Pith Number

pith:5MBX7X3Y

pith:2005:5MBX7X3YVO4TKLIAYSJQTO7OQE

not attested not anchored not stored refs pending

Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables

Christophe Reutenauer, Mercedes Rosas, Mike Zabrocki, Nantel Bergeron

arxiv:math/0502082 v1 · 2005-02-04 · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5MBX7X3YVO4TKLIAYSJQTO7OQE}

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	2026-05-18T01:00:03.435057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb037fdf78abb9352d00c49309bbee810f38806e646f8a5370651efa2d1a9be2

Aliases

arxiv: math/0502082 · arxiv_version: math/0502082v1 · doi: 10.48550/arxiv.math/0502082 · pith_short_12: 5MBX7X3YVO4T · pith_short_16: 5MBX7X3YVO4TKLIA · pith_short_8: 5MBX7X3Y

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/5MBX7X3YVO4TKLIAYSJQTO7OQE \
  | 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: eb037fdf78abb9352d00c49309bbee810f38806e646f8a5370651efa2d1a9be2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f60013c619331f08271a9d24e4870641f92edf8eed1842ae8a34c626e7d92b8",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2005-02-04T04:47:44Z",
    "title_canon_sha256": "772bd5ff2eae985aeaf9dfe233bf5c20739a60cdedd3ce270b86bf754ec6d613"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0502082",
    "kind": "arxiv",
    "version": 1
  }
}