Pith Number

pith:52WI56LZ

pith:2026:52WI56LZUI5PFP2WLT37VVZY4J

not attested not anchored not stored refs pending

Every fork-free graph is perfectly weight divisible

Feng Liu, Jiasheng Zeng, Qi Wu, Shuang Sun, Yan Wang

arxiv:2608.13519 v1 · 2026-08-13 · 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{52WI56LZUI5PFP2WLT37VVZY4J}

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	2026-08-14T01:24:56.761595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eeac8ef979a23af2bf565cf7fad738e269a96e215f5a6964788b498e0223d9d1

Aliases

arxiv: 2608.13519 · arxiv_version: 2608.13519v1 · doi: 10.48550/arxiv.2608.13519 · pith_short_12: 52WI56LZUI5P · pith_short_16: 52WI56LZUI5PFP2W · pith_short_8: 52WI56LZ

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/52WI56LZUI5PFP2WLT37VVZY4J \
  | 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: eeac8ef979a23af2bf565cf7fad738e269a96e215f5a6964788b498e0223d9d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a54ae8bacd7a15ff78e6eabdc68801a471c87a92937c24a8db8175efb6a44c64",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-13T17:38:36Z",
    "title_canon_sha256": "7f1e7851b95646447b7c02ccc1bb5f0932906237de6235132a7dc309d650f870"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.13519",
    "kind": "arxiv",
    "version": 1
  }
}