Pith Number

pith:XIL5GBHG

pith:2017:XIL5GBHGV6APPKXSG3OJXBZYWB

not attested not anchored not stored refs pending

Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erd\H{o}s-R\'enyi graphs

Benjamin Landon, Horng-Tzer Yau, Jiaoyang Huang

arxiv:1712.03936 v1 · 2017-12-11 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XIL5GBHGV6APPKXSG3OJXBZYWB}

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	2026-05-18T00:28:19.525204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba17d304e6af80f7aaf236dc9b8738b06a772c864f1acd6a8d06a88a35f085fe

Aliases

arxiv: 1712.03936 · arxiv_version: 1712.03936v1 · doi: 10.48550/arxiv.1712.03936 · pith_short_12: XIL5GBHGV6AP · pith_short_16: XIL5GBHGV6APPKXS · pith_short_8: XIL5GBHG

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/XIL5GBHGV6APPKXSG3OJXBZYWB \
  | 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: ba17d304e6af80f7aaf236dc9b8738b06a772c864f1acd6a8d06a88a35f085fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1597fb565d5d72ec39d52787610ca7153f0e7b886e077ea68053760c89d71ab0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-12-11T18:32:18Z",
    "title_canon_sha256": "e93c89440a79a5a8fc0ff7e781fb2e0c98de718e581fd2e6956f2dab536e654e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.03936",
    "kind": "arxiv",
    "version": 1
  }
}