Pith Number

pith:J7IELOJG

pith:2012:J7IELOJGVAN72CZLOX53I7XPVA

not attested not anchored not stored refs pending

On products of long cycles: short cycle dependence and separation probabilities

Amarpreet Rattan, Valentin F\'eray

arxiv:1211.6630 v3 · 2012-11-28 · 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{J7IELOJGVAN72CZLOX53I7XPVA}

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	2026-05-18T01:30:41.329509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fd045b926a81bfd0b2b75fbb47eefa82a00ce21ef63778ca421acf044d686f1

Aliases

arxiv: 1211.6630 · arxiv_version: 1211.6630v3 · doi: 10.48550/arxiv.1211.6630 · pith_short_12: J7IELOJGVAN7 · pith_short_16: J7IELOJGVAN72CZL · pith_short_8: J7IELOJG

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/J7IELOJGVAN72CZLOX53I7XPVA \
  | 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: 4fd045b926a81bfd0b2b75fbb47eefa82a00ce21ef63778ca421acf044d686f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fb2a9a300ded856ae150c3446296988af3c45bd7faf9b6c97232e7b5b393f3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-28T15:22:00Z",
    "title_canon_sha256": "6594adb476a9f1bc9458527072f83d741c2af84b2cd28f6232ca955eb5c65892"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6630",
    "kind": "arxiv",
    "version": 3
  }
}