Pith Number

pith:JM6ZHVZR

pith:2014:JM6ZHVZRVL55EYJS2D5USACZP2

not attested not anchored not stored refs pending

Ramanujan Complexes and bounded degree topological expanders

Alexander Lubotzky, David Kazhdan, Tali Kaufman

arxiv:1408.6351 v1 · 2014-08-27 · math.CO · cs.CC · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JM6ZHVZRVL55EYJS2D5USACZP2}

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	2026-05-18T02:38:45.829152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b3d93d731aafbd26132d0fb4900597e93b6e435497f5a72730eb875048c2cb7

Aliases

arxiv: 1408.6351 · arxiv_version: 1408.6351v1 · doi: 10.48550/arxiv.1408.6351 · pith_short_12: JM6ZHVZRVL55 · pith_short_16: JM6ZHVZRVL55EYJS · pith_short_8: JM6ZHVZR

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/JM6ZHVZRVL55EYJS2D5USACZP2 \
  | 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: 4b3d93d731aafbd26132d0fb4900597e93b6e435497f5a72730eb875048c2cb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0b0de5614d1a2871ce45575fd1efe6850792362d4376d45f51917edc4665271",
    "cross_cats_sorted": [
      "cs.CC",
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-08-27T08:56:35Z",
    "title_canon_sha256": "5a3a60120dd57f9fcd95cafb91842cf4c57bc9dcedb7cef57503873ee39e2d0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.6351",
    "kind": "arxiv",
    "version": 1
  }
}