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 pjt222/agent-almanac --skill derive-theoretical-resultgit clone --depth 1 https://github.com/pjt222/agent-almanacWrote 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/pjt222/agent-almanac/derive-theoretical-result)<a href="https://agentmods.dev/skills/pjt222/agent-almanac/derive-theoretical-result"><img src="https://agentmods.dev/badge/skills/pjt222/agent-almanac/derive-theoretical-result/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/pjt222/agent-almanac/derive-theoretical-result"><img src="https://agentmods.dev/badge/skills/pjt222/agent-almanac/derive-theoretical-result.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector pass
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 | $0.00086 | $0.02864 |
| Opus 5 | $0.00043 | $0.01432 |
| Sonnet 5 | $0.00017 | $0.00573 |
| Haiku 4.5 | $0.00009 | $0.00286 |
Grade A, and why
derive-theoretical-result 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 — 219 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Derive Theoretical Result
Produce a rigorous, step-by-step derivation of a theoretical result starting from stated axioms, first principles, or established theorems. Every algebraic or logical step is explicitly justified, limiting cases are verified, and the final result is presented with a complete notation glossary.
When to Use
- Deriving a formula, relation, or theorem from first principles (e.g., deriving the Euler-Lagrange equation from the action principle)
- Proving a mathematical statement by logical deduction from axioms
- Re-deriving a textbook result to verify it or adapt it to a modified context
- Extending a known result to a more general setting (e.g., from flat spacetime to curved spacetime)
- Producing a self-contained derivation for a paper, thesis, or technical report
Inputs
- Required: Target result to derive (equation, inequality, theorem statement, or relation)
- Required: Starting point (axioms, postulates, previously established results, or Lagrangian/Hamiltonian)
- Optional: Preferred proof technique (direct, by contradiction, by induction, variational, constructive)
- Optional: Notation conventions to follow (if matching a specific textbook or collaborator's conventions)
- Optional: Known intermediate results that may be cited without re-derivation
Procedure
Step 1: State Starting Assumptions and Target Result
Write the derivation's contract explicitly before any calculation:
- Axioms and postulates: List every assumption the derivation rests on. For physics, this includes the symmetry group, the action principle, or the postulates of quantum mechanics. For mathematics, this includes the axiom system and any previously proven lemmas.
- Target result: State the result to be derived in precise mathematical notation. If the result is an equation, write both sides. If it is an inequality, state the direction and the conditions for equality.
- Scope and restrictions: State the domain of validity (e.g., "valid for non-relativistic, spinless particles in three dimensions"). Identify what the derivation does not cover.
- Notation declaration: Define every symbol that will appear. This prevents ambiguity and makes the derivation self-contained.
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 · 219 lines · 86 tokens per session scan A 815133d62e1a
derive-theoretical-result is a skill published in the GitHub repository pjt222/agent-almanac (33 stars, last pushed 2d ago), licensed MIT. It adds 86 tokens to every session and 2,864 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 2026-09-03.
Other skills, from other repositories
tooluniverse-organic-chemistry
Organic chemistry reasoning guide for reaction product prediction, mechanism analysis (electrophilic/nucleophilic substitution, addition, elimination, pericyclic, radical), and spectroscopy interpretation (1H/13C NMR, IR, MS). Reasons from first principles (electron flow, kinetic vs thermodynamic) rather than…
evomath-tao
Use this skill whenever the user submits a non-trivial mathematical claim that needs a rigorous proof or audit. Trigger on IMO/Putnam/USAMO/Olympiad-style problems, ML/AI theoretical statements, research conjectures, suspected-false claims, multi-step proofs the user already failed on, proof drafts with possible…
analytics
Queries local analytics across OrchestKit projects for agent usage, skill frequency, hook timing, team activity, session replay, cost estimation, and model delegation trends. Privacy-safe with hashed project IDs. Supports time-range filtering and comparative analysis. Use when reviewing performance, estimating costs…
astro-dso-doc
Generates a complete, polished HTML documentation page, a processing checklist, an AstroBin post JSON, a PixInsight process icon set (XPSM), AND a ready-to-paste PixInsight project Description field for a deep-sky object (DSO) astrophotography project. Use this skill whenever the user mentions astrophotography, a DSO…
ape-visualize
Builds interactive, browser-based 3D Three.js visualizations of any mathematics or science concept as a single, self-contained HTML file. Takes a concept and a depth level (Simple, Intermediate, Advanced). Trigger on "ape visualize", "ape visualize math", "ape visualize science", "visualize math", "visualize science"…
dsm5
Assess and explain questions about mental health and neurocognitive conditions against DSM-5-TR diagnostic criteria, and guide evidence-based conversations for clinicians, patients, and family members. Use when someone asks about symptoms, possible conditions, differential diagnoses, diagnostic criteria, prevalence…