Pith Number

pith:XBJZ6WRX

pith:2010:XBJZ6WRXXUHEHHG7T6KNGMSUVO

not attested not anchored not stored refs pending

Periodic elements in Garside groups

Eon-Kyung Lee, Sang-Jin Lee

arxiv:1004.5308 v2 · 2010-04-29 · math.GT · 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{XBJZ6WRXXUHEHHG7T6KNGMSUVO}

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	2026-05-18T02:24:15.025951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8539f5a37bd0e439cdf9f94d33254ab8e3ec08e48216fc9b6ce5b2c9bb661f3

Aliases

arxiv: 1004.5308 · arxiv_version: 1004.5308v2 · doi: 10.48550/arxiv.1004.5308 · pith_short_12: XBJZ6WRXXUHE · pith_short_16: XBJZ6WRXXUHEHHG7 · pith_short_8: XBJZ6WRX

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/XBJZ6WRXXUHEHHG7T6KNGMSUVO \
  | 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: b8539f5a37bd0e439cdf9f94d33254ab8e3ec08e48216fc9b6ce5b2c9bb661f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58ae3d07bc11dee2a4f4f7527758b0fe366c7aeeaf990d816059ec43b1fbd564",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-04-29T14:41:17Z",
    "title_canon_sha256": "d6e3aac5fc23660a53a7f97841233d3c99ed452546dbb0788bf6589cd2f4179c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5308",
    "kind": "arxiv",
    "version": 2
  }
}