Pith Number

pith:TLWPOLBY

pith:2010:TLWPOLBYGZOIYT6YEIRCQABS3A

not attested not anchored not stored refs pending

Stable W-length

Danny Calegari, Dongping Zhuang

arxiv:1008.2219 v2 · 2010-08-12 · 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{TLWPOLBYGZOIYT6YEIRCQABS3A}

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	2026-05-18T04:02:50.490612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aecf72c38365c8c4fd82222280032d82a6e5dbee3b2423afb6444a81b7e16e6

Aliases

arxiv: 1008.2219 · arxiv_version: 1008.2219v2 · doi: 10.48550/arxiv.1008.2219 · pith_short_12: TLWPOLBYGZOI · pith_short_16: TLWPOLBYGZOIYT6Y · pith_short_8: TLWPOLBY

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/TLWPOLBYGZOIYT6YEIRCQABS3A \
  | 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: 9aecf72c38365c8c4fd82222280032d82a6e5dbee3b2423afb6444a81b7e16e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a064a613f2efc90e98f08845c5391784d345dacbe4cffa056fc11b3cba98c4b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-08-12T21:24:22Z",
    "title_canon_sha256": "3a1405c8e041735be53e72140b3f84fae75ac23c155965f8248bd62425603889"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2219",
    "kind": "arxiv",
    "version": 2
  }
}