Pith Number

pith:I7WNYYMA

pith:2009:I7WNYYMAHSM62MOPEGW6FB63RG

not attested not anchored not stored refs pending

Elementary embeddings in torsion-free hyperbolic groups

Chlo\'e Perin

arxiv:0903.0945 v3 · 2009-03-05 · math.GR · math.LO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I7WNYYMAHSM62MOPEGW6FB63RG}

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	2026-05-18T03:53:32.114022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47ecdc61803c99ed31cf21ade287db8985b086c8040534a0a370486d72e48fe1

Aliases

arxiv: 0903.0945 · arxiv_version: 0903.0945v3 · doi: 10.48550/arxiv.0903.0945 · pith_short_12: I7WNYYMAHSM6 · pith_short_16: I7WNYYMAHSM62MOP · pith_short_8: I7WNYYMA

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/I7WNYYMAHSM62MOPEGW6FB63RG \
  | 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: 47ecdc61803c99ed31cf21ade287db8985b086c8040534a0a370486d72e48fe1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91f384eddf478247c775e4a062a8a54f858acb7d1ad225390fa9abb4b4ba1071",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-03-05T09:53:41Z",
    "title_canon_sha256": "0520abaab37b0068259669bfc1e6906da4b21a4854bbb2480bbab91e5fa6db7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.0945",
    "kind": "arxiv",
    "version": 3
  }
}