Pith Number

pith:WUJ74AQV

pith:2011:WUJ74AQVCVLYNX5DTFDMUND2CL

not attested not anchored not stored refs pending

Upgrading Subgroup Triple Product Property Triples

Ivo Hedtke

arxiv:1107.5973 v1 · 2011-07-29 · math.GR · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WUJ74AQVCVLYNX5DTFDMUND2CL}

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	2026-05-18T02:20:37.313860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b513fe0215155786dfa39946ca347a12d0f8a8078066393fda33087ff4e9fe6a

Aliases

arxiv: 1107.5973 · arxiv_version: 1107.5973v1 · doi: 10.48550/arxiv.1107.5973 · pith_short_12: WUJ74AQVCVLY · pith_short_16: WUJ74AQVCVLYNX5D · pith_short_8: WUJ74AQV

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/WUJ74AQVCVLYNX5DTFDMUND2CL \
  | 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: b513fe0215155786dfa39946ca347a12d0f8a8078066393fda33087ff4e9fe6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c2ccc7d2597c85738bbdc523bf8f3dbb03140a52dbd6fe1c7ebf63a1d88cf56",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-07-29T13:55:25Z",
    "title_canon_sha256": "b44d8442b732f96f01586793199e365496c4c05b4541775064ce9cc9fd7a8caf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5973",
    "kind": "arxiv",
    "version": 1
  }
}