Topology or Metaphor? Substrate Combinatorics, Emergent Invariants, and Formal Obligations for Models of Language and Subject Development

Topological vocabulary appears in models of neural activity, semantic organization, linguistic structure, and development, and its inferential content depends on the object to which topology is assigned. This paper poses that question inside a background-independent substrate in which topology is not metaphorical: a group field generates two-complexes whose combinatorics constitute the theory's own data. The reformulation sharpens rather than dissolves the problem, because two questions separate. At the substrate level a new result shows that combinatorial topology is underdetermined by the subsystem's accessible boundary algebra: complexes differing by a closed component induce identical accessible states while differing in their invariants, so a system can carry literal topology that nothing available to it records. At the effective level, topological claims about language, categories, and development remain governed by a warrant architecture, and a two-level version of that architecture is supplied, together with the result that invariants do not transfer across coarse-graining without a stated preservation condition. Several separation results are retained. An observationally silent factor changes the fundamental group without changing behavior; recognition of unbounded bracket nesting and nontrivial fundamental group vary independently; a contractible carrier supports arbitrarily many category labels; homeomorphic carriers support dynamically inequivalent maps; and a bifurcation can occur on a fixed ambient topology. A positive construction is retained and rebased on accessible response laws: intervention-indexed responses induce a pseudometric on developmental histories whose metric quotient admits a Vietoris–Rips filtration, and uniform pairwise metric error at most δ yields a δ-interleaving and bottleneck error at most δ. The proposal that universal grammar is a topological invariant is preserved as an explicitly labelled conjecture with its obligations and its existing obstruction stated. The position is constructively conservative.