[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M79CSSDSTMTH330Z8H8DNZXA":3,"skill-same:01M79CSSDSTMTH330Z8H8DNZXA":59},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":18,"publishedAt":19,"linkOnly":20,"markdownContent":21,"markdownBody":22,"frontMatter":23,"refName":29,"commitSha":30,"skillDirectory":31,"forksCount":32,"repositoryHtmlUrl":33,"repositoryHomepageUrl":34,"ownerHtmlUrl":35,"ownerBlogUrl":36,"ownerDescription":37,"updatedAt":38,"install":39,"resources":52},"01M79CSSDSTMTH330Z8H8DNZXA","tensor-calculus-differential-forms",null,"Tensor Calculus and Differential Forms in Mathematics (Geometry). Theoretical foundations, governing equations, analytical problem-solving methods, and typical archetypes.","hamzabellouch\u002Fagent-skills","hamzabellouch","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F237856042?v=4","01M79BRYW7XAMK3YDWQEMTWGWS","Hamza Bellouch","01M79BRYWXQV3JK2TGVTX8GN2A",8,"MIT","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FMath\u002FMathematical_Methods_for_Physics_and_Engineering\u002Ftensor-calculus-differential-forms\u002FSKILL.md",[],[],"2026-11-15 14:19:17",false,"---\nname: tensor-calculus-differential-forms\ndescription: Tensor Calculus and Differential Forms in Mathematics (Geometry). Theoretical foundations, governing equations, analytical problem-solving methods, and typical archetypes.\nmetadata:\n  id: math.tensor_calculus\n  domain: Mathematics\n  subdomain: Geometry\n  difficulty: 5\u002F5\n---\n\n# Tensor Calculus and Differential Forms\n\n**ID:** `math.tensor_calculus`  \n**Domain:** Mathematics → Geometry  \n**Difficulty:** 5\u002F5\n\n## Prerequisites\n- math.vector_calculus\n- math.linear_algebra\n\n## Core Concepts\n- tensors\n- index notation\n- covariant\u002Fcontravariant\n- metric tensor\n- connection\n\n## Key Equations\n$$\nT^{\\mu\\nu} = \\Lambda^\\mu_{\\ \\alpha}\\Lambda^\\nu_{\\ \\beta}T^{\\alpha\\beta}\n$$\n$$\n\\Gamma^\\lambda_{\\mu\\nu} = \\tfrac12 g^{\\lambda\\sigma}(\\partial_\\mu g_{\\sigma\\nu} + \\partial_\\nu g_{\\sigma\\mu} - \\partial_\\sigma g_{\\mu\\nu})\n$$\n\n## Methods\n- Manipulate indices carefully\n- Raise\u002Flower with the metric\n- Compute covariant derivatives\n\n## Typical Problem Types\n- Stress-energy tensor\n- Curvature computation\n- Relativistic kinematics\n\n## Common Pitfalls\n- Summing over the wrong pair of indices\n- Mixing up upper\u002Flower indices\n\n## Related Skills\n- rel.general.geodesics\n- rel.special.four_vectors\n\n## References\n- Schutz Geometrical Methods\n- Misner Thorne Wheeler Ch.3\n","# Tensor Calculus and Differential Forms\n\n**ID:** `math.tensor_calculus`  \n**Domain:** Mathematics → Geometry  \n**Difficulty:** 5\u002F5\n\n## Prerequisites\n- math.vector_calculus\n- math.linear_algebra\n\n## Core Concepts\n- tensors\n- index notation\n- covariant\u002Fcontravariant\n- metric tensor\n- connection\n\n## Key Equations\n$$\nT^{\\mu\\nu} = \\Lambda^\\mu_{\\ \\alpha}\\Lambda^\\nu_{\\ \\beta}T^{\\alpha\\beta}\n$$\n$$\n\\Gamma^\\lambda_{\\mu\\nu} = \\tfrac12 g^{\\lambda\\sigma}(\\partial_\\mu g_{\\sigma\\nu} + \\partial_\\nu g_{\\sigma\\mu} - \\partial_\\sigma g_{\\mu\\nu})\n$$\n\n## Methods\n- Manipulate indices carefully\n- Raise\u002Flower with the metric\n- Compute covariant derivatives\n\n## Typical Problem Types\n- Stress-energy tensor\n- Curvature computation\n- Relativistic kinematics\n\n## Common Pitfalls\n- Summing over the wrong pair of indices\n- Mixing up upper\u002Flower indices\n\n## Related Skills\n- rel.general.geodesics\n- rel.special.four_vectors\n\n## References\n- Schutz Geometrical Methods\n- Misner Thorne Wheeler Ch.3\n",{"name":5,"metadata":24,"description":7},{"id":25,"domain":26,"subdomain":27,"difficulty":28},"math.tensor_calculus","Mathematics","Geometry","5\u002F5","main","e905af21e5f1e1c3ca605e9656c3a7930360a84e","Math\u002FMathematical_Methods_for_Physics_and_Engineering\u002Ftensor-calculus-differential-forms",1,"https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills","https:\u002F\u002Fhamzabellouch.github.io\u002F","https:\u002F\u002Fgithub.com\u002Fhamzabellouch","hamzabellouch.github.io","CEO & Founder of @tknoglobal | Researcher in Technology & Applied Sciences.","2026-10-17 03:20:19",{"source":8,"skillName":5,"commands":40,"prompt":50,"zipAvailable":51},[41,44,47],{"tool":42,"command":43},"npx","npx skills add hamzabellouch\u002Fagent-skills --skill tensor-calculus-differential-forms",{"tool":45,"command":46},"bunx","bunx skills add hamzabellouch\u002Fagent-skills --skill tensor-calculus-differential-forms",{"tool":48,"command":49},"pnpm","pnpm dlx skills add hamzabellouch\u002Fagent-skills --skill