CLAIM-180: Drift is retrieval failure outside a critical distance: a restatement close enough to an idea retrieves it, one that has drifted too far is taken for new, and a code bypasses retrieval by content altogether

The claim

In sparse distributed memory a cue retrieves a stored pattern only from within a critical distance. Flynn, Kanerva and Bhadkamkar (LIT-1848, pp. 15–16, read in NOTE-1454) state it first-hand. A cue “closer than a certain critical distance” to a stored pattern is read to a vector closer still, so iterated reads converge on it. A cue beyond it gives “a diverging sequence that will wander through address space”, which may fall into another pattern’s “attracting zone”. NOTE-242’s reading of LIT-269 gives the same definition: “the largest query–target distance from which iterated reads still converge to the target”. The report asserts the property and refers its derivation to Kanerva’s book (LIT-928, unread and Unavailable). The claim uses the property, not its derivation. Kanerva’s 1992 report (LIT-921) has only the signal-to-noise optimum (NOTE-779, 2026-10-14). Hopfield’s network (LIT-918, read in NOTE-819) has the same shape in dynamical form. A cue inside a memory’s basin of attraction settles into it, and one outside settles elsewhere, possibly into a spurious state.

A collaborator with no memory retrieves by content. When an idea comes up again, the only way to connect it to its earlier statement is that the two read alike. A restatement close to the original is recognized as the same idea. One that has drifted is taken for new, and re-derived. That is the failure CLAIM-177 records: the permissiveness objection re-derived six or more times as though new, the passive/active distinction restated without citation, the relativity analogy brought back after it was rejected. Each restatement read differently enough that it was not retrieved.

A code changes the retrieval. Pointing at CLAIM-024 or ARG-004 does not depend on rewording the idea closely enough to be recognized; the address names it. That is why addressability, not storage, makes an anchor (CLAIM-182). Hopfield’s model has no addresses. The contrast is in Kanerva’s report (LIT-921, NOTE-779): an SDM with radius zero and complete addresses is an ordinary RAM, which returns exactly what was written at an exact address and nothing for any other cue. Stored content can be reached only by a cue near it. An addressed item can be reached by its name from anywhere.

Two further points follow from the models, both untested here:

• Capacity. A Hopfield network past its load develops spurious states and loses retrieval. A record that leans on content alone, with many near-duplicate statements, should show the same: merged and confused ideas. That bears on flooding (CLAIM-179). Corrected 2026-10-14 (NOTE-819, THEORY-272). In Hopfield’s model, fusion comes from two memories being close, closer than about a tenth of N, at any load. Overload does not merge memories: it loses every memory at once, unless old ones are forgotten. Spurious states occur far below capacity too. “Many near-duplicate statements” names the closeness failure, not the load one. In SDM, load narrows the distance instead: “The greater the population of the memory, the smaller the critical distance” (LIT-1848, p. 15).
• Silent redefinition. A cue just outside one memory’s basin can settle into a neighbouring memory. Read across, a restated term can be taken for a nearby, different term, and the argument continues on the wrong one without noticing.

What it does not say

• It does not say a collaborator’s memory is an SDM or a Hopfield network. The models give a precise picture of retrieval by content and its limit, and the claim uses that picture.
• “Taken for new” has no Hopfield analogue (NOTE-819). The network never treats a cue as new: a cue far from every memory settles elsewhere, or, with a threshold, into a state that signals unfamiliarity. The nearest analogue of re-derivation is failing to recognise. Whether a duplicate is then written is outside the model.
• It does not say codes make retrieval free. A code must itself be remembered or found (QUESTION-038), and luria’s generated views and indexes are how it is found.
• The test it proposes is not run. It needs a measure of how far a restatement is from its original, and the reconstructed exchanges give the cases to measure.

Connections

• Ashby (LIT-787, Ch. 16, S. 16/14; THEORY-307, read in NOTE-851): separate stores for separate situations, with interference that grows with the similarity of the situations, because similar inputs use the same parts. Read across, a close restatement is the one most likely to overwrite its earlier form, the converse of this claim’s concern that a distant one is taken for new. Both follow from retrieval by content, and a code avoids both. Analogy only.

Note of 2026-10-30: what holds it back

The test it proposes has not been run: no restatement in the reconstructed exchanges has had its distance from the original measured and set against whether it was re-derived as though new, and no count compares re-derivation of coded and uncoded items. Its premise CLAIM-182 is Proposed for the same want. The critical distance no longer waits on a reading: LIT-1848 states it first-hand, and its derivation in Kanerva’s book (LIT-928), still unread, is not something the claim uses.