Martin (1992: 378-9):
Realisation then is a technical concept embracing all these meanings. Grammaticalising the concept through Token°Value structures such as field is realised through the ideational resources of lexicogrammar should not be taken as delimiting in any way the meaning of realisation as outlined above. Technically it may in the long run prove helpful to replace the term realisation with a less directional term like redound (cf. Halliday in Thibault 1987: 619: "it shows just how the context of situation 'redounds with' (construes and is construed by) the semantic system."
 This is not true. See previous posts.
 This is the theoretical meaning of 'realisation'. The lower level of symbolic abstraction (Token) realises (Process: relational: identifying: intensive: symbol) the higher level of symbolic abstraction (Value).
 This misunderstands stratification. Field, like the rest of context, is realised in semantics realised in lexicogrammar. However, because Martin's "field" is actually semantics, it is (inadvertently) true to say that it realised in lexicogrammar.
 Realisation is the fundamental relation of semiotic systems (see Halliday & Matthiessen 1999: 447). It is the relation between the signified and the signifier, the two complementary sides of a linguistic sign.
 This is a direct contradiction of the claim made on the previous page. Martin (1992: 378):
During any such consideration of the consideration of one level of meaning in another, it needs to be kept in mind that as a theoretical construct realisation is not directional.
 Note that the strata in Halliday's formulation are semantics and context, not discourse semantics and register.
 Construing is distinct from realising. To construe is to intellectually construct. Halliday & Matthiessen (1999: 511):
The word “construe” is used to suggest an intellectual construction — though one that, of course, we then use as a guide to action.
To say that the context of situation 'redounds with' the semantic system is to say that the context of situation intellectually constructs and is intellectually constructed by the semantic system.