Results for “proof-techniques”

Writes rigorous mathematical proofs for ML/AI theory. Use when asked to prove a theorem, lemma, proposition, or corollary, fill in missing proof steps, formalize a proof sketch, 补全证明, 写证明, 证明某个命题, or determine whether a claimed proof can actually be completed under the stated assumptions.

Synthesize source-indexed proof-material items into the final proof-usage playbook. Use when Codex needs to cluster proof items by proof shape, de-duplicate across sources, design reusable taxonomy entries, update proof-usage indexes and source maps, or preserve material-ID links from cooked proof entries.

Store and inspect source-indexed proof material extracted from papers, notes, PDFs, or LaTeX sources. Use when Codex needs stable material IDs, source locations, reusable abstractions, proof skeletons, tags, and public attribution before any proof ideas are cooked into proof-usage.

Prepare GPT-pro-ready proof planning or diagnosis bundles from a user's idea, packaging claims, sources, givens, and open questions for review without solving gaps locally.

Select the right Proof of Life (PoL) probe type based on hypothesis, risk, and resources to match validation method to the real learning goal.

Enforces running verification commands and confirming output before claiming work is complete, fixed, or passing, ensuring evidence precedes any success claims.

Define a lightweight, disposable Proof of Life probe to test a risky hypothesis cheaply and surface harsh truths before building real product.

Applied Calculus Testing Skill

Testing Verification Skill

Applied Logic Testing Skill

Algorithms Based Testing Skill

Three shapes get argued about as if one were correct.

Perl testing patterns using Test2::V0, Test::More, prove runner, mocking, coverage with Devel::Cover, and TDD methodology.

Unified math capabilities - computation, solving, and explanation. I route to the right tool.

Diagnose and fix a bug through a disciplined reproduce, isolate, diagnose, fix, verify loop driven by evidence and one hypothesis at a time — not guesswork.

Write effective unit tests with best practices for any project. Use when writing tests, creating test cases, improving test coverage, increasing confidence before release, or when the user mentions testing. Mutation score / assertion theater → test-mutation.

Verify code changes work by running them. Proves through execution, not just inspection.

Internal harness probe for the OI-3 readability-guidance spike. Use only when explicitly told to invoke spike-probe. Verifies that a freshly-created project skill renders into a subagent's context via the Skill tool.

Provides comprehensive testing patterns for Perl applications using Test2::V0, Test::More, prove runner, mocking, and coverage analysis with Devel::Cover.

Write and run Perl tests using Test2::V0, Test::More, prove, mocking, and Devel::Cover with a TDD workflow.

Validate skill outputs against assertion manifests to detect regressions, enforce quality gates, and bootstrap starter manifests from historical runs.

Enumerating failure modes via pre-mortem analysis. Systematically identifies failure scenarios for plans, designs, and features, scoring them with RPN/AP. Does not write code.

Perl testing patterns using Test2::V0, Test::More, prove runner, mocking, coverage with Devel::Cover, and TDD methodology.

Debugging is the scientific method under time pressure.

Verify that a change really works before you claim completion

基于证据优先的仓库执行工作流，适用于ECC。当用户需要运行命令、检查仓库、调试CI失败或推送带有精确执行和验证证明的窄修复时使用。

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Advanced Logic Testing Skill

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.

Require fresh evidence before claiming an implementation, fix, build, or test is complete.

Use when about to claim work is complete, fixed, or passing, before committing or creating PRs - requires running verification commands and confirming output before making any success claims; evidence before assertions always

Enforces running verification commands and confirming output before claiming work is complete, fixed, or passing, to prevent false success claims.

Write and run Perl tests using Test2::V0, Test::More, prove, mocking, and Devel::Cover coverage with a TDD workflow.