Pith Number

pith:ZBTB6BCQ

pith:2013:ZBTB6BCQYVOYMRT4RPWXH3GVPZ

not attested not anchored not stored refs pending

Improved bounds for the shortness coefficient of cyclically 4-edge connected cubic graphs and snarks

Klas Markstr\"om

arxiv:1309.3870 v2 · 2013-09-16 · 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{ZBTB6BCQYVOYMRT4RPWXH3GVPZ}

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	2026-05-18T03:03:09.708157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8661f0450c55d86467c8bed73ecd57e6f2c4d0915b9fe5256d82c03c3acdd0d

Aliases

arxiv: 1309.3870 · arxiv_version: 1309.3870v2 · doi: 10.48550/arxiv.1309.3870 · pith_short_12: ZBTB6BCQYVOY · pith_short_16: ZBTB6BCQYVOYMRT4 · pith_short_8: ZBTB6BCQ

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/ZBTB6BCQYVOYMRT4RPWXH3GVPZ \
  | 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: c8661f0450c55d86467c8bed73ecd57e6f2c4d0915b9fe5256d82c03c3acdd0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ff90cde3389c49c7fe94811d745808537008240f8c98f8f1c413b8c2da4e5ac",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-16T09:18:53Z",
    "title_canon_sha256": "0e194e749a67605a5269cd6ae9fa0aa476c2a0b2b8b77028b15bef2ec2d106f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3870",
    "kind": "arxiv",
    "version": 2
  }
}