Paik Heavy Industries, the Widmore Labs and the Hanso Foundation could have serious business together - mainly because of the DHARMA Initiative.
The Greek Letter Phi is an acronym for Paik Heavy Industries.
PHI could also be relating to Dan Brown's "The Da Vinci Code," in which Robert Langdon talks about PHI and Divine Intervention.
Could be somehow related to a note jotted on the Blast Door map in the upper right hand corner, which states "Possible manufacturing facility with light industrial equipment".
Paik Heavy Industries might have constructed the hatches on the island, or built airplanes for Oceanic.
Boeing builds airplanes for Oceanic.
The "Rabbit's Foot" in Mission Impossible 3 could be a product of Paik Heavy Industries. J.J. Abrams directed it, the Paik logo is on the building where Ethan (Tom Cruise) retrieve the "Rabbit's Foot", and The Hanso Foundation is mentioned in the special thanks section of the film's credits. Plus, it is never explained at the end of the movie, continuing the mystery.