Martin (1992: 130):
In addition there are four TRANSITIVITY functions, typically realised by nominal groups, which do not necessarily realise participants: Attribute, Range and Circumstances [sic] of Extent and Role.
Attributes describe or classify participants; they are realised by adjectives, indefinite nominal groups or attitudinal superlatives. Their indefinite deixis in contexts where they are describing participants that have already been introduced gives away the fact that they are not realising a participant themselves:
[3:67] He was silly/a silly man/the silliest thing
Carrier Process Attribute
 To be clear, Martin has defined 'participant' in terms of nominal groups functioning as the Agent or Medium of a clause. This definition already excludes Attribute, Scope (Range) and all circumstances.
Moreover, it also excludes all the other Range functions: Behaviour, (emanating) Phenomenon, Verbiage, Attribute, (decoding) Value, as well as all the Beneficiary functions: Client, Recipient, Receiver.
 To be clear, in SFL theory, Attributes are participants. An Attribute is the class to which an entity (the Carrier participant) is ascribed (Halliday & Matthiessen 2014: 267).
 This is only exceptionally true. In almost all cases, superlatives feature in identifying clauses, not attributive clauses.
 This confuses interpersonal deixis with textual reference. Non-specific Deictics serve no reference functions.
 This confuses ideational denotation with textual reference.
 This is a non-sequitur, even in Martin's terms (ideational denotation). Consider the following:
At the party, Jim met Anne. Anne was a lecturer.
In the first clause the participant Anne is introduced. In the second clause, the Attribute a lecturer realises the same participant.