Pith Number

pith:W5MATT5F

pith:2026:W5MATT5FNNODZTWQUSGAA7BCBI

not attested not anchored not stored refs pending

DynamicLogLog: Faster, Smaller, and More Accurate Cardinality Estimation

Brian Bushnell

DynamicLogLog stores relative leading-zero counts with a shared exponent to cut memory by one-third while removing HyperLogLog's error spike and adding an early-exit mask.

arxiv:2603.27405 v2 · 2026-03-28 · cs.DS

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W5MATT5FNNODZTWQUSGAA7BCBI}

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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

At 2,048 buckets with 512k simulations, DLL4's hybrid estimate achieves 1.830% mean and 1.834% peak absolute error using 1,024 bytes, compared to 1.84% mean and 34.1% peak for HLL using 1,536 bytes.

C2weakest assumption

That the early-exit mask and hybrid blend maintain their reported accuracy and speed on real-world data distributions rather than only on the synthetic streams used in the 512k simulations.

C3one line summary

DynamicLogLog cuts memory by 33%, speeds up queries over 10x in bandwidth-limited cases, and removes HyperLogLog's transition-region error spike while matching or beating accuracy.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:22.479757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b75809cfa56b5c3cced0a48c007c220a0b6d5ffcf163517ae0ff920a7017aa4b

Aliases

arxiv: 2603.27405 · arxiv_version: 2603.27405v2 · doi: 10.48550/arxiv.2603.27405 · pith_short_12: W5MATT5FNNOD · pith_short_16: W5MATT5FNNODZTWQ · pith_short_8: W5MATT5F

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/W5MATT5FNNODZTWQUSGAA7BCBI \
  | 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: b75809cfa56b5c3cced0a48c007c220a0b6d5ffcf163517ae0ff920a7017aa4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4099590fd48b779e4d13d6ae710a32829f6a9ee99fea85b3fb432f71cd0931c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-03-28T20:52:33Z",
    "title_canon_sha256": "938b2355904921a132b8933e1f24d352fdf3042ee73a5cbdbc39d69e42ce0595"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.27405",
    "kind": "arxiv",
    "version": 2
  }
}