The claim
CLAIM-303 prices filing as an upfront cost F against reconstruction c_r per use, with access and verification c_a and upkeep u per use once filed, and files when expected reuse n exceeds F/(c_r − c_a − u). Its last clause keeps recurrence out of the criterion: recurrence is evidence that reuse will come, and the criterion is the expected reuse itself.
That needs a forecast of n, and the record rarely has one. Without it, the question becomes what rule does well whatever the sequence of uses turns out to be. Karlin, Manasse, Rudolph and Sleator answer it for two states with fixed prices (THEORY-348): switch “when the cost of making the change equals the extra cost incurred due to being in state A instead of A’”. Here state A is reconstructing each time, A’ is having filed, the extra cost of staying in A is c_r − c_a − u per use, and the change costs F. The rule is to file at the use where the reconstruction overpaid so far reaches F.
Write d = c_r − c_a − u for the overpayment per use and a = c_a + u. The rule reconstructs k = ⌊F/d⌋ times and files at use k + 1. If reuse stops by use k, it paid exactly what hindsight pays. If it stops at a later use n, it paid kd + F + n·a against hindsight’s F + n·a, since (k + 1)d > F. The ratio is then at most 1 + kd/(F + (k + 1)a), which kd ≤ F bounds by 1 + d/c_r = 2 − a/c_r. That is at most 2, and reaches 2 only as a/c_r goes to 0. No deterministic rule without foresight guarantees better than this factor, up to a term that vanishes as F/d grows: an adversary stops reuse at the use where the rule files. The paper proves the bound of 2 for snoopy caching, whose filed state costs nothing per use (a = 0). The extension to a per-use cost is the record’s, and it tightens the factor. Rounding matters: filing once the overpayment so far has reached F can exceed 2 when F is not a multiple of d.
So where reuse cannot be forecast, the past recurrences, each weighted by what it cost to redo, are the criterion. The decision is a function of them, and it carries a guarantee that no forecast-based rule can carry when there is no forecast.
What it gives the record
ADR-032’s second-occurrence rule is the break-even rule when F is about one reconstruction’s overpayment. The rule should file sooner when filing is cheap, later when filing is dear, and at once when filing costs nearly nothing, as with setting a found brick aside (CASE-094). A11’s “rare, expensive-to-reconstruct argument” is filed by the break-even rule after its first expensive reconstruction. The unweighted count is what fails, not recurrence as such.
What it does not say
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That no rule at all does better. The lower bound of 2 is for deterministic rules, as THEORY-348 states. A randomized rule, which files at a random point, is known to guarantee e/(e − 1) ≈ 1.58 in expectation for rent-or-buy (Karlin, Manasse, McGeoch and Owicki). The record does not hold that source. The deterministic bound of 2 is also approached only when filing costs many reconstructions’ overpayment. When F is no more than one, filing at once is optimal.
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Anything about staleness. The theorem forbids stale reads rather than pricing them. CLAIM-303’s added term, that reusing an obsolete argument may cost more than recomputing it, is outside the result. A filed argument that can go wrong unnoticed is not the paper’s two fixed-price states.
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That the guarantee holds with drifting or unknown costs. F, c_r, c_a and u are fixed and known in the proof. The record’s reconstruction costs are estimates, and reconstruction gets cheaper as related arguments are filed.
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That recognition costs a fixed amount per use. CLAIM-314: certifying that stored answers cover a new question is NP-complete even for conjunctive queries, and its cost grows with what is stored. Where reuse is found by search, each filing raises the cost of using the others, and item-by-item decisions are not independent. The guarantee holds where a filed argument is reached by its code or index. Over the whole store it is not shown. Conceded.
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That worst-case rules beat expected-value rules. Where reuse can be forecast, a rule using the forecast can do better on average. There CLAIM-303’s criterion stands, and this objection narrows the clause instead of defeating it.
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That it covers more than two options. With a third, such as filing a pointer instead of the argument, the deterministic bound rises to 3 (THEORY-348).
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That the paper says this. Its case is when to stop maintaining a copy. Reading it as when to file is the record’s mirror-image use of the same principle (NOTE-893).
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Anything about ADR-032’s other reason. The second-occurrence rule is also a throttle on capture by agents, and this objection says nothing about that.
How CLAIM-303 could answer
It could restrict “the criterion” to the case where reuse is forecastable and concede the clause elsewhere. Or it could hold that the record always has some forecast, such as the line an argument belongs to or the question it answers, so that the worst case is the wrong standard. CLAIM-185’s threshold would then need to say which case the record is in.
Note of 2026-10-30: what holds it back
The bound corrected in version 3 has not yet been re-derived by a second reviewer. Promoting this objection makes its concession due on CLAIM-303, which has not answered: it could restrict its last clause to reuse that can be forecast, or hold that the record always has some forecast.