Pith Number

pith:ERH42LXN

pith:2026:ERH42LXNBL5PUJUQ5YAMZNB3OT

not attested not anchored not stored refs pending

Concentration Inequalities for Incomplete U-statistics over Arbitrary Sampling Graphs

Zheng Tracy Ke

arxiv:2607.17048 v1 · 2026-07-19 · 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{ERH42LXNBL5PUJUQ5YAMZNB3OT}

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	2026-07-21T01:21:12.165187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

244fcd2eed0afafa2690ee00ccb43b74fcd581dd615ab140ce69308bebfab151

Aliases

arxiv: 2607.17048 · arxiv_version: 2607.17048v1 · doi: 10.48550/arxiv.2607.17048 · pith_short_12: ERH42LXNBL5P · pith_short_16: ERH42LXNBL5PUJUQ · pith_short_8: ERH42LXN

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/ERH42LXNBL5PUJUQ5YAMZNB3OT \
  | 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: 244fcd2eed0afafa2690ee00ccb43b74fcd581dd615ab140ce69308bebfab151

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "503e9673760cdc47e0f2f6fc337dc221536e9ce265e44961a496109a05734aad",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-19T03:25:32Z",
    "title_canon_sha256": "add40a02906fb213c24277ae89535f72432801b0dca2851843735818e55b14bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17048",
    "kind": "arxiv",
    "version": 1
  }
}