Pith Number

pith:GOAQ2ZUC

pith:2012:GOAQ2ZUCHKFB4DVBG3LXZTZBKS

not attested not anchored not stored refs pending

On exponentiation and infinitesimal one-parameter subgroups of reductive groups

Paul Sobaje

arxiv:1209.5813 v1 · 2012-09-26 · 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{GOAQ2ZUCHKFB4DVBG3LXZTZBKS}

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	2026-05-18T03:44:46.290392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33810d66823a8a1e0ea136d77ccf2154850251e621a2f8abee452b864ec7e970

Aliases

arxiv: 1209.5813 · arxiv_version: 1209.5813v1 · doi: 10.48550/arxiv.1209.5813 · pith_short_12: GOAQ2ZUCHKFB · pith_short_16: GOAQ2ZUCHKFB4DVB · pith_short_8: GOAQ2ZUC

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/GOAQ2ZUCHKFB4DVBG3LXZTZBKS \
  | 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: 33810d66823a8a1e0ea136d77ccf2154850251e621a2f8abee452b864ec7e970

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "739719ef106377fb797a37c0ca6f0a49891d50d02df1c2ee479400c7171d35ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-09-26T02:05:23Z",
    "title_canon_sha256": "55e1c318fc67fc47eb309b18c671d070e0a80dbf17ca68f9ffafb3ec02f6df65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5813",
    "kind": "arxiv",
    "version": 1
  }
}