Pith Number

pith:DURGAPHA

pith:2011:DURGAPHAXDQR4AMDKMVKOHQFID

not attested not anchored not stored refs pending

On the Chromatic Thresholds of Hypergraphs

Dhruv Mubayi, Jane Butterfield, John Lenz, J\'ozsef Balogh, Ping Hu

arxiv:1103.1416 v5 · 2011-03-08 · 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{DURGAPHAXDQR4AMDKMVKOHQFID}

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	2026-05-17T23:53:36.703035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d22603ce0b8e11e0183532aa71e0540fc2acf63f8c877560dca765d0fa72742

Aliases

arxiv: 1103.1416 · arxiv_version: 1103.1416v5 · doi: 10.48550/arxiv.1103.1416 · pith_short_12: DURGAPHAXDQR · pith_short_16: DURGAPHAXDQR4AMD · pith_short_8: DURGAPHA

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/DURGAPHAXDQR4AMDKMVKOHQFID \
  | 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: 1d22603ce0b8e11e0183532aa71e0540fc2acf63f8c877560dca765d0fa72742

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92c92a141a9bf1e3caa5edf6f09c562f0ab9c9c9ce433c93f774e975ab7a27fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-08T02:24:40Z",
    "title_canon_sha256": "d6cd20e85467a6b327360e7403b4028df12d04fbc52dd2814fe8837b7d206ee5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1416",
    "kind": "arxiv",
    "version": 5
  }
}