# An Exposition of GPT Astra's Proof of Lower Bound on DP Continual Counting

arXiv: https://arxiv.org/abs/2609.28528 · HTML: https://mlsanity.com/paper/2609.28528/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 5 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 3 of 3)

- [Correlated Noise Mechanisms for Differentially Private Learning](https://mlsanity.com/paper/2506.08201/) (2025)
- [Count on Your Elders: Laplace vs Gaussian Noise](https://mlsanity.com/paper/2408.07021/) (2024)
- [Tight Lower Bounds for Differentially Private Continual Counting](https://mlsanity.com/paper/2609.17650/) (2026)

## Abstract (arXiv)

The goal of this note is to give a detailed proof, to the best of our understanding, of the recent presentation by Harrison and Leeman (arXiv:2609.17650v01 and arXiv:2609.17650v02) of the proof by Astra on the lower bound for differentially private continual counting. We believe a more natural and easy proof is possible and hope that this note will help in that effort. Prior to the initial preprint by Harrison and Leeman (arXiv:2609.17650v01), Bairaktari and Larsen (arXiv:2607.00876) gave an elegant proof to show a lower bound of Omega(log3/2(n)) for both pure and approximate-DP continual counting, and in personal communication had informed us that they have a proof of optimal Omega(log2(n)) for pure-differential private continual counting as well. They have subsequently published their Omega(log2(n)) bound, which is now a joint work of Bairaktari, Dahl, and Larsen (arXiv:2607.00876v3). Their new result is an elegant extension of their technique for approximate-differential privacy. Although the two proofs are technically different, the Astra argument uses related tree geometry introduced in Bairaktari and Larsen.