There are many different accounts of "information structure" ("information packaging", "topic-comment", "theme-rheme distinction"). Is there a "frameworkless" formal definition of what topic/focus is? Is information structure part of syntax or semantics or is it an independent level of representation? What does "discourse-configurational" mean?
There's a purely logical definition (given in the MIT Encyclopedia of cognitive science): If sentence s is uttered in context c, then p is a presupposition in s if c entails p. This definition is more or less identical with most linguistic definitions and is equal to that of Jerry Hobbs if "entails" is taken to mean "abductively proves". Rephrased less formally, presuppositions (topics) can be inferred from context (that is, they're predictable from previous discourse and/or shared background knowledge). The remainder of the sentence is focal ("preferred content" in the MIT Encyclopedia mentioned above).
Informally it's often said that the focus of a sentence is what's being said about its topic. In formal logic, focus is then taken to be an "Aristotelian" predicate. The unmarked sentence John sings (John topical, sings focal) is formalized as sing(John), whereas JOHN sings (John focal, sings topical) would be λP.P(John)(sing).
Discourse-configurational languages assign topic/focus structurally. Hungarian is said to be one (Kiss, who coined the term "discourse-configuratonal"), other examples include Russian (King) or Georgian (Meurer). This approach only accounts for nonemotive sentences since intonation can mix things up.
In most languages word order is more or less iconic with respect to information structure. Aside from word order and intonation, some languages have morphological discourse markers. There are topic markers in Japanese and Korean, focus markers in Eastern Armenian and both in (many dialects of) Quechua, to name just a few.
As for formal representation in frameworks, FGD uses an ordering on nodes in deep syntax trees to express information structure. In LFG, there's a separate i(nformation)-structure for discourse functions. In the abductive framework of Hobbs, there's no implicit formalization but whatever can't be inferred/proven is taken to be focal.
I have one for you, but it's not frameworkless. I don't see how there could ever be a frameworkless formal definition (since "formal" means it is part of a formalized theory).
A topic is a clause constituent bearing the grammatical relation 0. This is to be understood as part of an extended version of the theory Relational Grammar, due to Paul Postal and David Perlmutter (see Relational Grammar). The 0 is a term relation in the same series as 1 (subject), 2 (direct object), and 3 (indirect object). RG did not actually have a 0 -- I've added that.
The 0 relation for topic is subject to the same laws and constraints of RG as the other term relations, the most interesting of which is the Stratal Uniqueness Law, which requires that each term relation appear no more than once in a stratum. (A stratum is something like a derivational level.)
I don't know what a frameworkless account of anything would be, but this paper is not meat grinder-theoretic and is intelligible on its own.