Pith Number

pith:HVIQKQ4A

pith:2011:HVIQKQ4AZVKXP56GRMYW744PYZ

not attested not anchored not stored refs pending

Statistical hyperbolicity in groups

Christopher Mooney, Moon Duchin, Samuel Leli\`evre

arxiv:1104.4460 v1 · 2011-04-22 · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HVIQKQ4AZVKXP56GRMYW744PYZ}

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	2026-05-18T01:22:29.017285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d51054380cd5577f7c68b316ff38fc64e5f83f05d26cb1d0ab96726cdac64a7

Aliases

arxiv: 1104.4460 · arxiv_version: 1104.4460v1 · doi: 10.48550/arxiv.1104.4460 · pith_short_12: HVIQKQ4AZVKX · pith_short_16: HVIQKQ4AZVKXP56G · pith_short_8: HVIQKQ4A

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/HVIQKQ4AZVKXP56GRMYW744PYZ \
  | 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: 3d51054380cd5577f7c68b316ff38fc64e5f83f05d26cb1d0ab96726cdac64a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b946ab3de47e7160480f8bfca762e5a1adf7b7730e6215df012974209f46fd6",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-04-22T14:54:50Z",
    "title_canon_sha256": "a2b6e998adcb3dcc0d66b653eba948704f742b550b44afc5794fe08f55e80f4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4460",
    "kind": "arxiv",
    "version": 1
  }
}