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Generate formal specifications (definitions, predicates, invariants, pre/post-conditions) in Isabelle/HOL or Coq from informal requirements, source code, pseudocode, or mathematical descriptions. Use when users need to: (1) Formalize algorithms or data structures, (2) Create function specifications with contracts, (3) Generate predicates and properties for verification, (4) Translate informal requirements into formal logic, (5) Specify invariants for loops or data structures, or (6) Create formal definitions for mathematical concepts. Supports both Isabelle/HOL and Coq equally.

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Formally verify programs by writing Lean 4 proofs. Trigger this skill whenever the user wants to formally verify code, generate Lean 4 proofs, prove properties about algorithms or smart contracts, verify invariants, convert program logic into formal specifications, or anything involving Lean 4 and formal verification. Also trigger when the user mentions "qedgen", "lean proof", "formal proof", "verify my code", "prove correctness", "formal verification", or wants mathematical guarantees about their implementation.

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Expert-level formal methods covering formal specification, model checking, theorem proving, type theory, program verification, and formal languages.

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Develop mathematical proofs in Lean, a system that checks formal proofs, continue unfinished projects, or audit existing results. Check that the theorem matches the original claim, examine its assumptions, and prepare sources and commands for reproduction.

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• Turn a mathematical statement into a checked Lean proof
• Continue an unfinished Lean proof project
• Audit whether a theorem proves the original claim

Turn mathematical claims into definitions, lemmas, and proofs for Lean 4 and Mathlib. Check proofs with Lean’s trusted core, separately review whether the formal statement matches the original claim, and record verification evidence.

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• Verifying an important lemma with Lean 4
• Breaking a theorem into definitions and supporting lemmas
• Checking proofs for sorry, admit, and unauthorized axioms

Develop identification arguments in econometrics: establish whether observed data uniquely determine a target parameter, state assumptions and rank conditions, and write formal propositions. When uniqueness fails, characterize the range of parameter values consistent with the data.

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• Writing an identification proposition for a paper
• Checking assumptions for IV, DiD, or RDD
• Examining rank conditions for moment equations

Provides a starting structure for work on formal logic and mathematical foundations, with source checks and a review of unresolved gaps. The material is a legacy template awaiting research and validation.

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• Reviewing sources for formal logic topics
• Checking unresolved gaps before using topic modules
• Planning validation of mathematical foundations material

Cultural adaptation for translated content. Run AFTER blog-translate completes. Adjusts brand examples, CTAs, legal references, and formality for the target market (German, French, Japanese, Spanish, etc.). Deep cultural adaptation of translated blog posts. Goes beyond translation to swap brand examples, adapt CTAs, substitute legal references, localize statistic sources where possible, and adjust formality (Sie/du, tu/vous, formal/informal). Built-in profiles for DACH, Francophone, Hispanic, and Japanese markets, plus a custom-locale template. Makes content feel locally authored, not translated. Use when user says "localize blog", "blog localize", "cultural adaptation", "adapt for Germany", "adapt for France", "lokalisieren", "localiser", "adaptar".

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Cultural adaptation for translated content. Run AFTER blog-translate completes. Adjusts brand examples, CTAs, legal references, and formality for the target market (German, French, Japanese, Spanish, etc.). Deep cultural adaptation of translated blog posts. Goes beyond translation to swap brand examples, adapt CTAs, substitute legal references, localize statistic sources where possible, and adjust formality (Sie/du, tu/vous, formal/informal). Built-in profiles for DACH, Francophone, Hispanic, and Japanese markets, plus a custom-locale template. Makes content feel locally authored, not translated. Use when user says "localize blog", "blog localize", "cultural adaptation", "adapt for Germany", "adapt for France", "lokalisieren", "localiser", "adaptar".

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Mathematical foundations, logical structures, and formal verification guidance. Trigger when: - Designing protocol contracts, formal specifications, verifying state spaces, or using proof assistants. - Tasks involve: TLA+, Alloy, Lean, Coq, model checkers, invariants, temporal logic. - Prompt contains keywords: formal verification, alloy, tla+, lean, coq, invariant, state machine, model checker, liveness, safety.

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Produces a narrow-interval quality signal for a WinDAGs skill that a third party can verify without inspecting model weights or method internals. The mechanism is attribution-kNN over a tamper-evident outcome log (task→skills→accept/reject store), combined with a conformal-prediction calibration certificate that provides a formal coverage guarantee. Thompson/Beta sampling is explicitly rejected as a category error: it produces a selection signal for stationary i.i.d. rewards, not an attestation signal for context-dependent LLM output quality. The resulting bundle — outcome-log Merkle root + conformal threshold + optional TEE guardrail signature — constitutes a "narrow-interval trust" credential: verifiable, bounded, and internals-opaque.

