Pith Number

pith:CZSQTABP

pith:2014:CZSQTABPI6DXKMBX2DNI7F2TT7

not attested not anchored not stored refs pending

Improved lower bounds on the number of edges in list critical and online list critical graphs

Hal Kierstead, Landon Rabern

arxiv:1406.7355 v2 · 2014-06-28 · 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{CZSQTABPI6DXKMBX2DNI7F2TT7}

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	2026-05-18T01:23:45.423822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

166509802f4787753037d0da8f97539feaaf3a1af8aa132398886e2437d7b375

Aliases

arxiv: 1406.7355 · arxiv_version: 1406.7355v2 · doi: 10.48550/arxiv.1406.7355 · pith_short_12: CZSQTABPI6DX · pith_short_16: CZSQTABPI6DXKMBX · pith_short_8: CZSQTABP

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/CZSQTABPI6DXKMBX2DNI7F2TT7 \
  | 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: 166509802f4787753037d0da8f97539feaaf3a1af8aa132398886e2437d7b375

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efeed858d35b5ca43346d617e981e0920979618045441877e200f4f29798ee0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-06-28T04:44:58Z",
    "title_canon_sha256": "2d2b63613e2374f20cf8588b0892d723b5552c2c1999890ea5deb845d783cb20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.7355",
    "kind": "arxiv",
    "version": 2
  }
}