Pith Number

pith:KFHYDR7T

pith:2017:KFHYDR7T7JREHTZGGWSXX552HY

not attested not anchored not stored refs pending

Rational embeddings of hyperbolic groups

Collin Bleak, Francesco Matucci, James Belk

arxiv:1711.08369 v2 · 2017-11-22 · 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{KFHYDR7T7JREHTZGGWSXX552HY}

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	2026-05-18T00:02:13.144008Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

514f81c7f3fa6243cf2635a57bf7ba3e08d4d164c8bc6febfba0fd9ae9527f9f

Aliases

arxiv: 1711.08369 · arxiv_version: 1711.08369v2 · doi: 10.48550/arxiv.1711.08369 · pith_short_12: KFHYDR7T7JRE · pith_short_16: KFHYDR7T7JREHTZG · pith_short_8: KFHYDR7T

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/KFHYDR7T7JREHTZGGWSXX552HY \
  | 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: 514f81c7f3fa6243cf2635a57bf7ba3e08d4d164c8bc6febfba0fd9ae9527f9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fb37edb27cae44deac41dd852b90ccaf121f9817594c82f89fcdaac8d79299a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-11-22T16:21:15Z",
    "title_canon_sha256": "f0dd7d85b6dfb9879e9171bd9a73de9d50e0675a8ae9c2facb393eaacb73e939"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.08369",
    "kind": "arxiv",
    "version": 2
  }
}