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Approach engineering problems by checking assumptions, defining performance constraints, and choosing suitable tools before implementation. The skill guides algorithm analysis, complete code, performance optimization, and correctness checks through tests, assertions, or formal verification, meaning mathematical checks of correctness.

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• Checking algorithm complexity and design assumptions
• Choosing languages for numerical or distributed systems
• Implementing concurrent code with explicit error handling

Turn a Mermaid sequence diagram of a cryptographic protocol into a ProVerif model, a file for formal security checks. It includes queries for secrecy, authentication, replay resistance, and forward secrecy where applicable.

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• Converting a cryptographic protocol diagram into a .pv file
• Preparing session key secrecy checks
• Modeling authentication and replay resistance

Organize Nexent test assets into a traceable chain from requirements and bugs to cases, scripts, and results. Review existing coverage, maintain execution settings, and generate a registry and Excel views for formal testing.

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• Designing test cases for new requirements
• Reviewing regression coverage after a bug fix
• Adding missing tests after development

Review existing tests using 19 research-backed test smell categories, meaning patterns that can weaken test quality. Get findings ranked by demonstrated risk, with precise code evidence and fixes suited to the test framework in use.

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• Request a test review using formal academic categories
• Prioritize test problems by their demonstrated risk
• Find causes of flaky tests or misleading passes

Build reproducible empirical analyses in R, from data cleaning to statistical modeling and publication tables and figures. Covers economics, epidemiology, and machine learning approaches to causal inference, which estimates effects of interventions.

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• Build a reproducible R or Quarto analysis workflow
• Compare regression models with progressively added controls
• Test robustness across samples and statistical methods

Bring a project's formal verification back in line with the code after the code changes: find the commits that touched verified code, update the model, harness, or properties to describe the code as it is now, rerun, and say whether each failure is drift in the verification or a bug in the code. Use for /maintain-formal-verification-skill, "is the model still true to the code", or after merges and refactors that touched verified code without rechecking it.

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Generate a project-local skill that formally verifies the code where a bug costs the most and tests reach the least, in any language, with whichever verification tool fits. Use for /create-formal-verification-skill, "model-check this race", "prove this invariant", or when concurrency, retries, state machines, parsers, or unsafe code need more than tests.

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Bring a project's formal verification back in line with the code after the code changes: find the commits that touched verified code, update the model, harness, or properties to describe the code as it is now, rerun, and say whether each failure is drift in the verification or a bug in the code. Use for /maintain-formal-verification-skill, "is the model still true to the code", or after merges and refactors that touched verified code without rechecking it.

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Generate a project-local skill that formally verifies the code where a bug costs the most and tests reach the least, in any language, with whichever verification tool fits. Use for /create-formal-verification-skill, "model-check this race", "prove this invariant", or when concurrency, retries, state machines, parsers, or unsafe code need more than tests.

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Plan, draft, audit, globally revise, format, and verify a formal mathematical-modeling paper after the Standard evidence gate passes. Use for the sole S7/S8 formal manuscript path, not for legacy micro-unit scaffolds.

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Translate natural-language requirements or structured specification documents into formal temporal logic properties (LTL, CTL, safety/liveness properties). Use when users need to formalize requirements for model checking, formal verification, or property specification. Handles embedded/real-time systems, hardware verification, concurrent systems, and reactive systems. Resolves ambiguities, asks clarifying questions when needed, and outputs machine-checkable formulas with explanations. Supports multiple output formats (SPIN, NuSMV, Uppaal, TLA+, Maude).

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Generate formal specifications including preconditions, postconditions, invariants, and contracts from code or requirements. Use this skill when documenting APIs, creating formal verification annotations, defining function contracts, specifying class invariants, writing design-by-contract code, or preparing code for formal verification. Supports multiple specification languages including JML, ACSL, Dafny, Eiffel contracts, and documentation annotations.

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Automatically infer formal correctness properties from Verilog/SystemVerilog RTL code and generate SystemVerilog Assertions (SVA). Identifies control-flow invariants (mutual exclusion, valid-ready handshakes, pipeline ordering, safety properties), liveness expectations, and temporal properties. Use when working with RTL designs that need formal property generation, when adding assertions to existing RTL, or when users ask to infer properties, generate assertions, or create formal specifications from hardware designs.

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