Pith Number

pith:2YMCOWJO

pith:2016:2YMCOWJO46BEDX7QTFLEY2TU3S

not attested not anchored not stored refs pending

Sample complexity of the distinct elements problem

Pengkun Yang, Yihong Wu

arxiv:1612.03375 v2 · 2016-12-11 · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2YMCOWJO46BEDX7QTFLEY2TU3S}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T00:26:08.482894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d61827592ee78241dff099564c6a74dc9e2afee0427d671ddb2ca389f1960a4c

Aliases

arxiv: 1612.03375 · arxiv_version: 1612.03375v2 · doi: 10.48550/arxiv.1612.03375 · pith_short_12: 2YMCOWJO46BE · pith_short_16: 2YMCOWJO46BEDX7Q · pith_short_8: 2YMCOWJO

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/2YMCOWJO46BEDX7QTFLEY2TU3S \
  | 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: d61827592ee78241dff099564c6a74dc9e2afee0427d671ddb2ca389f1960a4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65d15938bd954218e4d1b7661d5ee2ef4adcf2f8acd6d01f56c0249e913b80d3",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2016-12-11T06:17:40Z",
    "title_canon_sha256": "5b97ed75c1b81bcc31256789f574e03fef1f28b816c708b2c2f47965cec66e1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03375",
    "kind": "arxiv",
    "version": 2
  }
}