Pith Number

pith:VTTZQUHT

pith:2010:VTTZQUHTZJHDUDKYYJ2CSDNCCK

not attested not anchored not stored refs pending

K\"ahler groups, real hyperbolic spaces and the Cremona group

Pierre Py, Thomas Delzant

arxiv:1012.1585 v2 · 2010-12-07 · math.AG · math.DG · 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{VTTZQUHTZJHDUDKYYJ2CSDNCCK}

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	2026-05-17T23:53:19.547857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ace79850f3ca4e3a0d58c274290da212bef390f72de813eefb27d6e61409322b

Aliases

arxiv: 1012.1585 · arxiv_version: 1012.1585v2 · doi: 10.48550/arxiv.1012.1585 · pith_short_12: VTTZQUHTZJHD · pith_short_16: VTTZQUHTZJHDUDKY · pith_short_8: VTTZQUHT

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/VTTZQUHTZJHDUDKYYJ2CSDNCCK \
  | 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: ace79850f3ca4e3a0d58c274290da212bef390f72de813eefb27d6e61409322b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72e466448bb6c6fb06297747674139b0a588a1b5f8526c3dd311500d47ddcc8e",
    "cross_cats_sorted": [
      "math.DG",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-12-07T19:51:58Z",
    "title_canon_sha256": "0f8f20ad8921777691156fafd4a5719afbf744e2adb0c3240f350d9c5a999a0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1585",
    "kind": "arxiv",
    "version": 2
  }
}