Pith Number

pith:VCF473SJ

pith:2016:VCF473SJKGAYTNGDI72UGE4CLP

not attested not anchored not stored refs pending

A better lower bound on average degree of k-list-critical graphs

Landon Rabern

arxiv:1608.06989 v1 · 2016-08-24 · 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{VCF473SJKGAYTNGDI72UGE4CLP}

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	2026-05-18T01:07:56.338495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a88bcfee49518189b4c347f54313825be1865b47637e3ad2769f4903eb45f823

Aliases

arxiv: 1608.06989 · arxiv_version: 1608.06989v1 · doi: 10.48550/arxiv.1608.06989 · pith_short_12: VCF473SJKGAY · pith_short_16: VCF473SJKGAYTNGD · pith_short_8: VCF473SJ

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/VCF473SJKGAYTNGDI72UGE4CLP \
  | 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: a88bcfee49518189b4c347f54313825be1865b47637e3ad2769f4903eb45f823

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aa064af05d5fe4ad3bfa96f4776838d4b2690b6e2384c2d8b945ca038b3c12c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-24T23:57:09Z",
    "title_canon_sha256": "98d810bdef9e40b6d01baa63873f04c79272d4c6c98241da529aae3dbf1166ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.06989",
    "kind": "arxiv",
    "version": 1
  }
}