Results for “proof-techniques”

Mine proof-heavy papers, notes, PDFs, Markdown, or LaTeX sources into source-indexed proof-material files. Use when the user wants to extract technically nontrivial lemmas, estimates, definitions, dependencies, reductions, constructions, or proof strategies, preserve paper locations and stable material IDs, run DeepSeek screening/backtests, and update the proof-material index rather than writing directly to proof-usage.

Philosophy of science methodology examining how research programs evolve through proofs and refutations

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.

Verify the article’s factual, product, citation, and link integrity before visual production.

Independent DeepSeek-backed adversarial proof-audit step for existing theorem, lemma, proposition, or proof artifacts in Markdown, LaTeX, or proof logs. Use when asked to check, audit, verify, red-team, or adversarially review a proof; when a completed proof task needs a correctness pass; or when a broader proof workflow dispatches an independent reviewer to find gaps, hidden assumptions, counterexamples, or unjustified steps.

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.

Runs a ten-round adversarial gauntlet to pressure-test absolute claims, refining them with explicit boundaries and an Oracle synthesis.

Look up and apply the cooked, indexed proof playbook built from proof-material. Use when the user is proving a theorem, planning a proof, seeking reusable proof moves by task shape, assumptions, tags, desired move, or material source ID, or adapting cooked local moves and macro strategies with public source attribution.

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.

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

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.

Supplements general deposition preparation with IP-specific examination frameworks for patent, trademark, copyright, and trade secret cases. Covers witness strategies for inventors, accused infringers, licensing witnesses, and experts. Use alongside @deposition-preparation and @deposition-expert-witness when planning IP depositions, drafting outlines, or analyzing witness strategy.

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 patterns and principles. Unit, integration, mocking strategies.

Testing Verification Skill

Applied Logic Testing Skill

Proofread and correct text for grammar, spelling, punctuation, style, clarity, and consistency, with support for multiple style guides and readability analysis. Use when the user requests proofreading or provides relevant inputs for this workflow.

Design lean validation experiments — hypothesis, method, success criteria, sample size, timeline, and decision rules

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.

Use this skill for property tests for parsers, validators, transforms, state machines, edge cases. Trigger when the task involves programming work related to Property Based Testing, implementation, audits, debugging, strategy, or validation.

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.