Pith Number

pith:Q6ZDLBCT

pith:2005:Q6ZDLBCTFKMSA37U6DHNPSA4OH

not attested not anchored not stored refs pending

The unbounded dead-end depth property is not a group invariant

Andrew D. Warshall, Tim R. Riley

arxiv:math/0504121 v2 · 2005-04-06 · 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{Q6ZDLBCTFKMSA37U6DHNPSA4OH}

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	2026-05-18T04:42:22.441622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87b23584532a99206ff4f0ced7c81c71fadfdc48a6b8378cb55ed50977a6d092

Aliases

arxiv: math/0504121 · arxiv_version: math/0504121v2 · doi: 10.48550/arxiv.math/0504121 · pith_short_12: Q6ZDLBCTFKMS · pith_short_16: Q6ZDLBCTFKMSA37U · pith_short_8: Q6ZDLBCT

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/Q6ZDLBCTFKMSA37U6DHNPSA4OH \
  | 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: 87b23584532a99206ff4f0ced7c81c71fadfdc48a6b8378cb55ed50977a6d092

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da2dbf187e6c8aef34ea99202eb56babb734f1479503a4807a886bbe19489ef2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-04-06T22:05:25Z",
    "title_canon_sha256": "6df25d46fb308ede5ca535c76204ecc839cb6f7d3be49fb1e08cd77743c38eb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504121",
    "kind": "arxiv",
    "version": 2
  }
}