Delete Names Five Operations: Erasure Semantics for Derived Agent Memory, and Why a State-Level Definition Cannot Be the Auditable One

@misc{mahendrakar2026delete,
  author       = {Mahendrakar, Pranay},
  title        = {{Delete Names Five Operations: Erasure Semantics for Derived Agent Memory, and Why a State-Level Definition Cannot Be the Auditable One}},
  year         = {2026},
  month        = sep,
  date         = {2026-09-06},
  publisher    = {Life of Research},
  doi          = {10.5281/zenodo.22425281},
  url          = {https://lifeofresearch.com/articles/30},
  abstract     = {(c) 2026 Pranay Mahendrakar. Licensed under CC BY 4.0. Persistent memory has become a standard component of language-model agents, and with it a standard assumption: that where a fact lives in a retrievable store rather than in weights, erasing it is a solved problem, because a store supports deletion and weights do not. Agent memory does not hold the records that assumption presumes. It holds derivations - extracted facts, consolidated summaries, reflections, learned procedures, and edits made to earlier entries because a later one arrived - and deleting a source does not remove what was derived from it. This paper separates the operations that the single word delete is used for in this literature: removing the stored item, withdrawing everything derived from it, barring it from supporting an outgoing claim, making the fact non-inferable from what remains, and restoring the store to the state that would have obtained had the item never been written. Three systems published in 2026 supply a semantics for one of these each, and they are not the same semantics. The paper argues that the second is the database view-deletion problem, which has a known structure - no unique source update, and two inequivalent minimality objectives - that the agent-memory literature is rediscovering without the vocabulary; that the fourth is not a property of a record at all, and that deletion is itself an inference signal; and that the fifth is not defined for LLM-mediated consolidation, because the same trajectories are reported to yield different memories under different update schedules. The parametric unlearning literature reached the parallel conclusion in 2021, that only an algorithmic-level definition is auditable. What is not known is stated flatly: no work located for this paper reports what fraction of a production memory store's entries carry a recoverable derivation link to their sources. Six measurements are specified. The literature search, drafting and citation verification for this paper were carried out with AI assistance under the author's direction. Every citation was machine-verified against the arXiv API and Crossref before inclusion, and every quantitative claim was read back against the cited source's own abstract or, where a claim is drawn from a paper's body, against the located passage. The author is responsible for the final text and for all claims made in it.},
  keywords     = {agent memory, right to erasure, machine unlearning, data provenance, view update problem, retrieval-augmented generation, privacy, deletion semantics},
  language     = {en},
  copyright    = {Creative Commons Attribution 4.0}
}