Pith Number

pith:DV2B5CK2

pith:1999:DV2B5CK2KUWVIEOIL6RITZUFWT

not attested not anchored not stored refs pending

Almost all extraspecial p-groups are Swan groups

David J. Green (University of Wuppertal, Germany), Pham Anh Minh (University of Hue, Vietnam)

arxiv:math/9911083 v1 · 1999-11-12 · math.AT · 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{DV2B5CK2KUWVIEOIL6RITZUFWT}

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	2026-05-18T02:26:39.789426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d741e895a552d5411c85fa289e685b4f043f4ce2dd8ca3c4fdf7274537547fa

Aliases

arxiv: math/9911083 · arxiv_version: math/9911083v1 · doi: 10.48550/arxiv.math/9911083 · pith_short_12: DV2B5CK2KUWV · pith_short_16: DV2B5CK2KUWVIEOI · pith_short_8: DV2B5CK2

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/DV2B5CK2KUWVIEOIL6RITZUFWT \
  | 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: 1d741e895a552d5411c85fa289e685b4f043f4ce2dd8ca3c4fdf7274537547fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd7f27f62d717048cb449d4ffc230f46a24a4c2adf1de1e69a0a35cf01f0dbb8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "1999-11-12T15:43:57Z",
    "title_canon_sha256": "dde7ce25383dc76152819216ac4d449fd0d3684e156408359eadd130a76b0627"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911083",
    "kind": "arxiv",
    "version": 1
  }
}