Pith Number

pith:E2BRPMVT

pith:2010:E2BRPMVTJUMNKXJBWDW445KEK3

not attested not anchored not stored refs pending

A Note on the Critical Group of a Line Graph

David Perkinson, Nicholas Salter, Tianyuan Xu

arxiv:1008.2557 v2 · 2010-08-15 · 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{E2BRPMVTJUMNKXJBWDW445KEK3}

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	2026-05-18T04:34:55.177846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

268317b2b34d18d55d21b0edce754456f96c558965e88759776f1544a1e7b7f7

Aliases

arxiv: 1008.2557 · arxiv_version: 1008.2557v2 · doi: 10.48550/arxiv.1008.2557 · pith_short_12: E2BRPMVTJUMN · pith_short_16: E2BRPMVTJUMNKXJB · pith_short_8: E2BRPMVT

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/E2BRPMVTJUMNKXJBWDW445KEK3 \
  | 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: 268317b2b34d18d55d21b0edce754456f96c558965e88759776f1544a1e7b7f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d133ba183a0dd02c6b5436e6084f65fa2c0cc9810d361548829af0f96248bb0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-08-15T23:20:03Z",
    "title_canon_sha256": "26cb26bf9a27e6db2bce927b7477d76986dac0a27c3b20cca4b2a335223174b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2557",
    "kind": "arxiv",
    "version": 2
  }
}