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arXiv · 2607.12204

What a Deletion Certificate Covers, and Where It Expires: Auditable Removal from a Support-Vector Memory

Vishwajith Ramesh
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Abstract

A dense key--value cache gives an operator no way to verify a deletion: it does not say which stored entries currently contribute nothing to the output, and it offers no reference state that the edited memory should match. We build a context memory whose entries carry explicit weights and ask what a deletion certificate over it can cover and where it expires. A one-class support-vector boundary fit around the keys of a context at test time supplies the coefficients used in the readout, so that each key is active (positive coefficient) or reserve (zero coefficient). Removing a reserve key leaves the readout unchanged without a re-solve, and deleting an active key with a decremental solver reaches the same state as re-solving on the remaining keys at the same coefficient cap. A three-key construction shows the limit of both properties: an inert key can acquire positive weight after one more token is admitted, so reserve status certifies the present solve and does not license permanent pruning. In $1,200$ double-precision trials on Gaussian, near-duplicate, clinical (MIMIC-IV vitals), and learned keys, every trial reached the reference state, all but one through the maintained update, with median gate-score disagreement below $10^{-6}$ in every regime and a worst case of $1.1\times10^{-2}$ associated with numerically near-tied solutions and partition disagreement; maintained deletion ran $24$--$223$ times faster than re-solving. Declaring a minimum-norm tie-break as part of the reference, at a tolerance above the two solvers' disagreement in objective value, brings the worst readout disagreement below $2\%$ of the readout range in every regime and leaves a gate-score disagreement of up to $4.2\times10^{-3}$. A deletion certificate should name its reference state and validity horizon. We show what a system must retain, or refuse to admit, to extend that horizon.

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Vishwajith Ramesh. 2026-07-13. What a Deletion Certificate Covers, and Where It Expires: Auditable Removal from a Support-Vector Memory. https://arxiv.org/abs/2607.12204

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