Results for “theorem-proving”

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.

Universal transformation λ(ο,K).τ with recursive self-improvement. USE WHEN routing reasoning, validating knowledge graphs, preparing CICM/ANZCA examinations, or when self-improvement of reasoning/architecture/context is required. Routes queries through R0-R3 complexity pipelines, validates topology (η≥target) and governance (KROG), emits per style (Φ), and compounds learnings into knowledge K. Triggers on complexity assessment, multi-step reasoning, examination mode, or /λ invocation.

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

Algebra Testing Expert Skill

Runs a hypothesis-driven debugging workflow that reproduces failures, forms discriminating tests, proves root cause via toggle, and delivers a fix, regression test, and postmortem.

lemmaly — Algorithm-First Proof

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

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

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

Algebra Based Analysis Skill

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bi

Algebra Based Synthesis Skill

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

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

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

Algebra Testing Advanced Skill

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

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

Algebra Modeling Expert Skill

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

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

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.

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。

当需要深化对某个主题的理解、检验知识掌握程度或克服“冒名顶替综合征”时

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

First-principles assumption auditor. Classifies each hidden assumption (fact / convention / belief / interest-driven), ranks by fragility × impact, and rebuilds conclusions from verified premises. Bilingual: auto-detects Chinese or English.

Coordinate proof runs across three interfaces: exhaust actionable local proof work first, package exact unresolved obligations for a provider-neutral external solver only when justified, and keep the user informed and in control of consequential choices.

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