Pith Number

pith:NWZMJCTG

pith:2020:NWZMJCTGGRXO4P3JZLO2WN4N22

not attested not anchored not stored refs pending

Expander spanning subgraphs with large girth

Gabor Kun, Itai Benjamini, Mikolaj Fraczyk

arxiv:2012.15502 v1 · 2020-12-31 · math.CO · math.MG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NWZMJCTGGRXO4P3JZLO2WN4N22}

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	2026-07-05T03:37:10.386114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6db2c48a66346eee3f69caddab378dd6b500a5808c74f7b1cd92499cc8f583fe

Aliases

arxiv: 2012.15502 · arxiv_version: 2012.15502v1 · doi: 10.48550/arxiv.2012.15502 · pith_short_12: NWZMJCTGGRXO · pith_short_16: NWZMJCTGGRXO4P3J · pith_short_8: NWZMJCTG

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/NWZMJCTGGRXO4P3JZLO2WN4N22 \
  | 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: 6db2c48a66346eee3f69caddab378dd6b500a5808c74f7b1cd92499cc8f583fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73a4fa7151579a305d67c9e20a135f176274f07d1a0994f73079ff766c4f6565",
    "cross_cats_sorted": [
      "math.MG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-12-31T08:38:52Z",
    "title_canon_sha256": "eb8e315929b97a286d8849472daffe2f97a7cd168b12f33924cd56f831b5f349"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.15502",
    "kind": "arxiv",
    "version": 1
  }
}