Pith Number

pith:QDY3L2IR

pith:2012:QDY3L2IR2UQGB7MUQKFP36BVIC

not attested not anchored not stored refs pending

A Dual Interpretation of the Gromov--Thurston Proof of Mostow Rigidity and Volume Rigidity for Representations of Hyperbolic Lattices

Alessandra Iozzi, Marc Burger, Michelle Bucher

arxiv:1205.1018 v1 · 2012-05-04 · math.MG · 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{QDY3L2IR2UQGB7MUQKFP36BVIC}

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	2026-05-18T03:56:23.341741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80f1b5e911d52060fd94828afdf83540b42aee5c87926a3c4b7a8bd711695186

Aliases

arxiv: 1205.1018 · arxiv_version: 1205.1018v1 · doi: 10.48550/arxiv.1205.1018 · pith_short_12: QDY3L2IR2UQG · pith_short_16: QDY3L2IR2UQGB7MU · pith_short_8: QDY3L2IR

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/QDY3L2IR2UQGB7MUQKFP36BVIC \
  | 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: 80f1b5e911d52060fd94828afdf83540b42aee5c87926a3c4b7a8bd711695186

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f4594b87600976e53c810a8386668c9470bce1c5e22a02317c203defd250ee4",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-05-04T17:53:39Z",
    "title_canon_sha256": "a30f414744f10d2ddc762b237f502cfe0fc1e00075ab00d32c19d733f965758b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1018",
    "kind": "arxiv",
    "version": 1
  }
}