Pith Number

pith:LFXQWYP4

pith:2012:LFXQWYP4JBGJIBBCHBB4RSLP5A

not attested not anchored not stored refs pending

On strong approximation for algebraic groups

Andrei S. Rapinchuk

arxiv:1207.4425 v1 · 2012-07-18 · math.NT · 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{LFXQWYP4JBGJIBBCHBB4RSLP5A}

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	2026-05-18T03:50:38.336607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

596f0b61fc484c9404223843c8c96fe836827cdbff6965bf56c12652fe53c454

Aliases

arxiv: 1207.4425 · arxiv_version: 1207.4425v1 · doi: 10.48550/arxiv.1207.4425 · pith_short_12: LFXQWYP4JBGJ · pith_short_16: LFXQWYP4JBGJIBBC · pith_short_8: LFXQWYP4

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/LFXQWYP4JBGJIBBCHBB4RSLP5A \
  | 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: 596f0b61fc484c9404223843c8c96fe836827cdbff6965bf56c12652fe53c454

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74f27e4cef775763db768f6d641275006b430c615bb57e893202ec00dfb8e809",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-18T17:57:24Z",
    "title_canon_sha256": "2e3c169df337c7acc44878f53af3b4755ea17c2fcb3800fbd89ef402dbcea9f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4425",
    "kind": "arxiv",
    "version": 1
  }
}