Pith Number

pith:Z3BBT5JT

pith:2009:Z3BBT5JT2QMDGIDUBLA4EFGLHR

not attested not anchored not stored refs pending

Universal deformation rings and generalized quaternion defect groups

Frauke M. Bleher

arxiv:0909.1031 v2 · 2009-09-05 · 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{Z3BBT5JT2QMDGIDUBLA4EFGLHR}

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	2026-05-18T04:40:56.162113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cec219f533d4183320740ac1c214cb3c6509379f8f02c88f438600f2de0fead9

Aliases

arxiv: 0909.1031 · arxiv_version: 0909.1031v2 · doi: 10.48550/arxiv.0909.1031 · pith_short_12: Z3BBT5JT2QMD · pith_short_16: Z3BBT5JT2QMDGIDU · pith_short_8: Z3BBT5JT

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/Z3BBT5JT2QMDGIDUBLA4EFGLHR \
  | 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: cec219f533d4183320740ac1c214cb3c6509379f8f02c88f438600f2de0fead9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aff6f2053e2c6d09bf699ba421deb57e9c21a457ff8c3b3d4d9ed601d43faa3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-05T14:15:36Z",
    "title_canon_sha256": "42fac4ebac7ffc7615cb04bdfd4d5de41b397022838d64fa87ef5ad160205c9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1031",
    "kind": "arxiv",
    "version": 2
  }
}