Pith Number

pith:LE4B23EH

pith:2016:LE4B23EHOKLRC6XDSBUCXCC2ZX

not attested not anchored not stored refs pending

An exact upper bound for sums of element orders in non-cyclic finite groups

Marcel Herzog, Mercede Maj, Patrizia Longobardi

arxiv:1610.03669 v1 · 2016-10-12 · 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{LE4B23EHOKLRC6XDSBUCXCC2ZX}

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	2026-05-18T01:02:29.619144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59381d6c877297117ae390682b885acdc7609974f7e7670d61300d97653ea385

Aliases

arxiv: 1610.03669 · arxiv_version: 1610.03669v1 · doi: 10.48550/arxiv.1610.03669 · pith_short_12: LE4B23EHOKLR · pith_short_16: LE4B23EHOKLRC6XD · pith_short_8: LE4B23EH

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/LE4B23EHOKLRC6XDSBUCXCC2ZX \
  | 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: 59381d6c877297117ae390682b885acdc7609974f7e7670d61300d97653ea385

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "139b4d155c0dfe4dcd78da22af05c90029a725db81d34e856db4cc82e5b10e4b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-10-12T11:07:28Z",
    "title_canon_sha256": "49648a2cf806300f9139b04143fa7c2d494ccb62bf5e5ad1ce2f3350485c57bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03669",
    "kind": "arxiv",
    "version": 1
  }
}