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lyap-define

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Mis à jour26 juin 2026 à 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.

Installation

Installer avec Codex ou Claude Copiez ce prompt, collez-le dans Codex, Claude ou un autre assistant, puis laissez-le vérifier la page du skill et l'installer pour vous.

Exécuter dans Manus

Source

pepflow-lib

pepflow-lib/PEPFlow

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Métiers associésSOC

Basé sur la classification professionnelle SOC

Développeurs de logicielsProfessions informatiques et mathématiques·SOC 15-1252

Explorateur de fichiers

3 fichiers

SKILL.md

readonly

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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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.