Pith Number

pith:W4NC5CUV

pith:2026:W4NC5CUVB6M5PLQ3DRRT5MALKG

not attested not anchored not stored refs pending

Universality in random graphs via optimal linking systems: trees and beyond

Asaf Cohen Antonir, Lyuben Lichev, Maksim Zhukovskii

arxiv:2608.06358 v1 · 2026-08-06 · math.CO · 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{W4NC5CUVB6M5PLQ3DRRT5MALKG}

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	2026-08-07T01:41:28.529697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b71a2e8a950f99d7ae1b1c633eb00b51b62d38d2efce0c49dd35cf3822a742ea

Aliases

arxiv: 2608.06358 · arxiv_version: 2608.06358v1 · doi: 10.48550/arxiv.2608.06358 · pith_short_12: W4NC5CUVB6M5 · pith_short_16: W4NC5CUVB6M5PLQ3 · pith_short_8: W4NC5CUV

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/W4NC5CUVB6M5PLQ3DRRT5MALKG \
  | 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: b71a2e8a950f99d7ae1b1c633eb00b51b62d38d2efce0c49dd35cf3822a742ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66897e8dfb2b6f055296f85cc50109a327e73cc6b9a087bab60df0dd85d7a490",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-06T17:55:25Z",
    "title_canon_sha256": "b5d7eefa4f2da8f78a53663b9c667f36a0e769edc6954f29152a81b1a61b44ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06358",
    "kind": "arxiv",
    "version": 1
  }
}