Pith Number

pith:7XRGZASY

pith:2011:7XRGZASYZL2EPWLATL5SZDGSRE

not attested not anchored not stored refs pending

Expanders and Property A

A. Khukhro, N. J. Wright

arxiv:1108.6232 v1 · 2011-08-31 · math.GT · math.GR · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7XRGZASYZL2EPWLATL5SZDGSRE}

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	2026-05-18T02:41:43.693656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde26c8258caf447d9609afb2c8cd2891f14386ec07f03abb483ed55cd1b569b

Aliases

arxiv: 1108.6232 · arxiv_version: 1108.6232v1 · doi: 10.48550/arxiv.1108.6232 · pith_short_12: 7XRGZASYZL2E · pith_short_16: 7XRGZASYZL2EPWLA · pith_short_8: 7XRGZASY

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/7XRGZASYZL2EPWLATL5SZDGSRE \
  | 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: fde26c8258caf447d9609afb2c8cd2891f14386ec07f03abb483ed55cd1b569b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1d4bf1ca1dbb3cf9a6aef2d135bd4abcd02aec39d95d13f567d6781fed1d9dd",
    "cross_cats_sorted": [
      "math.GR",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-08-31T13:59:15Z",
    "title_canon_sha256": "68d5a277dab3502d42eec68c589c4822368f241c6f167dd9c5a9f524c803c504"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.6232",
    "kind": "arxiv",
    "version": 1
  }
}