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.

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.

Turn a theory-first research idea into a proof-oriented research plan. Use after idea-creator-analysis, or when the user asks for theorem targets, assumptions, proof obligations, impossibility routes, analysis validation, or a non-experimental plan.

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.

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

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.

research-synthesis

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

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

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

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

Runs commands, inspects git state, debugs CI failures, and makes narrow fixes with exact proof of what was executed and verified.

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

Provides PhD-level mathematical analysis for machine learning, including optimization theory, statistical learning theory, and convergence proofs.

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

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

Verify the accuracy of claims and statements by extracting individual assertions, identifying authoritative sources, cross-referencing evidence, and assigning confidence-scored verdicts. Use when the user requests fact checking or provides relevant inputs for this workflow.

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.

Audits hidden assumptions in decisions by classifying them into four types, ranking by fragility and impact, and rebuilding conclusions from verified premises. Auto-detects Chinese or English.

Algebra Testing Advanced Skill

Conducts exhaustive multi-source research on a topic, tagging each claim with source class and confidence, and includes a mandatory adversarial counterpoint and open-questions list.

Turn a refined research proposal or method idea into a detailed, claim-driven experiment roadmap. Use when the user asks for a detailed experiment plan, ablation matrix, evaluation protocol, run order, compute budget, or paper-ready validation that supports the core problem, novelty, simplicity, and any LLM / VLM / Diffusion / RL-based contribution.

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