Pith Number

pith:56QLULJW

pith:2013:56QLULJWGPWYUHMSLOZRNXYCYZ

not attested not anchored not stored refs pending

Critical Groups of Graphs with Dihedral Actions

Criel Merino, Darren Glass

arxiv:1304.6011 v1 · 2013-04-22 · math.CO · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{56QLULJWGPWYUHMSLOZRNXYCYZ}

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	2026-05-18T03:27:23.521390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efa0ba2d3633ed8a1d925bb316df02c64a324d27e2451505487f345362d28229

Aliases

arxiv: 1304.6011 · arxiv_version: 1304.6011v1 · doi: 10.48550/arxiv.1304.6011 · pith_short_12: 56QLULJWGPWY · pith_short_16: 56QLULJWGPWYUHMS · pith_short_8: 56QLULJW

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/56QLULJWGPWYUHMSLOZRNXYCYZ \
  | 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: efa0ba2d3633ed8a1d925bb316df02c64a324d27e2451505487f345362d28229

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12efc8ffdfd4397e520ca1dcf1e126ad16f403164fc23df0f077df3f0dc45117",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-04-22T16:45:46Z",
    "title_canon_sha256": "52cd9ef19a07a0f9956bb3bd16e900bae5305c0850d1364e643a5d8de8eccd67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.6011",
    "kind": "arxiv",
    "version": 1
  }
}