「proof」の検索結果

Use when the user asks to "package our proof points", "build reusable stat cards and case snippets", or "put proof where each pillar makes its claim"; turns claims-ledger-approved proofs into reusable proof modules — stat cards, case snippets, testimonial blocks, comparison proofs — each pinned to a message-house pillar and the ledger claim ID it substantiates, and flags any pillar making a claim with no approved proof behind it. Never adjudicates a proof: unverified or ledger-absent proofs are marked '[needs source]' and routed to the claims candidates. Not for adjudicating or substantiating claims — use offer-claims-registry; not for fabricating a benchmark to fill a gap — a missing proof is flagged, not invented; not for scoring narrative quality — use narrative-quality-auditor. 证据模块/证据卡/客户案例/主张对齐

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Use when the user asks to "package our proof points", "build reusable stat cards and case snippets", or "put proof where each pillar makes its claim"; turns claims-ledger-approved proofs into reusable proof modules — stat cards, case snippets, testimonial blocks, comparison proofs — each pinned to a message-house pillar and the ledger claim ID it substantiates, and flags any pillar making a claim with no approved proof behind it. Never adjudicates a proof: unverified or ledger-absent proofs are marked '[needs source]' and routed to the claims candidates. Not for adjudicating or substantiating claims — use offer-claims-registry; not for fabricating a benchmark to fill a gap — a missing proof is flagged, not invented; not for scoring narrative quality — use narrative-quality-auditor. 证据模块/证据卡/客户案例/主张对齐

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Summarize long Isabelle or Coq proof scripts into high-level logical steps and reasoning flow. Use when users need to: (1) Understand the structure of a complex proof, (2) Document proof strategies for others, (3) Extract the key reasoning steps from verbose proof scripts, (4) Create readable proof outlines from detailed tactical proofs. Produces hierarchical outlines with moderate detail showing proof structure, main cases, key lemmas, and reasoning flow for both Isabelle/Isar and Coq proofs.

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Family-G proof & derivation integrity forensics: does a THIRD PARTY's written proof/derivation actually establish its theorem, or does it skip an obligation, assume its own conclusion, take an invalid step, drift a symbol's meaning, or smuggle an unstated assumption? Decides from the WRITTEN proof/derivation — verdict-bearing at L1 (the LaTeX source; PDF-extracted math is unreliable, so an L0 PDF-only run surfaces info only) — never asserts 'fabricated', only that the step shown does not hold. A fresh cross-model reviewer reads the theorem/proof + an extraction-only obligation scaffold and proposes per-obligation findings, each span-anchored to the evidence ledger (claims.json); reviewer≠adjudicator. Emits proof-derivation-forensics.findings.json; NEVER computes the verdict. dimension=proof, can be critical. Triggers: "proof forensics", "check this proof", "derivation integrity", "audit the math", "证明审计", "推导有没有漏洞".

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Build and maintain a provenance-clean proof library — inventory every real proof asset (analytics, reviews, permitted testimonials, case studies, press, certifications), categorize it, rewrite each cleared item in 3 lengths, fuse top assets with narrative, and gate everything through FTC testimonial rules before it can ship. Use when "proof library", "gather our proof", "authority builder", "collect testimonials", "social proof assets", "proof points for the sales page", "what results can we claim", or any request to assemble evidence for marketing claims. NEVER invents proof — missing proof is reported as a gap.

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Generate structured proof skeletons with tactics, strategies, and intermediate lemmas for theorems in Isabelle/HOL or Coq. Use when users need to: (1) Create proof outlines for theorem statements, (2) Generate proof structure with tactic placeholders, (3) Identify key lemmas needed for a proof, (4) Plan proof strategies (induction, case analysis, forward/backward reasoning), (5) Scaffold proofs with intermediate steps and subgoals, or (6) Convert theorem statements into detailed proof templates. Supports both Isabelle/HOL and Coq equally.

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Analyze failed or stuck proofs and propose auxiliary lemmas to help complete the proof in Isabelle/HOL or Coq. Use when encountering proof failures, stuck proof states, unprovable subgoals, or when needing to strengthen induction hypotheses. Identifies missing lemmas, suggests proof strategies, and generates helper lemmas with appropriate statements and proof sketches. Supports inductive proofs, case analysis, rewriting, and complex proof obligations.

