Why it is a question
At U55 the owner asked the assistant to “develop this further”, and A198 built a ten-section construction on character-like signatures (TERM-041) for communicative kinds (TERM-040). Its §V brought in Tannaka reconstruction as a model, which the workbench says it “correctly labelled ‘an inspiration rather than an applicable theorem’”, and it asked the question above (workbench 2026/10/10/040457).
The model. Tannaka (1939), and later Krein, showed that a compact group can be recovered from its representations: from the category of its representations together with the functor that forgets each one down to its underlying vector space. Grothendieck and Deligne generalized this to Tannakian categories. This summary is the assistant’s, given from memory. The record holds no reading of Tannaka or Krein.
Read across. A communicative kind would play the group’s part. Its observable realizations (translations, retellings, renderings in other media) would play the representations, and the transformations between them the morphisms. The question is whether the kind’s admissible symmetries, what it can undergo and remain itself, could be recovered from enough of its realizations alone. That would make QUESTION-029’s “how can it be recognized apart from any one representation” exact, which is why this question refines it.
What an answer needs. A precise sense of “sufficiently rich”. Something that plays the role of the forgetful functor. And the structure on the realizations that Tannaka reconstruction depends on, such as a tensor product, which communicative realizations may simply lack. The label A198 gave it, inspiration rather than theorem, says that none of this is in hand. An answer could also be negative: a showing that communicative realizations lack the structure any such reconstruction needs.
Neighbours. QUESTION-001 asks whether pragmatic identity can be reconstructed from context-relative judgements, which is reconstruction from a different kind of data. QUESTION-027 asks for a relational signature that is stable and discriminating, which is the invariant side of the same problem.
How it was dropped. A198 posed it. One turn later the second crystallized argument (A203, TERM-052) left out Tannaka with no turn deciding to. Whether the question dissolved as the argument matured or was simply not carried forward, the exchange does not say. Filing it gives it a status, which is how the record can tell the two apart.
Note of 2026-10-11: material in the record that may bear on this
A synthesis review of 2026-10-11 found these entries bearing on this
question without being linked to it. Each is listed for what its title
says; none has yet been assessed as an answer, and none is linked by
answers.
- CLAIM-132: Characters classify finite-dimensional representations of a finite or compact group up to isomorphism only…
- THEORY-019: Symmetry forces spectral degeneracy but degeneracy does not identify a symmetry: an operator commuting…
- THEORY-002: Convergence of representations, in the Platonic hypothesis’s sense, is convergence of kernels, which fixes…
CLAIM-132 and THEORY-019 both lean toward a negative answer: characters fix neither the group nor its action, and spectral degeneracy does not identify a symmetry.
Note of 2026-10-12: an assessed result filed on 2026-10-10
The note of 2026-10-11 says none of the listed material has been assessed. PR #121’s round of 2026-10-10 filed one assessed result on the construction this question comes from. CLAIM-249, granted and Active, says “The transformations the line studies are not group elements”, and that the group “has to be a symmetry group of the situation that the analyst chooses”. It also shows that “the same character” across realizations is relative to a chosen correspondence. That leans toward the negative answer this question allows for, beside CLAIM-132 and THEORY-019. CASE-057 is a constructed case of such a chosen symmetry: swapping the two persons of a dyad changes nonreciprocal T/V address and leaves reciprocal address fixed.