Pith Number

pith:MJZH6QCZ

pith:2009:MJZH6QCZH652L3SXHMLRNZZGYM

not attested not anchored not stored refs pending

Hall polynomials via automorphisms of short exact sequences

Markus Schmidmeier

arxiv:0910.1962 v1 · 2009-10-11 · math.RT · 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{MJZH6QCZH652L3SXHMLRNZZGYM}

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	2026-05-17T23:42:14.646691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62727f40593fbba5ee573b1716e726c3313862987e212ca4ef2ffd8a70e2742f

Aliases

arxiv: 0910.1962 · arxiv_version: 0910.1962v1 · doi: 10.48550/arxiv.0910.1962 · pith_short_12: MJZH6QCZH652 · pith_short_16: MJZH6QCZH652L3SX · pith_short_8: MJZH6QCZ

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/MJZH6QCZH652L3SXHMLRNZZGYM \
  | 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: 62727f40593fbba5ee573b1716e726c3313862987e212ca4ef2ffd8a70e2742f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13d4da040dbb407acd028cf6f5bb5a9bc1d6a97a87d214f05b68ef82e2b96c52",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2009-10-11T02:30:38Z",
    "title_canon_sha256": "835921fcf2c91327388d0188ee2ef558697b6dad3023b09391509321bfd48756"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.1962",
    "kind": "arxiv",
    "version": 1
  }
}