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Operate a reusable technical book manuscript workspace with writing structure, reader persona SSOT, review rules, and optional Markdown to Re:VIEW/PDF support. Use when organizing a book manuscript repo, defining or reviewing target readers, standardizing chapter/section files, setting writing/review agents, handling publisher proof comments, or assessing an existing writing workspace. Triggers on book writing workspace, reader persona, reader audience, 読者ペルソナ, persona SSOT, technical book project, 執筆ワークスペース, manuscript workflow, Re:VIEW workspace, proof PDF, annotated proof, publisher proof comments, 校正, 校正注釈, and 初校.

Audit an existing Lamport-style hierarchical mathematical proof forward for validity and whether its hierarchy, scope, dependencies, side conditions, and proof constructs discharge the stated theorem. Use when the central question concerns a top-down proof with numbered levels, subproofs, ASSUME/PROVE, SUFFICES, PICK, CASE, DEFINE, Q.E.D., or prose equivalents. For an ordinary proof that first needs source-preserving hierarchy, use convert-lamport; for conclusion-first AND/OR obligation reconstruction, use reverse-lamport. Do not use to generate or replace a proof, or to audit Lean, Coq, Isabelle, or other proof-assistant source.

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Manage a stateful, run-directory-based proof project with Codex: continuation across runs, run-local source bookkeeping, manual GPT Pro handoff packages when a local attempt stalls, and an optional DeepSeek second opinion as additional evidence only. Use when the user asks for proof-run orchestration, a GPT Pro handoff, or cross-run proof continuation — use /proof-writer for ordinary proof drafting and /proof-checker for rigorous verification or submission acceptance.

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Manage a stateful, run-directory-based proof project: continuation across runs, run-local source bookkeeping, manual GPT Pro handoff packages when a local attempt stalls, and an optional DeepSeek second opinion as additional evidence only. Use when the user asks for proof-run orchestration, a GPT Pro handoff, or cross-run proof continuation — use /proof-writer for ordinary proof drafting and /proof-checker for rigorous verification or submission acceptance.

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Make a custom AI agent — Python or TypeScript/JavaScript, on a framework or hand-built — report what it did to Failproof AI, and run your own evaluator worker (the "eval pod") that scores those runs. Reach for it on vague phrasing too: "add observability to my agent", "why isn't my agent showing up?", "run an LLM judge on our own infra". Trigger when the user wants to: • plan an integration — which points in the agent loop to record; • instrument — add `failproofai-sdk` (Python) or `@failproofai/sdk` (Node, Bun, Deno, Next.js): turn on an adapter (LangChain/LangGraph, CrewAI, LlamaIndex, Pydantic AI, Vercel AI SDK, Mastra) or wire a hand-built loop; • verify — confirm events are written, or debug an integration that produces nothing; • evaluate — write, deploy or debug an Evaluator worker in Python or TypeScript. NOT for reading telemetry or scores that already landed (that's `fp-cloud-cli`), or deciding what is worth evaluating (that's `failproofai-eval-brainstorm`).

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The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?"

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Prove geometric theorems using Euclidean axiomatic methods, coordinate geometry, or vector methods with rigorous step-by-step logical structure. Covers direct proof, proof by contradiction, coordinate proofs, vector proofs, and handling of special cases and degenerate configurations. Use when given a geometric statement to prove, verifying a conjecture, establishing a lemma, converting geometric intuition into a rigorous proof, or comparing the effectiveness of different proof methods.

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Audit an existing mathematical, logical, algorithmic, or technical proof from its stated conclusion backward as a bounded AND/OR graph of exact obligations. Use to reconstruct conclusion dependencies, determine whether a proof-supplied route establishes the conclusion, or expose hidden assumptions, unmet side conditions, cycles, overly strong steps, or silent route switches. For a source-mapped Lamport rendering use convert-lamport, and for forward hierarchy, construct, and scope conformance use forward-lamport before this skill. This does not decide full theorem-level entailment by searching for a different proof; do not turn the audit into a linear reversed proof, exhaustive proof search, or replacement proof.

