Why it is a question
THEORY-256, narrowed on 2026-10-19, holds two things. When a generator’s operators factor as a tensor product, its predictive state embeds losslessly and linearly in per-factor subspaces of total dimension Σ(d_n − 1). And 4-layer GPT-2-style transformers trained by next-token prediction on five Mess3 and Bloch Walk factors settle near that dimension, and reach it first under the token-noise construction tested. Until that date, THEORY-256’s promote_when asked for a replication. At the owner’s direction, from the promotion audit’s batch 019 (ADR-047 v3: one study read in full can carry a title that claims no more than it measured), the THEORY was narrowed and promoted, and the condition moved here unchanged.
It is open because LIT-986 varies the data within one synthetic family and keeps the objective fixed, and it argues the loss gap in the noisy case from the construction rather than reporting it (NOTE-758). It refines QUESTION-060’s question of whether the objective or the architecture fixes what a trained network represents.
What would answer it
The condition formerly on THEORY-256, unchanged. A replication on a different family of factored generators, or under a second objective on the same data, that measures the dimension and per-factor orthogonality of the learned representation. In the noise experiment it would also report the loss gap between the factored and joint representations at each noise level. The account is refuted by a transformer trained on a lossless factored process, with room for the joint representation, that settles near the joint dimension. It is also refuted by a lossy process on which training reaches the joint representation without first passing near the factored one. Linear decodability of each factor’s belief alone cannot settle it, since a representation with overlapping factor subspaces also supports accurate linear readout (LIT-986, App. H.1.2).