In this case, the small ship began with broken boards and after repairs the entire ship consisted of new boards, but the experience and history never left. That small ship began assumingly
at one point as a new ship and endured many obstacles over time to get to the point of needing complete repair. Answering the question whether the ship is the same even after the repairs, I believe it is, to think that the ship would stay in the same physical form forever is foolish. No matter what the object is, it will undergo change and just because change has occurred does not mean it is a complete different identity as it was prior. Identity is made up of a past, for the ship or even a human, a past filled with memories that cannot be erased. Furthermore, if identity was based off physical states how would one decipher two objects that are identical? For the ship, viewing its identity as a physical state would mean the ship not only changed when new boards were put on or when the new crew and new name occurred, but would have gone through numerous identities in the long lifespan of change. To view an identity purely as physical, the first identity would have no association to any current or future identities and in turn the history and experiences that the ship faced would not associate as well.