Pith Number

pith:RD7OGKXK

pith:2015:RD7OGKXKMJO26NAX2KLJIW53E7

not attested not anchored not stored refs pending

Cutoff on all Ramanujan graphs

Eyal Lubetzky, Yuval Peres

arxiv:1507.04725 v5 · 2015-07-16 · math.PR · 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{RD7OGKXKMJO26NAX2KLJIW53E7}

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.

Cited by

1 paper in Pith

Cutoff for random lifts of weighted graphs

Receipt and verification

First computed	2026-05-18T01:07:58.492822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88fee32aea625daf3417d296945bbb27d104b862911daa25f6ab78751ceab12f

Aliases

arxiv: 1507.04725 · arxiv_version: 1507.04725v5 · doi: 10.48550/arxiv.1507.04725 · pith_short_12: RD7OGKXKMJO2 · pith_short_16: RD7OGKXKMJO26NAX · pith_short_8: RD7OGKXK

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/RD7OGKXKMJO26NAX2KLJIW53E7 \
  | 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: 88fee32aea625daf3417d296945bbb27d104b862911daa25f6ab78751ceab12f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecdc53a97790f40ec2a2e6e9578f32ebefeaea7b756dd8607a6b8f84a03c7fc9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-07-16T19:40:55Z",
    "title_canon_sha256": "be4b7e1e5a6130524cbf435d5d948d3f9320b44931b4549f0a1d82b61e65f824"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04725",
    "kind": "arxiv",
    "version": 5
  }
}