Pith Number

pith:ZKBJE2BM

pith:2009:ZKBJE2BMR6FS4B4MCWEFNNPXIL

not attested not anchored not stored refs pending

Infinite families of regular expanders of arbitrary constant degree obtained via the modified zig-zag product

Cristina Ballantine, Matthew Horton

arxiv:0905.3862 v2 · 2009-05-23 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKBJE2BMR6FS4B4MCWEFNNPXIL}

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	2026-05-18T04:41:44.119019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca8292682c8f8b2e078c158856b5f742d13d3ca08d8b290bd4dc1c6897a53773

Aliases

arxiv: 0905.3862 · arxiv_version: 0905.3862v2 · doi: 10.48550/arxiv.0905.3862 · pith_short_12: ZKBJE2BMR6FS · pith_short_16: ZKBJE2BMR6FS4B4M · pith_short_8: ZKBJE2BM

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/ZKBJE2BMR6FS4B4MCWEFNNPXIL \
  | 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: ca8292682c8f8b2e078c158856b5f742d13d3ca08d8b290bd4dc1c6897a53773

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16b5375d1fa8d9b5b0b95f78fa86ca575326323b132bb841029ea4b4b9515735",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-05-23T23:49:27Z",
    "title_canon_sha256": "6f58e41a7efed29cda49fda4ea092716a21b64f8945ae4cf51da5a24d210c487"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.3862",
    "kind": "arxiv",
    "version": 2
  }
}