Pith Number

pith:32NGHU6U

pith:2012:32NGHU6UODVDN3JCXWEPLU6C7X

not attested not anchored not stored refs pending

Constructing graphs with no immersion of large complete graphs

Karen L. Collins, Megan E. Heenehan

arxiv:1206.1545 v1 · 2012-06-07 · 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{32NGHU6UODVDN3JCXWEPLU6C7X}

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	2026-05-18T03:54:04.856663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de9a63d3d470ea36ed22bd88f5d3c2fdcc22adda2063cf4db63095e826914924

Aliases

arxiv: 1206.1545 · arxiv_version: 1206.1545v1 · doi: 10.48550/arxiv.1206.1545 · pith_short_12: 32NGHU6UODVD · pith_short_16: 32NGHU6UODVDN3JC · pith_short_8: 32NGHU6U

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/32NGHU6UODVDN3JCXWEPLU6C7X \
  | 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: de9a63d3d470ea36ed22bd88f5d3c2fdcc22adda2063cf4db63095e826914924

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0d78c7166233d4dd8d704e42eb8ab6a2ac89aaa483bd1f4fd101fe1b1324790",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-06-07T16:29:21Z",
    "title_canon_sha256": "e5b6a748c267086c45dd0fd554b0303786261c28642a6f4725b70a0d09ae64a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1545",
    "kind": "arxiv",
    "version": 1
  }
}