Pith Number

pith:3Z63322C

pith:2015:3Z63322CZZF247EBRHMXCVNLBX

not attested not anchored not stored refs pending

Non-backtracking spectrum of random graphs: community detection and non-regular Ramanujan graphs

Charles Bordenave, Laurent Massouli\'e, Marc Lelarge

arxiv:1501.06087 v2 · 2015-01-24 · math.PR · cs.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3Z63322CZZF247EBRHMXCVNLBX}

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

Community Recovery on Noisy Stochastic Block Models

Receipt and verification

First computed	2026-05-18T02:18:13.365996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de7dbdeb42ce4bae7c8189d97155ab0dd5650656b24bd214d61d3a4efc37ffc6

Aliases

arxiv: 1501.06087 · arxiv_version: 1501.06087v2 · doi: 10.48550/arxiv.1501.06087 · pith_short_12: 3Z63322CZZF2 · pith_short_16: 3Z63322CZZF247EB · pith_short_8: 3Z63322C

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/3Z63322CZZF247EBRHMXCVNLBX \
  | 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: de7dbdeb42ce4bae7c8189d97155ab0dd5650656b24bd214d61d3a4efc37ffc6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0574a77b2e6680783025377ac3a503e7c944487649a988cf8b17a8aeaeff5104",
    "cross_cats_sorted": [
      "cs.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-24T22:02:50Z",
    "title_canon_sha256": "e3515eb3df72265622a7418d3cfddb90630b4ac1a2462b592a16becb0ad3f1b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06087",
    "kind": "arxiv",
    "version": 2
  }
}