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 guliqianxun/research-skills --skill math-proofgit clone --depth 1 https://github.com/guliqianxun/research-skillsWrote 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/guliqianxun/research-skills/math-proof)<a href="https://agentmods.dev/skills/guliqianxun/research-skills/math-proof"><img src="https://agentmods.dev/badge/skills/guliqianxun/research-skills/math-proof/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/guliqianxun/research-skills/math-proof"><img src="https://agentmods.dev/badge/skills/guliqianxun/research-skills/math-proof.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 | $0.00184 | $0.02184 |
| Opus 5 | $0.00092 | $0.01092 |
| Sonnet 5 | $0.00037 | $0.00437 |
| Haiku 4.5 | $0.00018 | $0.00218 |
Grade A, and why
math-proof 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 12d 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 — 148 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Mathematical Proof for ML
This skill turns you into a rigorous ML theorist. It covers strategy selection, proof construction, verification, and the bridge from theory to design decisions.
Follow NeurIPS/ICML/ICLR standards throughout.
Proof Strategy Selection
Choose based on the claim structure — don't default to direct proof:
| Claim Pattern | Strategy | Why |
|---|---|---|
| "Algorithm converges in $T$ steps" | Induction on iteration count | Base case = initialization, inductive step = per-iteration progress |
| "No algorithm can achieve error $< \varepsilon$" | Contradiction — assume one does, derive impossible bound | Lower bounds almost always need contradiction or information theory |
| "This estimator generalizes" | Probabilistic — concentration + union bound or PAC-Bayes | Generalization is inherently statistical |
| "Architecture $X$ is equivariant to group $G$" | Direct — verify $f(g \cdot x) = g \cdot f(x)$ for generators of $G$ | Algebraic — just check the group action commutes |
| "Gradient flow doesn't vanish" | Constructive — exhibit a Jacobian bound bounded away from 0 | Need concrete bounds, not existence |
| "Method A is strictly better than B" | Separation — construct an instance where A succeeds and B fails | Needs a concrete counterexample for B |
| "Network can approximate any continuous function" | Density argument — Stone-Weierstrass or constructive approximation | Show the function class is dense in $C(K)$ under sup-norm |
| "Loss landscape has no spurious local minima" | Landscape analysis — characterize critical points via Hessian | Show every local min is global, or every saddle has a negative eigenvalue |
| "Generative model learns the target distribution" | Coupling / OT argument — bound Wasserstein or KL between model and target | Transport inequalities connect optimization to distribution distance |
| "Adaptive method matches lower bound over $T$ steps" | Amortized analysis — potential function argument | Per-step costs vary but total is controlled by potential |
| "Score estimator converges to true score" | Denoising score matching equivalence — show $\mathbb{E}[|s_\theta - \nabla \log p_\sigma|^2]$ equals DSM objective up to constant | Avoids intractable $\nabla \log p$; reduces to regression |
What ships with it
4 files 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.
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.
- 12d ago First seen · 148 lines · 184 tokens per session scan A 7c0d03fdfc90
math-proof is a skill published in the GitHub repository guliqianxun/research-skills (5 stars, last pushed 4mo ago), licensed MIT. It adds 184 tokens to every session and 2,184 once invoked, about $0.0009 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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