Pith Number

pith:F4EKXKXR

pith:2010:F4EKXKXR7OZ27QRTRSA3SS7BGL

not attested not anchored not stored refs pending

Injective colorings of graphs with low average degree

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

arxiv:1006.3776 v1 · 2010-06-18 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F4EKXKXR7OZ27QRTRSA3SS7BGL}

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	2026-05-18T04:11:18.035429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f08abaaf1fbb3afc2338c81b94be132e13b9cd0a1cc7dc80c5a7f923cea81f3

Aliases

arxiv: 1006.3776 · arxiv_version: 1006.3776v1 · doi: 10.48550/arxiv.1006.3776 · pith_short_12: F4EKXKXR7OZ2 · pith_short_16: F4EKXKXR7OZ27QRT · pith_short_8: F4EKXKXR

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/F4EKXKXR7OZ27QRTRSA3SS7BGL \
  | 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: 2f08abaaf1fbb3afc2338c81b94be132e13b9cd0a1cc7dc80c5a7f923cea81f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8751ed679b49c3dc6dcf0162e99362aa9e1729b0fc405d8538c4a09c35c0a12c",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-06-18T19:06:34Z",
    "title_canon_sha256": "d0c304e030d8058cc78c6168e663f7e30b6cd432d7a467489c92353d715be86d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3776",
    "kind": "arxiv",
    "version": 1
  }
}