Pith Number

pith:FXOE74RN

pith:2026:FXOE74RNILRMHESQ3H3WFNPYUY

not attested not anchored not stored refs resolved

A Note on Second-Order Expected Maximum-Load Bounds for Binary Linear Hashing

Nader H. Bshouty

Binary linear hashing matches fully independent hashing on the second-order term in expected maximum load.

arxiv:2605.18335 v1 · 2026-05-18 · cs.DS

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\usepackage{pith}
\pithnumber{FXOE74RNILRMHESQ3H3WFNPYUY}

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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

For every R>1 satisfying R ℓ^{1-1/R} ≥ D ln ℓ, Pr[M(S,h) ≥ R log n / log log n] ≤ O( (log log n)^2 / (R^2 (log n)^{2-2/R}) ), which integrates to E[M(S,h)] ≤ (1 + (1+o(1)) log log log n / log log n) * log n / log log n.

C2weakest assumption

The base optimization of the exponential-potential function in the proof from Jaber et al. (STOC 2025) can be carried through without introducing new error terms that invalidate the improved exponent 2-2/R in the tail bound (see the derivation of the tail estimate in the note).

C3one line summary

Binary linear hashing matches fully independent hashing in the leading term and dominant second-order correction of expected maximum load up to a 1+o(1) factor.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] Is linear hashing good? InProceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 465–474, 1997 1997

[2] Linear hash functions.Journal of the ACM, 46(5):667–683, 1999 1999

[3] Kumar, and David Zuckerman

[4] Also available as arXiv:2505.14061

[5] Balls into bins 1998

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:55.767935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ddc4ff22d42e2c39250d9f762b5f8a6276743a8f29ba97631aa5b48d251e426

Aliases

arxiv: 2605.18335 · arxiv_version: 2605.18335v1 · doi: 10.48550/arxiv.2605.18335 · pith_short_12: FXOE74RNILRM · pith_short_16: FXOE74RNILRMHESQ · pith_short_8: FXOE74RN

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/FXOE74RNILRMHESQ3H3WFNPYUY \
  | 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: 2ddc4ff22d42e2c39250d9f762b5f8a6276743a8f29ba97631aa5b48d251e426

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db429c0c8b53c9eaf56c9cb1e1c2d7336cd6046192fbae2e8edfc4acb0bf184c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-18T12:51:10Z",
    "title_canon_sha256": "3887c5235e275e953a17b80fd67cc83fd2c3d0e96964d032061ffc221b871f44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18335",
    "kind": "arxiv",
    "version": 1
  }
}