Pith Number

pith:K4XT4RDZ

pith:2013:K4XT4RDZKNIM23D7IN3U5BLNY4

not attested not anchored not stored refs pending

Independence ratio and random eigenvectors in transitive graphs

B\'alint Vir\'ag, Viktor Harangi

arxiv:1308.5173 v2 · 2013-08-23 · 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{K4XT4RDZKNIM23D7IN3U5BLNY4}

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	2026-05-18T01:09:32.576530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

572f3e44795350cd6c7f43774e856dc706022b35f77c82a837cacae6ad6f6df6

Aliases

arxiv: 1308.5173 · arxiv_version: 1308.5173v2 · doi: 10.48550/arxiv.1308.5173 · pith_short_12: K4XT4RDZKNIM · pith_short_16: K4XT4RDZKNIM23D7 · pith_short_8: K4XT4RDZ

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/K4XT4RDZKNIM23D7IN3U5BLNY4 \
  | 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: 572f3e44795350cd6c7f43774e856dc706022b35f77c82a837cacae6ad6f6df6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6098e70421fb386fb38c94b995ced32826607c435cda55d4e69bcd45d78f84c1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-08-23T16:27:12Z",
    "title_canon_sha256": "1f737a2da8d3dd2fc82afd0b928b6539caacf75a17b2a0f2708dc0136a98e64e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5173",
    "kind": "arxiv",
    "version": 2
  }
}