Pith Number

pith:A3B3Y4YK

pith:2010:A3B3Y4YK4V5VSLH5SKUPTLMV23

not attested not anchored not stored refs pending

Spectral distributions of adjacency and Laplacian matrices of random graphs

Tiefeng Jiang, Xue Ding

arxiv:1011.2608 v1 · 2010-11-11 · 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{A3B3Y4YK4V5VSLH5SKUPTLMV23}

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	2026-05-18T04:36:09.909969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06c3bc730ae57b592cfd92a8f9ad95d6f00ff82f85a3c3a9bd6c51fb4624dfcb

Aliases

arxiv: 1011.2608 · arxiv_version: 1011.2608v1 · doi: 10.48550/arxiv.1011.2608 · pith_short_12: A3B3Y4YK4V5V · pith_short_16: A3B3Y4YK4V5VSLH5 · pith_short_8: A3B3Y4YK

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/A3B3Y4YK4V5VSLH5SKUPTLMV23 \
  | 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: 06c3bc730ae57b592cfd92a8f9ad95d6f00ff82f85a3c3a9bd6c51fb4624dfcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b9b7845ca04cc63972970b8c6887d72385f790863c39cf97af200b71d34b94e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-11T10:36:16Z",
    "title_canon_sha256": "0b81e1f4a42f77e9bbe8905727bf733f3711f02393c0eb9aa9c924c27f2f92c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2608",
    "kind": "arxiv",
    "version": 1
  }
}