Pith Number

pith:ZLXP4ROX

pith:2026:ZLXP4ROXJ2JJZQX3UDHVJZUZBG

not attested not anchored not stored refs pending

A Generative Model for Extremely Sparse Edge-Exchangeable Networks

Valentin Kilian

arxiv:2606.22105 v1 · 2026-06-20 · 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{ZLXP4ROXJ2JJZQX3UDHVJZUZBG}

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	2026-06-23T02:13:28.357196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caeefe45d74e929cc2fba0cf54e69909a7e91520458b78de1eb960a7197a0a05

Aliases

arxiv: 2606.22105 · arxiv_version: 2606.22105v1 · doi: 10.48550/arxiv.2606.22105 · pith_short_12: ZLXP4ROXJ2JJ · pith_short_16: ZLXP4ROXJ2JJZQX3 · pith_short_8: ZLXP4ROX

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/ZLXP4ROXJ2JJZQX3UDHVJZUZBG \
  | 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: caeefe45d74e929cc2fba0cf54e69909a7e91520458b78de1eb960a7197a0a05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7ba4a7373a3946b189336c8cf7557cda24e2afd48fb46c178bf9a8518ca525a",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-06-20T15:37:44Z",
    "title_canon_sha256": "62b511e306a0a4022b74b541fd633d9c9eca60150205e311826f78fba3dafb3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22105",
    "kind": "arxiv",
    "version": 1
  }
}