Pith Number

pith:XJ6PBNWE

pith:2016:XJ6PBNWE4NEKSEBXESGWNBIPMU

not attested not anchored not stored refs pending

Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements

Alexander Bors

arxiv:1601.04311 v3 · 2016-01-17 · 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{XJ6PBNWE4NEKSEBXESGWNBIPMU}

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	2026-05-18T01:13:04.727148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba7cf0b6c4e348a91037248d66850f652daff75db286fb800c34514de3b5deaf

Aliases

arxiv: 1601.04311 · arxiv_version: 1601.04311v3 · doi: 10.48550/arxiv.1601.04311 · pith_short_12: XJ6PBNWE4NEK · pith_short_16: XJ6PBNWE4NEKSEBX · pith_short_8: XJ6PBNWE

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/XJ6PBNWE4NEKSEBXESGWNBIPMU \
  | 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: ba7cf0b6c4e348a91037248d66850f652daff75db286fb800c34514de3b5deaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "168971bb3ba14b2d28bf40146472800771cc99926e050110556227dbc27d12bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-01-17T16:54:43Z",
    "title_canon_sha256": "92e2711ff1b87f86aa83664edf4b77b6f9df6ca9d77058ad3d9b4fae5882bc5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04311",
    "kind": "arxiv",
    "version": 3
  }
}