Pith Number

pith:VD4AQ7JF

pith:2016:VD4AQ7JFAU35TLNVNSKOYNJDQA

not attested not anchored not stored refs pending

A better lower bound on average degree of 4-list-critical graphs

Landon Rabern

arxiv:1602.08532 v1 · 2016-02-26 · 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{VD4AQ7JFAU35TLNVNSKOYNJDQA}

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	2026-05-18T01:19:52.568217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8f8087d250537d9adb56c94ec3523802cd9e1996b32b8cb9df95d71950d5c92

Aliases

arxiv: 1602.08532 · arxiv_version: 1602.08532v1 · doi: 10.48550/arxiv.1602.08532 · pith_short_12: VD4AQ7JFAU35 · pith_short_16: VD4AQ7JFAU35TLNV · pith_short_8: VD4AQ7JF

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/VD4AQ7JFAU35TLNVNSKOYNJDQA \
  | 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: a8f8087d250537d9adb56c94ec3523802cd9e1996b32b8cb9df95d71950d5c92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e7b1f1c66d21f79435fa128257767f0a43c2db5d9fc1fc198d10302bf2d6160",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-26T23:55:42Z",
    "title_canon_sha256": "e65eea03e03dcaee4146f256c3ce61c49c8ddfbdb0b1084c94f0debacb97f716"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.08532",
    "kind": "arxiv",
    "version": 1
  }
}