Pith Number

pith:MSGV7OZF

pith:2012:MSGV7OZFE6K3SOE3XC7WX2N4I2

not attested not anchored not stored refs pending

Growth of periodic quotients of hyperbolic groups

R\'emi Coulon

arxiv:1211.4271 v1 · 2012-11-18 · 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{MSGV7OZFE6K3SOE3XC7WX2N4I2}

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	2026-05-18T02:41:42.773698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

648d5fbb252795b9389bb8bf6be9bc4682ae158f9a4e8a76439caa15e2d2ac5e

Aliases

arxiv: 1211.4271 · arxiv_version: 1211.4271v1 · doi: 10.48550/arxiv.1211.4271 · pith_short_12: MSGV7OZFE6K3 · pith_short_16: MSGV7OZFE6K3SOE3 · pith_short_8: MSGV7OZF

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/MSGV7OZFE6K3SOE3XC7WX2N4I2 \
  | 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: 648d5fbb252795b9389bb8bf6be9bc4682ae158f9a4e8a76439caa15e2d2ac5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "586ec8910613c8640502b28ba8f07f46869bca41c3aa8b4197d8654ea5f94049",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-18T23:34:47Z",
    "title_canon_sha256": "db57bf5b3d3ffc76ed883a7d7cb081abe5ddefa7a1e467d363d2db77546dbfa8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4271",
    "kind": "arxiv",
    "version": 1
  }
}