원클릭으로 Manus에서 모든 스킬 실행

lyap-define

스타19

포크0

업데이트2026년 6월 26일 10:35

Build Lyapunov partial-sum sequences from PEPFlow full-PEP dual certificates and verify their rank profile. Use when the user asks for /lyap-define, lyap-define, Block 3, defining the Lyapunov function, constructing V_k partial sums, or generating examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b3.json from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b2.json.

설치

Codex 또는 Claude로 설치 이 Prompt를 복사해 Codex, Claude 또는 다른 어시스턴트에 붙여 넣으면 Skill 페이지를 검토하고 설치를 진행할 수 있습니다.

Manus에서 실행

출처

pepflow-lib

pepflow-lib/PEPFlow

GitHub 저장소 열기 Creator 저장소 보기

다운로드

Manus에서 실행

Lyap Define

Quick Start

Read references/workflow.md, then execute it as the authoritative Block 3 workflow.

Start from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b2.json and preserve the workflow's dual extraction, grouping-code construction, partial-sum verification, and examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b3.json output.

Codex Adaptation

Recreate the PEP context exactly as in the setup module before evaluating expressions.
Keep interpolation duals and extra named duals separate until the grouping is verified.
Prefer small, inspectable grouping code that can be stored in JSON and re-executed by lyap-vectors.
Before using a generic LDL decomposition for S, inspect any existing examples_peppy/_references/{ALGO_NAME}/ notebook/module for verified S_guess, S_piece, square-term, or rank-profile constructions; adapt those proof-specific pieces first, and do not treat missing per-step fields in {ALGO_NAME}_b2.json as proof that no known decomposition exists.
Use the PEPFlow Lyapunov sign convention: define V_k so the final proof makes V_k nonincreasing (or at least V_k <= V_0) under the chosen residual convention. Do not accept a grouping merely because its symbolic residual is zero; also verify the inequality direction used in the telescoping proof.
Verify the rank profile numerically and state the tolerance.
In notebooks, the visible partial-sum construction cell should print ranks one per line as rank V_k: r, include a blank line after rank V_0, then print the interior-rank consistency check in the same cell; do not print every grouped dual term or add a separate rank-profile dump cell by default.
Keep workflow artifacts under examples_peppy/{ALGO_NAME}/state/.
If ranks are inconsistent, inspect indexing and dual grouping before changing the mathematical ansatz.

Related Skills

Run lyap-vectors next to identify special spanning vectors.

이 저장소의 다른 Skills

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lyap-closed-form

pepflow-lib/PEPFlow

Derive closed-form Lyapunov coefficients from Block 4 structure, solve symbolic recursions, verify proof identities, and produce a Lyapunov proof notebook. Use when the user asks for /lyap-closed-form, lyap-closed-form, Block 5, closed-form Lyapunov proof, symbolic recursion for V_k, or updating examples_peppy/{ALGO_NAME}/{ALGO_NAME}_example_lyap.ipynb from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b4.json.

2026-06-2619

lyap-vectors

pepflow-lib/PEPFlow

Identify special vectors spanning Lyapunov partial sums and extract coefficient patterns as functions of k. Use when the user asks for /lyap-vectors, lyap-vectors, Block 4, special Lyapunov vectors, low-rank decomposition of V_k, coefficient pattern extraction, or generating examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b4.json from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b3.json.

2026-06-2619

pep-full-proof

pepflow-lib/PEPFlow

Find tight PEPFlow performance guarantees with explicit full-PEP dual certificates, sparse lambda structure, S matrices, and algebraic proof state. Use when the user asks for /pep-full-proof, pep-full-proof, Block 2, full PEP proof, sparse dual certificates, or generating examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b2.json from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b1.json.

2026-06-2619

pep-implement

pepflow-lib/PEPFlow

Create or validate a PEPFlow algorithm setup module, initialize the Lyapunov notebook, and run initial numerical convergence checks. Use when the user asks for /pep-implement, pep-implement, Block 1, implementing a new PEPFlow example, creating examples_peppy/{ALGO_NAME}/{ALGO_NAME}_setup.py, or turning an algorithm description into a PEPFlow setup plus examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b1.json state.

2026-06-2619

name	lyap-define
description	Build Lyapunov partial-sum sequences from PEPFlow full-PEP dual certificates and verify their rank profile. Use when the user asks for /lyap-define, lyap-define, Block 3, defining the Lyapunov function, constructing V_k partial sums, or generating examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b3.json from examples_peppy/{ALGO_NAME}/state/{ALGO_NAME}_b2.json.

Lyap Define

Quick Start

Read references/workflow.md, then execute it as the authoritative Block 3 workflow.

Codex Adaptation

Recreate the PEP context exactly as in the setup module before evaluating expressions.
Keep interpolation duals and extra named duals separate until the grouping is verified.
Prefer small, inspectable grouping code that can be stored in JSON and re-executed by lyap-vectors.
Before using a generic LDL decomposition for S, inspect any existing examples_peppy/_references/{ALGO_NAME}/ notebook/module for verified S_guess, S_piece, square-term, or rank-profile constructions; adapt those proof-specific pieces first, and do not treat missing per-step fields in {ALGO_NAME}_b2.json as proof that no known decomposition exists.
Use the PEPFlow Lyapunov sign convention: define V_k so the final proof makes V_k nonincreasing (or at least V_k <= V_0) under the chosen residual convention. Do not accept a grouping merely because its symbolic residual is zero; also verify the inequality direction used in the telescoping proof.
Verify the rank profile numerically and state the tolerance.
In notebooks, the visible partial-sum construction cell should print ranks one per line as rank V_k: r, include a blank line after rank V_0, then print the interior-rank consistency check in the same cell; do not print every grouped dual term or add a separate rank-profile dump cell by default.
Keep workflow artifacts under examples_peppy/{ALGO_NAME}/state/.
If ranks are inconsistent, inspect indexing and dual grouping before changing the mathematical ansatz.

Related Skills

Run lyap-vectors next to identify special spanning vectors.