This thread is about the concept of ID. The killer had an ID. I.e. he had an identity. The most important historical aspect of the ID is the strictly personal identity, which is connected to the biography of a specific individual. Strictly means it must be connected to this individual but not to many others.
The fewer individuals with the same personal identity, the better. Otherwise it will not be strictly personal. So a strictly personal ID is the theoretical concept.
A very important aspect of the strictly personal identity is the recurrence of the same type of indications for it in a case. The indications should be connected to one strictly personal identity but not to others.
The more indications you find the more reliable the case will be, since it is very difficult to get a larger set of indications for one ID.
The strictly personal ID is very useful when analyzing the case. You can use it on the victimology, the signature and the MO.
To be able to do this you need to know something about the individual and his personal ID. If you don´t, you can´t do it.
Let´s try this on Lechmere. The hypothesis is that Lechmere had a component in his ID which connected him to the murder sites. This component is his "geographical pattern" (GP). The GP is constructed from his home address, working address and the address of his mother.
Now - is the GP connected to Lechmere´s strictly personal ID?
Is Lechmere the only person, or even one of a few people, who lived and worked in the area and had his mother in the same area?
No. He was just one of many, many others. Hundreds, thousands in fact.
So – this is the result of testing the ID of Lechmere on the case - the GP is not strictly personal and does not reveal Lechmere´s ID as being connected to the murders, since a lot of people had his GP.
So the concept of the strictly personal ID is useful for the assumptions about who the killer was. You can test different aspects of an ID on the case data.