Pith Number

pith:NWOAU556

pith:2018:NWOAU556UGKJ7GPD3ZXHOXO5MO

not attested not anchored not stored refs pending

Generic free subgroups and statistical hyperbolicity

Suzhen Han, Wen-yuan Yang

arxiv:1812.06265 v1 · 2018-12-15 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NWOAU556UGKJ7GPD3ZXHOXO5MO}

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	2026-05-17T23:58:10.744775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d9c0a77bea1949f99e3de6e775ddd63b71fc373655e645dd265569835f7d020

Aliases

arxiv: 1812.06265 · arxiv_version: 1812.06265v1 · doi: 10.48550/arxiv.1812.06265 · pith_short_12: NWOAU556UGKJ · pith_short_16: NWOAU556UGKJ7GPD · pith_short_8: NWOAU556

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/NWOAU556UGKJ7GPD3ZXHOXO5MO \
  | 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: 6d9c0a77bea1949f99e3de6e775ddd63b71fc373655e645dd265569835f7d020

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5612df956d2781c213ee2d43d9b20a2153d0382a608044045b1a185e612b5f0",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-12-15T10:29:09Z",
    "title_canon_sha256": "dc2f6121fe6292a1d8799aac04bfadfada3ca3afe064d189a6ed9c33b4913cae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.06265",
    "kind": "arxiv",
    "version": 1
  }
}