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Ejecuta cualquier Skill en Manus con un clic

lyap-define

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Actualizado26 de junio de 2026 a las 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.

Instalación

Instalar con Codex o Claude Copia este prompt, pégalo en Codex, Claude u otro asistente, y deja que revise la página de la skill y la instale por ti.

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Fuente

pepflow-lib

pepflow-lib/PEPFlow

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SKILL.md

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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.

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.

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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.

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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.