tensor-calculus-differential-forms","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FMath\u002FMathematical_Methods_for_Physics_and_Engineering\u002Ftensor-calculus-differential-forms\u002FSKILL.md",true,[53],{"path":54,"resourceType":55,"resourceTypeDesc":56,"sizeBytes":57,"sourceHtmlUrl":58},"metadata.json","REFERENCE","参考文档",1211,"https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FMath\u002FMathematical_Methods_for_Physics_and_Engineering\u002Ftensor-calculus-differential-forms\u002Fmetadata.json",[60,67,74,81,88,95],{"skillNo":61,"name":62,"nameZh":6,"description":63,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":64,"categories":65,"keywords":66,"publishedAt":19},"01M79FHH2H815A9TAP6WNKH4Q8","security-audit","Comprehensive security guidance, source code audit, vulnerability assessment, and penetration test review for codebases, APIs, microservices, CLI tools, libraries, and LLM-backed applications. Triggers on requests to audit a codebase, conduct security reviews, find vulnerabilities or flaws, pen-test source code, or when the user asks in Arabic (فحص أمني، تدقيق الكود أمنياً، مراجعة الثغرات، فحص أمان المشروع). Supports Guidance mode (focused review) and Full Audit mode (deterministic 6-phase harness).","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FSecurity\u002FSecurity_Audit_and_Code_Review\u002Fsecurity-audit\u002FSKILL.md",[],[],{"skillNo":68,"name":69,"nameZh":6,"description":70,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":71,"categories":72,"keywords":73,"publishedAt":19},"01M79FHBGXVBY6VQ1X7ETAZMF1","malware-analysis-reversing","Production malware analysis workflows, reverse engineering methodologies, isolated sandbox triage, static\u002Fdynamic binary analysis, memory forensics, and YARA detection rule authoring.","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FSecurity\u002FOffensive_Security_and_Pentesting\u002Fmalware-analysis-reversing\u002FSKILL.md",[],[],{"skillNo":75,"name":76,"nameZh":6,"description":77,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":78,"categories":79,"keywords":80,"publishedAt":19},"01M79FH6EACDR801TZCE4R8SAC","application-security-pentesting","Production Application Security (AppSec) standards, OWASP Top 10 vulnerability remediation, SAST\u002FDAST pipeline integration, secure code review, threat modeling, and defensive security posture.","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FSecurity\u002FOffensive_Security_and_Pentesting\u002Fapplication-security-pentesting\u002FSKILL.md",[],[],{"skillNo":82,"name":83,"nameZh":6,"description":84,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":85,"categories":86,"keywords":87,"publishedAt":19},"01M79FH0VKVT44FK923K520ZQA","oauth2-oidc-security-flows","Implement enterprise OAuth 2.1 and OpenID Connect (OIDC) authorization code flow with Proof Key for Code Exchange (PKCE), state and nonce verification, refresh token rotation, token revocation, and centralized IdP federation (Keycloak, Auth0, Okta). Trigger when building secure authentication, single sign-on (SSO), or third-party delegated authorization.","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FSecurity\u002FIdentity_and_Access_Management_IAM\u002Foauth2-oidc-security-flows\u002FSKILL.md",[],[],{"skillNo":89,"name":90,"nameZh":6,"description":91,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":92,"categories":93,"keywords":94,"publishedAt":19},"01M79FGVVB3R4T88XXD8FRSV5B","jwt-session-management-hardening","Harden JWT-based authentication and session lifecycles using asymmetric signing (RS256\u002FEdDSA), JWKS rotation, strict claims validation, Redis-backed sliding window sessions, revocation lists, and secure HttpOnly cookie storage. Trigger when implementing token validation, session revocation, or hardening API authentication.","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FSecurity\u002FIdentity_and_Access_Management_IAM\u002Fjwt-session-management-hardening\u002FSKILL.md",[],[],{"skillNo":96,"name":97,"nameZh":6,"description":98,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":99,"categories":100,"keywords":101,"publishedAt":19},"01M79FGNCPZ85CVEY0B3NE4H3B","soc2-compliance-automation","Best practices for implementing SOC 2 Type II compliance controls, continuous evidence collection, infrastructure policy-as-code, and automated security monitoring. Use when automating Trust Services Criteria (Security, Availability, Confidentiality, Processing Integrity, Privacy), audit logging, IAM least privilege, or CI\u002FCD security gates.","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FSecurity\u002FGovernance_Compliance_and_Legal_Tech\u002Fsoc2-compliance-automation\u002FSKILL.md",[],[]]