Pith Number

pith:L5DFL6VU

pith:2017:L5DFL6VU3U34T5B6CV65SGRURD

not attested not anchored not stored refs pending

Random walks on Ramanujan complexes and digraphs

Alex Lubotzky, Eyal Lubetzky, Ori Parzanchevski

arxiv:1702.05452 v2 · 2017-02-17 · math.CO · math.PR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5DFL6VU3U34T5B6CV65SGRURD}

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	2026-07-05T01:48:59.346183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f4655fab4dd37c9f43e157dd91a3488e84ae68c650e4c9eab52a330483cc7f4

Aliases

arxiv: 1702.05452 · arxiv_version: 1702.05452v2 · doi: 10.48550/arxiv.1702.05452 · pith_short_12: L5DFL6VU3U34 · pith_short_16: L5DFL6VU3U34T5B6 · pith_short_8: L5DFL6VU

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/L5DFL6VU3U34T5B6CV65SGRURD \
  | 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: 5f4655fab4dd37c9f43e157dd91a3488e84ae68c650e4c9eab52a330483cc7f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d16e99f6489dc6acb07e80167c29e9150fba2834a269e6334ea98a72f601fad",
    "cross_cats_sorted": [
      "math.PR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-02-17T17:35:37Z",
    "title_canon_sha256": "961f284cecd107a8acb3e74137c132975d987c8bb5781d4b940a80c0862bc6e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.05452",
    "kind": "arxiv",
    "version": 2
  }
}