Pith Number

pith:YKJBPJU5

pith:2011:YKJBPJU5JDUIFCOGGYX5NZGJZB

not attested not anchored not stored refs pending

A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups

Ben Green, Emmanuel Breuillard, Terence Tao

arxiv:1101.2552 v1 · 2011-01-13 · 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{YKJBPJU5JDUIFCOGGYX5NZGJZB}

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	2026-05-18T04:31:41.879849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c29217a69d48e88289c6362fd6e4c9c87a983d96e4ea8c62530a12d35425b45a

Aliases

arxiv: 1101.2552 · arxiv_version: 1101.2552v1 · doi: 10.48550/arxiv.1101.2552 · pith_short_12: YKJBPJU5JDUI · pith_short_16: YKJBPJU5JDUIFCOG · pith_short_8: YKJBPJU5

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/YKJBPJU5JDUIFCOGGYX5NZGJZB \
  | 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: c29217a69d48e88289c6362fd6e4c9c87a983d96e4ea8c62530a12d35425b45a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0130ca002ea728f1100a24ece5e249522818b0aca794ce47f3762644d75f3188",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-01-13T13:16:48Z",
    "title_canon_sha256": "d1c46effee5ba5f782ecb5d7780a6d2b8afa7d5bd4fd74e32d6bab5db0b4ed80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2552",
    "kind": "arxiv",
    "version": 1
  }
}