Pith Number

pith:VNRI7QDQ

pith:2016:VNRI7QDQGKI4NOLIE5N4T47U2V

not attested not anchored not stored refs pending

A Bieberbach theorem for crystallographic group extensions

John G. Ratcliffe, Steven T. Tschantz

arxiv:1607.03503 v1 · 2016-07-12 · 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{VNRI7QDQGKI4NOLIE5N4T47U2V}

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	2026-05-18T01:11:07.779539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab628fc0703291c6b968275bc9f3f4d57a34129cf80da7f609a6fe1daee5ecd6

Aliases

arxiv: 1607.03503 · arxiv_version: 1607.03503v1 · doi: 10.48550/arxiv.1607.03503 · pith_short_12: VNRI7QDQGKI4 · pith_short_16: VNRI7QDQGKI4NOLI · pith_short_8: VNRI7QDQ

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/VNRI7QDQGKI4NOLIE5N4T47U2V \
  | 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: ab628fc0703291c6b968275bc9f3f4d57a34129cf80da7f609a6fe1daee5ecd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b35c60e2b770b057f3b0648d5acfd1684e0c79a3ea3ab25642319d4580549640",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-12T20:19:52Z",
    "title_canon_sha256": "98fd69caae69cbff6dd7a724915f0029587d4b7e152ef768449bd806ac8f66fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03503",
    "kind": "arxiv",
    "version": 1
  }
}