Pith Number

pith:EM3JCR3M

pith:2015:EM3JCR3MANM6M6GCNYAYOQNC5F

not attested not anchored not stored refs pending

Representing Random Permutations as the Product of Two Involutions

Charles Burnette, Eric Schmutz

arxiv:1507.05701 v1 · 2015-07-21 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EM3JCR3MANM6M6GCNYAYOQNC5F}

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	2026-05-18T01:35:06.742668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

233691476c0359e678c26e018741a2e97a1ebcd62f1a41b20efe91dcd7612256

Aliases

arxiv: 1507.05701 · arxiv_version: 1507.05701v1 · doi: 10.48550/arxiv.1507.05701 · pith_short_12: EM3JCR3MANM6 · pith_short_16: EM3JCR3MANM6M6GC · pith_short_8: EM3JCR3M

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/EM3JCR3MANM6M6GCNYAYOQNC5F \
  | 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: 233691476c0359e678c26e018741a2e97a1ebcd62f1a41b20efe91dcd7612256

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32cea48bf1c52e0eec9baadb8f3d48614a021e9d37f59790cfad8e69e45abeb9",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-21T04:09:06Z",
    "title_canon_sha256": "4c4e4ecee76d1ab50ad1ddd9cea5e8ab5e82e805113892edb5e84f61dc017525"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05701",
    "kind": "arxiv",
    "version": 1
  }
}