Pith Number

pith:5ZPHR4C4

pith:2014:5ZPHR4C4LGIMVRX2ZTYZPQNWFL

not attested not anchored not stored refs pending

Weak expansiveness for actions of sofic groups

Guo Hua Zhang, Nhan-Phu Chung

arxiv:1402.6963 v3 · 2014-02-27 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ZPHR4C4LGIMVRX2ZTYZPQNWFL}

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	2026-05-18T02:30:47.430380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee5e78f05c5990cac6faccf197c1b62aec8aee2acc1121a3c5c5b1113ac0e45c

Aliases

arxiv: 1402.6963 · arxiv_version: 1402.6963v3 · doi: 10.48550/arxiv.1402.6963 · pith_short_12: 5ZPHR4C4LGIM · pith_short_16: 5ZPHR4C4LGIMVRX2 · pith_short_8: 5ZPHR4C4

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/5ZPHR4C4LGIMVRX2ZTYZPQNWFL \
  | 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: ee5e78f05c5990cac6faccf197c1b62aec8aee2acc1121a3c5c5b1113ac0e45c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c2476189688e815539ae409903d85952d411e7a43a1fdd2cec4fa0dc5b60fa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-02-27T16:40:34Z",
    "title_canon_sha256": "0102486e4b8d42f3ac7c28d883c51903f34a0491021e1e13eea37a52a9930baa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.6963",
    "kind": "arxiv",
    "version": 3
  }
}