Pith Number

pith:UUMKJWVG

pith:2012:UUMKJWVGPT34QX6QSTIX3NH7GL

not attested not anchored not stored refs pending

On equivariant embeddings of generalized Baumslag-Solitar groups

Alain Valette, Yves Cornulier

arxiv:1212.6765 v1 · 2012-12-30 · 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{UUMKJWVGPT34QX6QSTIX3NH7GL}

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	2026-05-18T01:28:35.599468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a518a4daa67cf7c85fd094d17db4ff32e974f52dda8145cd2d1478ebdbc86fc6

Aliases

arxiv: 1212.6765 · arxiv_version: 1212.6765v1 · doi: 10.48550/arxiv.1212.6765 · pith_short_12: UUMKJWVGPT34 · pith_short_16: UUMKJWVGPT34QX6Q · pith_short_8: UUMKJWVG

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/UUMKJWVGPT34QX6QSTIX3NH7GL \
  | 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: a518a4daa67cf7c85fd094d17db4ff32e974f52dda8145cd2d1478ebdbc86fc6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77e69326ea1beea985d12196da5846f15d40a604aa92ff646cc73ed76f4ff0cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-12-30T19:31:13Z",
    "title_canon_sha256": "b259af8ac9a43087b2e1be7b84841736e30797a6ffb8d60112628fd6ef458462"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6765",
    "kind": "arxiv",
    "version": 1
  }
}