Why it is a question
Three criteria.
- Evidence (CLAIM-154). Keep a distinction when d’² exceeds the Occam cost. It is about the data and grows with copies.
- Retrieval (CLAIM-307). Build a distinction when finding an item in time requires it. It is about tasks and deadlines and falls with copies.
- Persistence. The owner’s LEGO monograph, Part III, worked example “Archetype Persistence via Rank, Blowup, Compression”. Its co-occurrence matrix over four parts (wing, engine, window, door) is M = ½·11ᵀ + 0.3·uuᵀ + 0.1·ssᵀ. Here u = (1, 1, −1, −1) separates spaceship from castle and s = (1, −1, 0, 0) splits wings from engines. Its spectrum is {2, 1.2, 0.2, 0}, checked here. Pruning modes below 0.25 drops the wing–engine split and keeps the spaceship–castle axis, which “persists” through refinement and compression. MOM-CLM-138 rejected the nominal compatibilism built on this. Calling archetypes “structurally forced” is the realist commitment under another name. It kept the observation: “Some descriptors are far more stable than others under refinement … and that stability is measurable.” CLAIM-164 says what such a mode picks out: the gap picks the object.
How they might relate. Persistence looks like evidence summed over scales: a mode with a wide gap is one the data supports at every resolution tried. If so, criteria 1 and 3 are one criterion and only retrieval is separate. But persistence is relative to the refinements tried and the threshold chosen (0.25 in the example), which evidence is not. And a persistent category can still fail retrieval, if its members are similar to one another and the one wanted is rare.
The owner’s objection, in the source
The owner pressed the monograph’s drafting on this point twice, in its Part III (“Eigenmodes, Archetypes, Platonics, Stable Cores”). The first objection is not quoted there, but the draft’s reply concedes it: “acts like an object” risks triviality, since any valid descriptor persists and is shareable. The second is quoted: “our definition of “object like” needs to apply to objects as well.” A criterion for when a description earns a name has to separate descriptions from one another and to apply to particulars too. Evidence and retrieval (criteria 1 and 2) already apply to both: a particular brick is worth a bin of its own for the same reasons a kind is. Whether persistence does is part of this question. CASE-097 shows that, stated for eigenvectors, persistence fails even in the monograph’s own example.
What would answer it
A derivation, or a counterexample, relating a mode’s persistence across a family of refinements to its Bayes factor at each. And for retrieval, a case where a category persistent in the data is split for speed, or one retrieval forces is pruned by both other criteria.