Pith Number

pith:ZQH5DT6U

pith:2018:ZQH5DT6UFO2AZDBIXD6XAFNUHR

not attested not anchored not stored refs pending

On the Minimal Edge Density of $K_4$-free 6-critical Graphs

Luke Postle, Wenbo Gao

arxiv:1811.02940 v1 · 2018-11-07 · 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{ZQH5DT6UFO2AZDBIXD6XAFNUHR}

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	2026-05-18T00:01:20.335227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc0fd1cfd42bb40c8c28b8fd7015b43c451c652c45ae2f5ce94fbde769bac348

Aliases

arxiv: 1811.02940 · arxiv_version: 1811.02940v1 · doi: 10.48550/arxiv.1811.02940 · pith_short_12: ZQH5DT6UFO2A · pith_short_16: ZQH5DT6UFO2AZDBI · pith_short_8: ZQH5DT6U

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/ZQH5DT6UFO2AZDBIXD6XAFNUHR \
  | 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: cc0fd1cfd42bb40c8c28b8fd7015b43c451c652c45ae2f5ce94fbde769bac348

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3e0f9bf2d101314c4cb49182fcdfcb3f696dd393ebd18817aa8e8197d7603cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-11-07T15:38:24Z",
    "title_canon_sha256": "d9afbc346ddceda4a40f5b7dc9ec4d407d75dfd7c5335bc6341df57e8d8f0cfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.02940",
    "kind": "arxiv",
    "version": 1
  }
}