Pith Number

pith:M5EF4M32

pith:2002:M5EF4M32RRBLERB3E6DSGFNDE4

not attested not anchored not stored refs pending

Loops and the Lagrange property

Andrew Rajah, Michael K. Kinyon, Orin Chein, Petr Vojtechovsky

arxiv:math/0205141 v1 · 2002-05-13 · 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{M5EF4M32RRBLERB3E6DSGFNDE4}

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	2026-05-18T01:05:29.566511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67485e337a8c42b2443b27872315a32726d1fca7dff1d6044ad92f869cef0547

Aliases

arxiv: math/0205141 · arxiv_version: math/0205141v1 · doi: 10.48550/arxiv.math/0205141 · pith_short_12: M5EF4M32RRBL · pith_short_16: M5EF4M32RRBLERB3 · pith_short_8: M5EF4M32

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/M5EF4M32RRBLERB3E6DSGFNDE4 \
  | 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: 67485e337a8c42b2443b27872315a32726d1fca7dff1d6044ad92f869cef0547

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ed07afa9c6845264fa41b93dcd8f2fe4f68972571543d824df02f3aa7faabbf",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2002-05-13T22:34:28Z",
    "title_canon_sha256": "92fe6298945299232fedabff6f493e1d34571721af0b4cfc6f87dc92b938a71e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0205141",
    "kind": "arxiv",
    "version": 1
  }
}