Pith Number

pith:5UZCICJ3

pith:2019:5UZCICJ3N5SUDK7X6EITHZJE4P

not attested not anchored not stored refs pending

On hyperbolicity and virtual freeness of automorphism groups

Olga Varghese

arxiv:1903.05471 v2 · 2019-03-13 · 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{5UZCICJ3N5SUDK7X6EITHZJE4P}

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	2026-05-17T23:50:48.495395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed3224093b6f6541abf7f11133e524e3f99d868b30cd43707a8f0ce49610abcd

Aliases

arxiv: 1903.05471 · arxiv_version: 1903.05471v2 · doi: 10.48550/arxiv.1903.05471 · pith_short_12: 5UZCICJ3N5SU · pith_short_16: 5UZCICJ3N5SUDK7X · pith_short_8: 5UZCICJ3

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/5UZCICJ3N5SUDK7X6EITHZJE4P \
  | 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: ed3224093b6f6541abf7f11133e524e3f99d868b30cd43707a8f0ce49610abcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "595a78bf7b224be8a4dc0704dd67afddfc6474aa574e832a3083a50a750c4b2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-03-13T13:10:44Z",
    "title_canon_sha256": "40187623d5ad6cbee147c8b9cc113e971d85bde2326d9311a76179c143abe8c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.05471",
    "kind": "arxiv",
    "version": 2
  }
}