Pith Number

pith:QKA2ASYH

pith:2015:QKA2ASYH5VCM5IUI3UDWRZTA22

not attested not anchored not stored refs pending

Expanders and box spaces

Alain Valette, Ana Khukhro

arxiv:1509.01394 v1 · 2015-09-04 · math.GR · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QKA2ASYH5VCM5IUI3UDWRZTA22}

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	2026-05-18T01:33:57.766007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8281a04b07ed44cea288dd0768e660d6aa16b6622e99fdcb5186d4e1c4e4a019

Aliases

arxiv: 1509.01394 · arxiv_version: 1509.01394v1 · doi: 10.48550/arxiv.1509.01394 · pith_short_12: QKA2ASYH5VCM · pith_short_16: QKA2ASYH5VCM5IUI · pith_short_8: QKA2ASYH

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/QKA2ASYH5VCM5IUI3UDWRZTA22 \
  | 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: 8281a04b07ed44cea288dd0768e660d6aa16b6622e99fdcb5186d4e1c4e4a019

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56a35183344bbd00f8b12d29499ba6e98d17aeac29e00a8fbd9dd64a49a0626c",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-04T10:14:52Z",
    "title_canon_sha256": "45e51995bf026382a9b6372fd761eb36159a927c4d7a24c55f0b7a6c469379fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01394",
    "kind": "arxiv",
    "version": 1
  }
}