Pith Number

pith:NTYGSZ57

pith:2010:NTYGSZ57LHCSBOUOZDJWX5S4YF

not attested not anchored not stored refs pending

Supercharacters and pattern subgroups in the upper triangular groups

Tung Le

arxiv:1008.2269 v2 · 2010-08-13 · math.RT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NTYGSZ57LHCSBOUOZDJWX5S4YF}

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	2026-05-18T03:16:50.071235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cf06967bf59c520ba8ec8d36bf65cc153528d29fe8041d65979711015a22778

Aliases

arxiv: 1008.2269 · arxiv_version: 1008.2269v2 · doi: 10.48550/arxiv.1008.2269 · pith_short_12: NTYGSZ57LHCS · pith_short_16: NTYGSZ57LHCSBOUO · pith_short_8: NTYGSZ57

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/NTYGSZ57LHCSBOUOZDJWX5S4YF \
  | 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: 6cf06967bf59c520ba8ec8d36bf65cc153528d29fe8041d65979711015a22778

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f9d1e4275f613cc10204e3b3dc5afe3c81909efa71c92e622f8a668f7722b1e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2010-08-13T08:48:44Z",
    "title_canon_sha256": "6a3e237c4dc7eb74c713f74acd1443bd821d59488e086b2515494aa3b6ded827"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2269",
    "kind": "arxiv",
    "version": 2
  }
}