The claim
MOM-CLM-166: “Keep both criteria and stop calling them one.” Detection asks whether a distinction is in the data, and a large margin is evidence that it is (CLAIM-154: keep it when d’² exceeds the Occam cost). Retrieval asks whether the distinction must be built to act in time, and a large margin means it need not, because the item already stands out: “if it’s a single black brick in a box of white bricks: ok, it’s buried but its’ still detectable” (CASE-094).
Copy count separates them. Take a kind with c copies among m similar items, effect μ, noise σ and prior scale s.
- Evidence. d’² = cμ²/σ², against an Occam cost of ln(1 + cs²/σ²). Evidence grows linearly in c, the cost only logarithmically.
- Search. With the bin in random order, the expected number of other items examined before the first copy is m/(c+1). It falls as 1/c.
MOM-CLM-166’s table, with m = 200, μ = 0.8, σ = 1, s = 3 and a deadline of D = 12 items, re-run here:
| c | d’² | Occam | detection | m/(c+1) | simulated | retrieval |
|---|---|---|---|---|---|---|
| 1 | 0.64 | 2.30 | prune | 100.00 | 100.53 | carve |
| 2 | 1.28 | 2.94 | prune | 66.67 | 67.05 | carve |
| 5 | 3.20 | 3.83 | prune | 33.33 | 33.74 | carve |
| 20 | 12.80 | 5.20 | keep | 9.52 | 9.48 | leave |
| 100 | 64.00 | 6.80 | keep | 1.98 | 2.02 | leave |
| 400 | 256.00 | 8.19 | keep | 0.50 | 0.51 | leave |
The simulation shuffles the bin and counts the items examined before the first copy, with 20,000 draws per row (4,000 for the last two). The closed form is exact.
That the criteria disagree on every row is a fact of these parameters, not a theorem. With a deadline of 5, the row c = 20 both keeps and carves. What is general is the direction: one criterion rises with c and the other falls, so the copy counts where each says “make a bin” lie at opposite ends. “Very few of but use often” (CASE-094) is the cell where retrieval demands a bin and the evidence is weakest.
Use frequency enters retrieval and not detection. A bin pays when the search it saves, summed over the retrievals expected, exceeds its cost. If the bin is made when the item is found, as in CASE-094, that cost is little more than the bin. Detection does not depend on how often the item is wanted. So the categories retrieval forces depend on the system’s tasks and deadlines as well as its data, which is MOM-CLM-166’s reading of the parable: “the concepts are the ones the system’s deadlines forced it to build, and those are not derivable from the data alone.”
Why it is Active
The two monotonicities are elementary, and both were checked: d’² and the Occam term from CLAIM-154’s own statement, the search cost against a simulation. The reading of them as two criteria, entitled to carve against must carve, is MOM-CLM-166’s. Nothing here depends on how any real person searches.
What it does not say
- Not that evidence does not matter. A system carving by retrieval alone would make bins for distinctions that are not there. MOM-CLM-166: a system “carves a category when the second fails, and it is entitled to carve one when the first succeeds.”
- Not that search is always serial. m/(c+1) is a scan through items that must each be checked. Treisman and Gelade (LIT-1082) found such scans where the wanted item differs from the others only in a combination of features. An item with a feature none of the others has (CASE-094’s black brick) was found almost regardless of their number. That is the case in which retrieval says no bin is needed. Their absent-target scans, about twice the per-item time of present-target ones, also make a failed search expensive to complete.
- Not a psychological claim. The parameters are MOM’s, chosen to show the opposition, and nothing was measured.
Note of 2026-10-15: a related case in graph indexes
In a proximity-graph index over clustered data, items in small isolated clusters became unfindable when each new item was linked only to its nearest neighbours, and findable when the linking rule kept links between clusters (THEORY-385, Proposed: one set of the authors’ own tests). An arrangement fitted to the common case loses rare items that resemble their neighbours, which is this claim’s opposition in another medium. It concerns links, not copy counts, and it was not built as a test of the claim.