Pith Number

pith:VR55JE3Z

pith:2011:VR55JE3ZRQ5F7NGEQBZIQQLSYL

not attested not anchored not stored refs pending

Spectra of Symmetrized Shuffling Operators

Franco Saliola, Victor Reiner, Volkmar Welker

arxiv:1102.2460 v2 · 2011-02-11 · math.CO · math.PR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VR55JE3ZRQ5F7NGEQBZIQQLSYL}

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	2026-05-18T04:23:45.321345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac7bd493798c3a5fb4c48072884172c2eb0517e668a52881b610b1c8838632c5

Aliases

arxiv: 1102.2460 · arxiv_version: 1102.2460v2 · doi: 10.48550/arxiv.1102.2460 · pith_short_12: VR55JE3ZRQ5F · pith_short_16: VR55JE3ZRQ5F7NGE · pith_short_8: VR55JE3Z

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/VR55JE3ZRQ5F7NGEQBZIQQLSYL \
  | 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: ac7bd493798c3a5fb4c48072884172c2eb0517e668a52881b610b1c8838632c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6a5233debbd4952adfe5a5bc58de5190c931133f215d772ad62de5c161202fa",
    "cross_cats_sorted": [
      "math.PR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-11T23:31:37Z",
    "title_canon_sha256": "717196e5b420ef4abc1ff87122f19c28f2741639998042edf4fac60a8190b724"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2460",
    "kind": "arxiv",
    "version": 2
  }
}