Pith Number

pith:V7KCGDCJ

pith:2014:V7KCGDCJQRQJEL2MSPYGAYPGKL

not attested not anchored not stored refs pending

The Rapid Decay property and centroids in groups

Mark Sapir

arxiv:1405.0757 v4 · 2014-05-05 · 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{V7KCGDCJQRQJEL2MSPYGAYPGKL}

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	2026-05-18T01:24:11.245444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afd4230c498460922f4c93f06061e652f62296b200650b61ca3c377db48ac01d

Aliases

arxiv: 1405.0757 · arxiv_version: 1405.0757v4 · doi: 10.48550/arxiv.1405.0757 · pith_short_12: V7KCGDCJQRQJ · pith_short_16: V7KCGDCJQRQJEL2M · pith_short_8: V7KCGDCJ

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/V7KCGDCJQRQJEL2MSPYGAYPGKL \
  | 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: afd4230c498460922f4c93f06061e652f62296b200650b61ca3c377db48ac01d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d12e7f220fd3290db3d22a187e943d3e6a6781ace52368cb54dc2ca369c22b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-05-05T00:32:00Z",
    "title_canon_sha256": "95ad8218241ae8777e0078a61c1a40d9db1d07c1761960264306247006810d67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.0757",
    "kind": "arxiv",
    "version": 4
  }
}