Pith Number

pith:NNEX43XW

pith:2015:NNEX43XWRZAKFIQBQX347S6IXY

not attested not anchored not stored refs pending

Crystallographic groups with trivial center and outer automorphism group

Andrzej Szczepa\'nski, Rafa{\l} Lutowski

arxiv:1501.03648 v1 · 2015-01-15 · 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{NNEX43XWRZAKFIQBQX347S6IXY}

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	2026-05-18T00:18:47.137384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b497e6ef68e40a2a20185f7cfcbc8be378809d4a3d8de2f26238acd442f410a

Aliases

arxiv: 1501.03648 · arxiv_version: 1501.03648v1 · doi: 10.48550/arxiv.1501.03648 · pith_short_12: NNEX43XWRZAK · pith_short_16: NNEX43XWRZAKFIQB · pith_short_8: NNEX43XW

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/NNEX43XWRZAKFIQBQX347S6IXY \
  | 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: 6b497e6ef68e40a2a20185f7cfcbc8be378809d4a3d8de2f26238acd442f410a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76d0d073f764fc4bd1e8e46845706c854eb3da8d38f8781ec5d64d5897fa4f0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-01-15T12:37:05Z",
    "title_canon_sha256": "638634713644598d6b7908c864cbc9763bb2faee835b061da6c27a28e9339fc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03648",
    "kind": "arxiv",
    "version": 1
  }
}