Pith Number

pith:MU4TK6NW

pith:2021:MU4TK6NWK746YS5L7KLPTXQ2BV

not attested not anchored not stored refs pending

$U$-statistics on bipartite exchangeable networks

T\^am Le Minh

arxiv:2103.12597 v6 · 2021-03-23 · math.PR · 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{MU4TK6NWK746YS5L7KLPTXQ2BV}

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	2026-07-05T07:30:41.613189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65393579b657f9ec4babfa96f9de1a0d5e78ec25b9b601fad5e715b2a7ed9a05

Aliases

arxiv: 2103.12597 · arxiv_version: 2103.12597v6 · doi: 10.48550/arxiv.2103.12597 · pith_short_12: MU4TK6NWK746 · pith_short_16: MU4TK6NWK746YS5L · pith_short_8: MU4TK6NW

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/MU4TK6NWK746YS5L7KLPTXQ2BV \
  | 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: 65393579b657f9ec4babfa96f9de1a0d5e78ec25b9b601fad5e715b2a7ed9a05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab89831cd0d301338791b55c7fa7ad280e59a20da607084c818d079142d77644",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-03-23T14:51:44Z",
    "title_canon_sha256": "f284cd3481f493b9e52154a2cc1f65a5901d23aa41bb3d08ac31c1af50714739"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.12597",
    "kind": "arxiv",
    "version": 6
  }
}