Pith Number

pith:7XT2NZ7O

pith:2013:7XT2NZ7OBTWPQI3OF2SON72W7U

not attested not anchored not stored refs pending

Hypergraphs with Zero Chromatic Threshold

John Lenz, J\'ozsef Balogh

arxiv:1307.7363 v1 · 2013-07-28 · 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{7XT2NZ7OBTWPQI3OF2SON72W7U}

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	2026-05-18T03:17:23.487908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde7a6e7ee0cecf8236e2ea4e6ff56fd03fd379fcea22ca53733e9e698498eb6

Aliases

arxiv: 1307.7363 · arxiv_version: 1307.7363v1 · doi: 10.48550/arxiv.1307.7363 · pith_short_12: 7XT2NZ7OBTWP · pith_short_16: 7XT2NZ7OBTWPQI3O · pith_short_8: 7XT2NZ7O

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/7XT2NZ7OBTWPQI3OF2SON72W7U \
  | 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: fde7a6e7ee0cecf8236e2ea4e6ff56fd03fd379fcea22ca53733e9e698498eb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ec717d689c749c717b9bfa8c52ae9e458e4fe45e1b991164f4192bad6816f12",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-28T14:00:58Z",
    "title_canon_sha256": "00b7f76ab30ef8ea3376ff27035833d8f9420512bb719745da6ce42648df70d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7363",
    "kind": "arxiv",
    "version": 1
  }
}