The claim
CLAIM-308 applies the rent-or-buy rule to one filed argument at a time. Its per-use cost once filed is c_a + u, access and verification plus upkeep, fixed and known, and its guarantee of twice the hindsight optimum needs exactly that. CLAIM-308 already names the condition and says reconstruction costs drift. This objection says one cost drifts in a particular direction, and for a structural reason.
Using a filed answer for a new question first requires recognizing that it answers the question. For the simplest formal case, conjunctive queries with stored conjunctive definitions, that recognition is a search: a stored view can serve a query exactly when its definition maps homomorphically into the query’s, and deciding whether the stored views answer the query exactly is NP-complete in the size of the query and the definitions (THEORY-389, from Levy, Mendelzon, Sagiv and Srivastava; THEORY-371, from Chandra and Merlin). Two sources of difficulty are independent: the number of ways each stored item could map into the question, and which parts of the question the items jointly cover.
Three things follow for CLAIM-308’s accounting.
- c_a is not a constant per item. The search runs over every stored definition that might apply, so its cost grows with what has been filed, not with the item being used.
- Filing has a cost that falls on other items. Each new filing adds a candidate to every later recognition. That cost is paid at later uses of other arguments, so it appears in no single item’s F, c_a or u, and a rule that decides item by item cannot see it. Per-item break-even decisions are therefore not independent. This is the same shape as upkeep that depends on what else is stored (THEORY-350), where choosing one item at a time can go arbitrarily wrong.
- Without a definition there is nothing to recognize. Every result assumes each stored answer carries a statement of what it answers. For the record that is a claim’s title or the question it answers. An item filed without one cannot be recognized at all, so writing that statement belongs inside F.
What it does not say
- That recognition is costly in practice. The hardness is worst case, in the size of short definitions, and the stored data does not enter. The authors expect polynomial methods to cover many practical cases. Most of the record’s reuse is a lookup by code, not a search for what covers a question.
- That partial reuse is hard. A maximally contained rewriting, using what the stored answers cover and redoing the rest, can be built in polynomial time (THEORY-374). Only certifying exact coverage is hard. The cost then moves into reconstructing the remainder.
- Anything about prose. Conjunctive queries are a small positive language, which is why the problem is decidable at all. For arguments in prose, coverage is not shown to be decidable, let alone in NP. The formal case is a floor on the difficulty, not a model of it.
- That CLAIM-308’s arithmetic is wrong. Where recognition can be treated as fixed, for instance when an argument is reached by its code, the break-even rule and its guarantee stand.
How CLAIM-308 could answer
It could hold that the record’s recognition is mostly lookup by code and index, so c_a is close enough to fixed. Or it could fold the cost each filing imposes on later recognition into u, as upkeep charged to the store rather than the item, and ask whether a rent-or-buy rule over the whole store keeps a bound. The readings give no such bound: the nearest, THEORY-350, has guarantees only for restricted structures.
Note of 2026-10-30: what holds it back
CLAIM-308 concedes it at this review, and it keeps the status its evidence gives it (ADR-059). Its title says without condition that each filing raises the cost of later reuse, while its body says most of the record’s reuse is lookup by code and that the conjunctive case does not model prose. Nothing in the record measures the cost of recognizing what a filed argument answers in the record’s own reuse, or shows that coverage for prose arguments is at least as hard as the conjunctive case.