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Rigorous mathematical proof verification and fixing workflow. Reads a LaTeX proof, identifies gaps via fresh-agent Codex GPT-6-Astra ultra review, fixes each gap with full derivations, re-reviews, and generates an audit report. Base review is same-family provisional. Use when user says "检查证明", "verify proof", "proof check", "审证明", "check this proof", or wants rigorous mathematical verification of a theory paper.

日本語の概要は準備中です。原文の説明を表示しています。

Rigorous mathematical proof verification and fixing workflow. Reads a LaTeX proof, identifies gaps via cross-model review (external reviewer backend, ultra reasoning), fixes each gap with full derivations, re-reviews, and generates an audit report. Use when user says "检查证明", "verify proof", "proof check", "审证明", "check this proof", or wants rigorous mathematical verification of a theory paper.

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The way to answer "how are my production AI agents doing?" and to run the team's agent-observability deployment — reach for it even on casual phrasing that names no tool. Trigger when the user wants to: • inspect agent telemetry — did agents error/fail/go flaky; sessions, events, latency, token usage, slowest models; eval/quality scores and whether quality dropped; • operate the deployment — ack/assign/resolve/mute/dismiss issues (alerts, reports, and audit findings) with notes; run and triage audits; see who has access and change roles (e.g. read-only); create or scope API keys (e.g. a push-only CI key); change settings; run saved or ad-hoc ClickHouse queries. Served by the `fp` CLI against FailproofAI Cloud. NOT for writing or designing an evaluator service / scoring logic (that's `agenteye-evaluator`), adding SDK/instrumentation to your app (that's `failproofai-sdk`, imported as `failproofai_sdk`), debugging the collector/daemon, or unrelated dev work (why a build/CI run failed, rotating non-FailproofAI Cloud secrets).

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Publish, read, comment on, or edit markdown in Proof. Use for Proof links, sharing specs/plans/drafts, or publish handoffs from planning workflows; avoid proofread, math, evidence, or proof-of-concept meanings.

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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.

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Writes and reviews structured Lean 4 proofs and designs Lean libraries following Mathlib conventions. Use when proving theorems in Lean, formalizing mathematics or specifications in Lean 4, defining new types or definitions in a Lean library, reviewing Lean proofs for readability and maintainability, refactoring long tactic proofs into lemmas, filling in sorry placeholders in a Lean development, setting up CI or linters for a Lean project, diagnosing slow proofs or maxHeartbeats timeouts, or writing custom tactics, macros, or linters.

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Run the proofreading protocol on academic writing — papers or manuscripts. Checks grammar, typos, layout issues, consistency, and academic writing quality. Produces a report without editing files. Make sure to use this skill whenever the user wants surface-level writing errors found — not substantive academic critique. Triggers include: "proofread", "check for typos", "grammar check", "look for errors in my draft", "proofread all", "polish this", "check my writing", "are there any mistakes", "proofread before I send this", or when the user wants a clean-up pass rather than feedback on arguments or methods.

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This skill covers formal identification arguments and proofs in structural and reduced-form econometrics. Use when the user needs to prove or formalize that a parameter is identified — including writing identification propositions, stating regularity conditions, deriving rank conditions, or showing observational equivalence fails. Triggers on "identification proof", "identification argument", "identify the parameter", "show identification", "identification condition", "exclusion restriction proof", "rank condition", "order condition", "identification strategy formal", "nonparametric identification", "parametric identification", "local identification", "global identification", "observational equivalence", "identification at infinity", "completeness condition", "regularity conditions", "Rothenberg", "proof of identification", "identification result", "identified parameter", "point identified", "set identified", "partial identification".

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Analyze and explain why Isabelle or Coq proofs fail, identifying the root cause such as type mismatches, missing assumptions, incorrect goals, unification failures, or inapplicable tactics. Use when the user encounters proof failures, error messages in formal verification, stuck proof states, or asks why their Isabelle/Coq proof doesn't work.

日本語の概要は準備中です。原文の説明を表示しています。