodes that bar. The burden of proof for "A ≅ B" is NOT "A and B share some features." It is: a map Φ: A → B that is (1) well-defined on all of A, (2) preserves the relevant structure (the operations/relations that matter — the composition of symmetries, the action of the generator, or whatever structure the artifact asserts is shared), (3) is invertible (or at least: the claimed correspondence is bijective on the objects we care about — the kernel/null/zero sets). Anything less is a homomorphism, a functor, an embedding, a loose analogy — each strictly weaker, and we must say which.

The ladder of strength (assign the claim its true rung)

From strongest to weakest. The attack's job is to find the highest rung the claim can actually defend, then demote our wording to match:

  1. Isomorphism — bijective, structure-preserving both ways. The full claim.
  2. Isomorphism on a substructure — true only for the kernel/zero-mode sets, not the whole spaces. (Plausibly where many multi-language claims actually land — and that would still be a real, strong result if stated honestly.)
  3. Homomorphism / functor — structure-preserving one way, not invertible. Maps objects to objects but loses information.
  4. Shared invariant — all claimed sides have a quantity that coincides (e.g. all "zero sets" have the same dimension) but no map is exhibited. Numerical coincidence, not identity.
  5. Analogy — suggestive parallel, no formal correspondence. The honest label if 1–4 all fail.

Read the full file on GitHub · 52 lines

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. 7d ago First seen · 52 lines · 94 tokens per session scan A b028cfa666c3

Subscribe to this mod's changes

isomorphism-falsification is a skill published in the GitHub repository yogsoth-ai/stress-test (2 stars, last pushed 2mo ago), licensed Apache-2.0. It adds 94 tokens to every session and 1,222 once invoked, about $0.0005 per session on Opus 5. A static security scan graded it A with 1 finding (makes network calls). No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.

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