Pith Number

pith:ZYXZMQRO

pith:2010:ZYXZMQROU4FHPITI5P2TXV5YJE

not attested not anchored not stored refs pending

Injective colorings of sparse graphs

Daniel W. Cranston, Gexin Yu, Seog-Jin Kim

arxiv:1007.0786 v1 · 2010-07-05 · 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{ZYXZMQROU4FHPITI5P2TXV5YJE}

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	2026-05-18T04:11:18.011595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce2f96422ea70a77a268ebf53bd7b849185919094b8c58b21097dc2a50262349

Aliases

arxiv: 1007.0786 · arxiv_version: 1007.0786v1 · doi: 10.48550/arxiv.1007.0786 · pith_short_12: ZYXZMQROU4FH · pith_short_16: ZYXZMQROU4FHPITI · pith_short_8: ZYXZMQRO

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/ZYXZMQROU4FHPITI5P2TXV5YJE \
  | 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: ce2f96422ea70a77a268ebf53bd7b849185919094b8c58b21097dc2a50262349

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59ff96ce7d1d6649ed9a410316858147696aea78080fb0f0eaa8009fd9410322",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-05T23:58:47Z",
    "title_canon_sha256": "2079d887469b17061ad54b2adfc7fe819e589df48d4e1137f9931e969dd2d8cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0786",
    "kind": "arxiv",
    "version": 1
  }
}