Pith Number

pith:5AW4A6DE

pith:2012:5AW4A6DEU223FTXBUOV4AHQKIJ

not attested not anchored not stored refs pending

On groups and fields interpretable in torsion-free hyperbolic groups

Anand Pillay, Chlo\'e Perin, Katrin Tent, Rizos Sklinos

arxiv:1210.5757 v2 · 2012-10-21 · math.LO · 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{5AW4A6DEU223FTXBUOV4AHQKIJ}

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	2026-05-18T03:33:13.801679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e82dc07864a6b5b2cee1a3abc01e0a42700bbacc583bb0e6c41adeba36e5fe44

Aliases

arxiv: 1210.5757 · arxiv_version: 1210.5757v2 · doi: 10.48550/arxiv.1210.5757 · pith_short_12: 5AW4A6DEU223 · pith_short_16: 5AW4A6DEU223FTXB · pith_short_8: 5AW4A6DE

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/5AW4A6DEU223FTXBUOV4AHQKIJ \
  | 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: e82dc07864a6b5b2cee1a3abc01e0a42700bbacc583bb0e6c41adeba36e5fe44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9a7578ad824442f0e88822e7f0170bf212c7accf10de1721f037769af45ebfe",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2012-10-21T19:46:24Z",
    "title_canon_sha256": "eb5cff0203eebb4f38451baec94f8bafcb2a938adc8db7552bacf2f8ab430b74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5757",
    "kind": "arxiv",
    "version": 2
  }
}