# NFT-Based Framework for Digital Twin Management in Aviation Component Lifecycle Tracking
## 3 Results
### Mathematical Framework for NFT-Based Lifecycle Management in Aviation
The data typically consist of details of the maintenance tasks performed (e.g., repairs, replacements, adjustments, inspections), parts or components involved in the maintenance process, tools, materials, and resources used during the maintenance, technicians or personnel responsible for performing the maintenance, the time and date when the maintenance was carried out, any observations or issues encountered during the maintenance, and the results of the maintenance (e.g., whether the part was restored to serviceable condition). Linking this maintenance NFT to the part's NFT:  
\[N_{i}^{updated}=N_{i}\bigoplus N_{M_{j}}\]  
3. Certification and compliance For certification, a unique \(N_{C_{n}}\) is created for each certification process \(C_{n}\). This NFT tracks the entire certification lifecycle:  
\[N_{C_{n}}=f\Big{(}C_{n},A_{appl}\Big{)}\]  
where \(A_{appl}\) refers to the application for certification data. This represents the initial request or submission made for the certification of an aircraft part, system, or process. The data typically includes the details of the part or system seeking certification, information about the applicant (manufacturer, operator, or other entity), the specific certification requirements or standards being applied for, supporting documentation related to compliance, testing, and prior assessments, any regulatory references or guidelines that the certification must adhere to. \(N_{C_{n}}\) is updated with assessments, testing results, and final certification status:  
\[N_{C_{n}}^{t+1}=N_{C_{n}}^{t}\bigoplus\Big{(}A_{test},T_{result},C_{certified} \Big{)}\]  
where \(A_{test}\) is the assessment, \(T_{result}\) is the test result, and \(C_{certified}\) is the certification issuance. 4. Supply chain management  
The NFT \(N_{i}\) for each part \(P_{i}\) is created upon manufacturing and updated through the supply chain process:  
\[N_{i}^{t+1}=N_{i}^{t}\bigoplus\Big{(}L_{warehouse},O_{order},S_{shiping},R_{ received}\Big{)}\]  
where \(L_{warehouse}\) is the warehouse location, \(O_{order}\) is the order data, \(S_{shiping}\) is the shipping information, and \(R_{received}\) confirms receipt of the part. 5. Flight logs  
For each flight \(F_{k}\), an NFT \(N_{F_{k}}\) is created at the beginning of the flight:  
\[N_{F_{k}}=f\Big{(}F_{k},\ D_{pre-flight}\Big{)}\]  
where \(D_{pre-flight}\) refers to the pre-flight data. These include all relevant information and checks performed before an aircraft's flight. The data typically consist of flight plan details, such as the route, departure, and destination; aircraft status, including fuel levels, weight distribution; and any pre-flight inspections, crew assignments (including pilot and crew member information, qualifications, and duty hours); weather conditions and forecasts that may affect the flight; aircraft systems checks, covering engines, avionics, hydraulics, and other critical systems; regulatory compliance checks, ensuring that the aircraft and crew meet all legal and safety requirements before departure; any notable issues or observations during the pre-flight inspection. \(N_{F_{k}}\) is updated throughout the flight, recording in-flight data and post-flight details:  
\[N_{F_{k}}^{t+1}=N_{F_{k}}^{t}\bigoplus\Big{(}D_{in-flight},D_{post-flight},C_{ verified}\Big{)}\]  
where \(D_{in-flight}\) is in-flight data, \(D_{post-flight}\) is post-flight data, and \(C_{verified}\) is compliance verification. 6. Ownership and leasing  
Each aircraft is assigned a unique NFT \(N_{A}\) upon manufacture. Ownership or lease events update the NFT with ownership transfers \(O_{transfer}\) or lease agreements \(L_{lease}\):  
\[N_{i}^{t+1}=N_{i}^{t}\bigoplus\left(D_{inst},A_{craft},H_{flight},D_{op},M_{i}\right)\]0  
where \(R_{return}\) is the return of the aircraft at the end of a lease. 7. Technical documentation For each technical document \(D_{l}\), an NFT \(N_{D_{l}}\) is created to represent the document.