Pith Number

pith:IHPQ2CIB

pith:2014:IHPQ2CIBDBYUA5J5L3JPC7IPVC

not attested not anchored not stored refs pending

A gap theorem for the ZL-amenability constant of a finite group

Yemon Choi

arxiv:1410.5134 v2 · 2014-10-20 · math.GR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IHPQ2CIBDBYUA5J5L3JPC7IPVC}

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	2026-05-18T02:05:24.247004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41df0d0901187140753d5ed2f17d0fa89f0ac18430a11236e9f7da5730d149ef

Aliases

arxiv: 1410.5134 · arxiv_version: 1410.5134v2 · doi: 10.48550/arxiv.1410.5134 · pith_short_12: IHPQ2CIBDBYU · pith_short_16: IHPQ2CIBDBYUA5J5 · pith_short_8: IHPQ2CIB

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/IHPQ2CIBDBYUA5J5L3JPC7IPVC \
  | 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: 41df0d0901187140753d5ed2f17d0fa89f0ac18430a11236e9f7da5730d149ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "894cec91885d02029e5857d1d9f4d04d31b37f35b59588022066f9d4ed7d80a6",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-10-20T01:22:20Z",
    "title_canon_sha256": "e0fc52ea8b7aa8cbef289c0996b928675b79784a31c2705049b330f02d51b4c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.5134",
    "kind": "arxiv",
    "version": 2
  }
}