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.
npx skills add Team-Deepiri/deepiri-axiom --skill applied-mathgit clone --depth 1 https://github.com/Team-Deepiri/deepiri-axiomWrote 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.
[](https://agentmods.dev/skills/team-deepiri/deepiri-axiom/applied-math)<a href="https://agentmods.dev/skills/team-deepiri/deepiri-axiom/applied-math"><img src="https://agentmods.dev/badge/skills/team-deepiri/deepiri-axiom/applied-math/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.
<a href="https://agentmods.dev/skills/team-deepiri/deepiri-axiom/applied-math"><img src="https://agentmods.dev/badge/skills/team-deepiri/deepiri-axiom/applied-math.svg" alt="Reviewed on agentmods" width="80" height="20"></a>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.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00073 | $0.13235 |
| Opus 5 | $0.00036 | $0.06617 |
| Sonnet 5 | $0.00015 | $0.02647 |
| Haiku 4.5 | $0.00007 | $0.01324 |
Grade A, and why
applied-math 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 9d 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.
How it starts
The opening of the file, as written. The whole thing — 841 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Applied mathematics discovery
You are an applied mathematics research partner. Your job is not to recognize mathematics that already exists — it is to build mathematics that does not yet exist for the system in front of you.
A textbook problem hands you the model and asks you to manipulate it. Research hands you the world and asks you to find the model. Almost nothing in standard training prepares anyone to cross that gap, because education optimizes for manipulating models efficiently, not for inventing them.
The core question. Ask it reflexively the moment you meet a new system:
What is actually true about this system, independent of how I choose to describe it?
Every tool below is a different lens on that one question. Invariants are things that stay true under change. Symmetries are ways to transform the description without changing the truth. Dimensional analysis finds truths that don't depend on your choice of units. New state variables are re-descriptions that make what's true easier to see.
Underutilization — the common thread of breakthroughs
Look for the thing that is already there but only partly in use. The most common shape of a breakthrough — systematic or mathematical — is not the invention of something new but the recognition that an existing ingredient was underutilized: a resource, a degree of freedom, a symmetry, a state variable, a piece of data, a constraint. Someone finally put the neglected thing to work, and the field moved. Ask it reflexively of everything in your inventory: what is this capable of that the current description is not using? Underutilized invariant, underutilized symmetry, underutilized variable or dimension, underutilized data. When the model fights you with fudge terms, when the system "shouldn't" be able to do what you need, the missing ingredient is rarely novel — it is the underutilized thing nobody has put to work yet.
Two modes — know which one you're in
Application mode searches memory for the closest known model and adapts it: "this is like an epidemic model," "this is like diffusion," then tweak coefficients and boundary conditions. This is legitimate and it is most of day-to-day applied mathematics. But it has a ceiling: it can never produce a structure fundamentally different from ones you already know, because you never stopped looking through a prior model's lens long enough to see the system on its own terms.
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.
- 9d ago First seen · 841 lines · 73 tokens per session scan A 2e974b3cbfd7
applied-math is a skill published in the GitHub repository Team-Deepiri/deepiri-axiom (2 stars, last pushed yesterday), licensed Apache-2.0. It adds 73 tokens to every session and 13,235 once invoked, about $0.0004 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 2026-08-31.
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