Pith Number

pith:RJ2SO4MA

pith:2010:RJ2SO4MAEPAOUS4ZHCM6ATSJUJ

not attested not anchored not stored refs pending

Loop subgroups of F_r and the image of their stabilizer subgroups in GL_r(Z)

Joachim Breitner

arxiv:1012.2729 v2 · 2010-12-13 · 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{RJ2SO4MAEPAOUS4ZHCM6ATSJUJ}

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	2026-05-18T04:05:38.923994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a7527718023c0ea4b993899e04e49a26d78976503b744f9b5336116990b1df1

Aliases

arxiv: 1012.2729 · arxiv_version: 1012.2729v2 · doi: 10.48550/arxiv.1012.2729 · pith_short_12: RJ2SO4MAEPAO · pith_short_16: RJ2SO4MAEPAOUS4Z · pith_short_8: RJ2SO4MA

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/RJ2SO4MAEPAOUS4ZHCM6ATSJUJ \
  | 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: 8a7527718023c0ea4b993899e04e49a26d78976503b744f9b5336116990b1df1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98cdb57c52fee246f4bb949194ee01b23e110484e6dcc1cba1755c2249a6ccf7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-13T13:52:35Z",
    "title_canon_sha256": "e06d4ae935e8c9d3eb416418dc06778981d8dc02424f5c80e16c78bd4376c813"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2729",
    "kind": "arxiv",
    "version": 2
  }
}