Pith Number

pith:2WLNQN6M

pith:2026:2WLNQN6M3YCKMWPX6NW3FWVZCB

not attested not anchored not stored refs resolved

Adversarially Robust Approximate Furthest Neighbor

Jeff Giliberti, Kiarash Banihashem, MohammadTaghi Hajiaghayi, Morteza Monemizadeh, Prashant Gokhale, Samira Goudarzi, Sandeep Silwal, Yuhao Liu

A data structure answers c-approximate furthest neighbor queries correctly against adaptive adversaries at query time Õ(min(d n^{1/c²}, n^{2/c²} + d)).

arxiv:2605.16618 v1 · 2026-05-15 · cs.DS · cs.CG

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\usepackage{pith}
\pithnumber{2WLNQN6M3YCKMWPX6NW3FWVZCB}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We present the first adversarially robust data structure for c-approximate furthest neighbor queries that achieves query time Õ(min(d n^{1/c²}, n^{2/c²} + d)).

C2weakest assumption

The construction assumes a fixed point set P known in advance that can be preprocessed, and that the underlying distance computations and data-structure primitives (such as those from Indyk 2003) can be invoked in the stated time bounds under the adaptive adversary model.

C3one line summary

First adversarially robust data structure for c-approximate furthest neighbor search with query time matching the best known oblivious results for many parameter regimes.

References

73 extracted · 73 resolved · 2 Pith anchors

[1] Ahle, T. D. Optimal las vegas locality sensitive data structures. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pp.\ 938--949. IEEE, 2017 2017

[2] P., and Zhou, S 2022 · doi:10.1145/3517804.3526228

[3] Adversarial laws of large numbers and optimal regret in online classification 2021

[4] Altman, N. S. An introduction to kernel and nearest-neighbor nonparametric regression. The American Statistician, 46 0 (3): 0 175--185, 1992 1992

[5] C., Shiragur, K., and Xu, H 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:32.825767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d596d837ccde04a659f7f36db2dab9104b4b79d3e7de730aa5aac1e3872d284d

Aliases

arxiv: 2605.16618 · arxiv_version: 2605.16618v1 · doi: 10.48550/arxiv.2605.16618 · pith_short_12: 2WLNQN6M3YCK · pith_short_16: 2WLNQN6M3YCKMWPX · pith_short_8: 2WLNQN6M

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2WLNQN6M3YCKMWPX6NW3FWVZCB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d596d837ccde04a659f7f36db2dab9104b4b79d3e7de730aa5aac1e3872d284d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18d0df79beb5fa66f12fb968f388996af0a10e75228ba7c19f77c5320e2ef25b",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-15T20:40:24Z",
    "title_canon_sha256": "e1f72fc82eef0c717c5c46e694115199da275155839433e03c6a63024ce85f45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16618",
    "kind": "arxiv",
    "version": 1
  }
}