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 agentmods add skills/nrdxp/predicate/formal-foundationsnpx skills add nrdxp/predicate --skill formal-foundationsgit clone --depth 1 https://github.com/nrdxp/predicateWhat 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 | $0.00091 | $0.03448 |
| Opus 5 | $0.00046 | $0.01724 |
| Sonnet 5 | $0.00018 | $0.00690 |
| Haiku 4.5 | $0.00009 | $0.00345 |
Grade A, and why
formal-foundations 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.
How it starts
The opening of the file, as written. The whole thing — 200 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Formal Mathematical Foundations
Reference corpus — /form, /spec, boundary. This skill survives as the mathematical-language authority; the mandate to apply it is ambient, rooted in the workflows that invoke it as a lens. It supplies the foundational vocabulary for form's structural representations, the verification semantics for spec's formal tiers, and the theoretical grounding consulted by boundary. The formalisms here anchor the symbolic path of the Verification Dual: types-as-propositions (Curry-Howard), bisimulation as behavioral equivalence, and adjoint functors as the semantic spine of data migration.
Disposition directive: Recognize that the structures you encounter in software engineering — types, protocols, state machines, data schemas — are instances of deeper mathematical patterns. This skill equips you with the vocabulary to see those patterns. The sdma skill provides the domain-specific toolkit for applying these foundations to concrete problems; this skill provides the language.
1. Categorical Foundations
Category theory is the algebra of composition. Its value to engineering is not abstraction for abstraction's sake — it provides a universal language for describing how things combine, transform, and relate.
1.1. Symmetric Monoidal Categories (SMC)
A symmetric monoidal category is a quintuple (C, ⊗, I, α, λ, ρ, γ) defining a category C equipped with a bifunctor ⊗: C × C → C and a unit object I.
- Associator (α): A natural isomorphism α_{X,Y,Z}: (X ⊗ Y) ⊗ Z ≅ X ⊗ (Y ⊗ Z). Grouping doesn't matter — only the components and their order.
- Left and Right Unitors (λ, ρ): Natural isomorphisms λX: I ⊗ X ≅ X and ρ_X: X ⊗ I ≅ X. _The unit is invisible — combining with "nothing" changes nothing.
- Braiding (γ): A natural isomorphism γ_{X,Y}: X ⊗ Y ≅ Y ⊗ X such that γ_{Y,X} ∘ γ_{X,Y} = id_{X ⊗ Y}. Order can be swapped — swapping twice returns to the original.
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.
- 2d ago First seen · 200 lines · 91 tokens per session scan A 036d421ace02
formal-foundations is a skill published in the GitHub repository nrdxp/predicate (10 stars, last pushed 8d ago), licensed MIT. It adds 91 tokens to every session and 3,448 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 2026-08-31.
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