Aircraft technician reported incorrect serial number part was found installed during PW4000 engine disassembly.

Narrative

On Day 0; I was working dayshift PW4000 subassembly with a trainee. The workscope for Engine S/N XXXXXX; stated the Low Pressure Turbine (LPT) module; (module 1; S/N XXXXXY) was to be disassembled to access a low cycles remaining 3rd stage airseal. After removing the disk/airseal assy.; we discovered the serial number on the airseal did not match maintenance software system records. Maintenance software system record shows Part X was onlogged to this module several years ago on Day 0; however the S/N of the installed airseal is Part Y; and maintenance software system records shows that airseal installed on PW4000 engine S/N XXXXXZ. Fortunately; engine XXXXXZ was recently removed from service and is currently waiting induction to the ZZZ1 engine shop. Although we won't know for sure until we can verify the S/N; it is highly likely that S/N XXXX airseal will be found installed on this engine.Further investigation showed that two LPT modules with successive numbers (module 2 and module 3); were being built at almost the same time. Module 3 had it's airseal installed on Day 2 whereas module 2 had it's airseal installed on Day 16. Standard procedure is to build up and balance the disk assemblies in order (3rd-4th-5th-6th) and then place them on a pie cart where they are later used in module build-up. During this timeframe; we were having problems with fitment of 3rd stage disk/airseal assemblies during module build. The tie rod bolts would not fit through all the holes; and it was common to reject the disk during module build and return it to the disk build-up and balance area. However; after a check of job cards for both engines; I could find no record that any swapping of parts occurred. There is no non-routine; nor is there any 2nd build paperwork indicating the airseal was replaced at a later date. Any later swapping of airseals would require that the disk assembly be returned to the disk build-up and balance area to be rebalanced. This leads one to believe that the Technician balancing the disk/blade assembly accidentally installed the wrong airseal; but signed off the correct paperwork. However that conclusion would be wrong.We know that the balance Technician could not have installed the wrong airseal at disk build-up and balance as both airseals were not uninstalled and present at the same time. Onlogging of engine parts occurs in a separate building; and when all or most parts are present; the module is moved to 4000 subassembly for disk build-up and balance. Airseal XXXX was onlogged Day 0; then moved to subassembly and was installed Day 2 per Inspect and Repair (I&R) Tag; completing that disk assembly. This assembly was then moved to the module build-up area. Airseal XXXY was in a separate building when it was onlogged on Day 13; then later moved to 4000 subassembly for disk build-up and balance. Airseal XXXY was installed on Day 21 per I&R Tag; completing that disk assembly. Both airseals were onlogged and installed by four different people. It is highly unlikely that two different onlog Inspectors and two different Technicians failed to verify the serial number on a onlogged life limited part (LLP) part. So; the only logical conclusion is that both Onlog Inspectors onlogged the correct S/N airseal; Technicians installed the correct S/N airseal on each disk assembly and later during the module build-up process a bolt alignment problem occurred. At someone's suggestion; airseals were swapped to see if that solved the bolt alignment problem; which it did. Then both disk assemblies were rebalanced and returned to their respective modules for assembly. For reasons unknown; no paperwork was generated to justify this work; nor was Inspection notified so the maintenance software system records could be corrected. As outrageous as this appears; it is the only scenario that makes sense.Suggestions: Since both parts have the same part number; and the part number was valid for this configuration; then an incorrect part number was not installed; however an incorrect Serial Number was installed. The 3rd stage airseal is a Life Limited Part (LLP); and maintenance records needs to verify that we did not exceed hours/cycles for this engine (S/N XXXXXX). When the other airseal is located; then maintenance records must also verify hours/cycles were not exceeded for that engine. When possible; it would be helpful not to use sequential numbers for builds...module 2 should not be built at the same time as module 3 is being built.