Pith Number

pith:UPMB3GT6

pith:2007:UPMB3GT6ZJGVLXTGYNRVVMTTWA

not attested not anchored not stored refs pending

An EL-labeling of the subgroup lattice

Russ Woodroofe

arxiv:0708.3539 v3 · 2007-08-27 · math.CO · 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{UPMB3GT6ZJGVLXTGYNRVVMTTWA}

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	2026-05-18T04:30:58.561472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3d81d9a7eca4d55de66c3635ab273b031a146fc7df88feb4abc0f2965f875d0

Aliases

arxiv: 0708.3539 · arxiv_version: 0708.3539v3 · doi: 10.48550/arxiv.0708.3539 · pith_short_12: UPMB3GT6ZJGV · pith_short_16: UPMB3GT6ZJGVLXTG · pith_short_8: UPMB3GT6

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/UPMB3GT6ZJGVLXTGYNRVVMTTWA \
  | 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: a3d81d9a7eca4d55de66c3635ab273b031a146fc7df88feb4abc0f2965f875d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d086a42cef566190ef6c3446cd1643793b7cf3799ddbf409884ab6d65d48decb",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2007-08-27T07:47:39Z",
    "title_canon_sha256": "60c69c82acd63f4f12a784d4ed70ca9a4e99ab6f148be02440b8c664ef9ac5e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.3539",
    "kind": "arxiv",
    "version": 3
  }
}