Pith Number

pith:XUCWYIN4

pith:2016:XUCWYIN4XMSG6QWK5AAF7MGPRX

not attested not anchored not stored refs pending

Sparse exchangeable graphs and their limits via graphon processes

Christian Borgs, Henry Cohn, Jennifer T. Chayes, Nina Holden

arxiv:1601.07134 v4 · 2016-01-26 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XUCWYIN4XMSG6QWK5AAF7MGPRX}

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	2026-05-18T00:12:50.943717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd056c21bcbb246f42cae8005fb0cf8de0a54f0d3a34c324f324422cacd40d09

Aliases

arxiv: 1601.07134 · arxiv_version: 1601.07134v4 · doi: 10.48550/arxiv.1601.07134 · pith_short_12: XUCWYIN4XMSG · pith_short_16: XUCWYIN4XMSG6QWK · pith_short_8: XUCWYIN4

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/XUCWYIN4XMSG6QWK5AAF7MGPRX \
  | 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: bd056c21bcbb246f42cae8005fb0cf8de0a54f0d3a34c324f324422cacd40d09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afea21fa54dc3d89b48606f77ac113ea3542cb038445b43ab5871cbdde570c1b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-01-26T19:10:14Z",
    "title_canon_sha256": "f5f5b79fb6be4375cb917a33bf72728aba1b2e3be7153085b90cd652369a5403"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.07134",
    "kind": "arxiv",
    "version": 4
  }
}