Pith Number

pith:E2C4KS5E

pith:2012:E2C4KS5EYWKJFC3CJGZ3QG7TKN

not attested not anchored not stored refs pending

On the triangle space of a random graph

Arran Hamm, Bobby DeMarco, Jeff Kahn

arxiv:1207.6717 v1 · 2012-07-28 · math.PR · 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{E2C4KS5EYWKJFC3CJGZ3QG7TKN}

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	2026-05-18T03:49:48.931394Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2685c54ba4c594928b6249b3b81bf3534cfa5a37a7345990c1e26edabadd975a

Aliases

arxiv: 1207.6717 · arxiv_version: 1207.6717v1 · doi: 10.48550/arxiv.1207.6717 · pith_short_12: E2C4KS5EYWKJ · pith_short_16: E2C4KS5EYWKJFC3C · pith_short_8: E2C4KS5E

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/E2C4KS5EYWKJFC3CJGZ3QG7TKN \
  | 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: 2685c54ba4c594928b6249b3b81bf3534cfa5a37a7345990c1e26edabadd975a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "561db6d22d6f423d8b2fd876917edb00c4ebbcdf048e94d7c8758c181524f343",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-28T18:09:19Z",
    "title_canon_sha256": "f655f9653f39f4f5cb2482bfeecfb68c128b77a39f5727fa4d85c394f2392789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6717",
    "kind": "arxiv",
    "version": 1
  }
}