Pith Number

pith:6PCYSP37

pith:2010:6PCYSP37UYFCAJ5G6GSI4W2ZTH

not attested not anchored not stored refs pending

Giant vacant component left by a random walk in a random d-regular graph

Augusto Teixeira, David Windisch, Jiri Cerny

arxiv:1012.5117 v1 · 2010-12-22 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6PCYSP37UYFCAJ5G6GSI4W2ZTH}

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	2026-05-18T02:04:18.299981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3c5893f7fa60a2027a6f1a48e5b5999f6bb04c7e7815b27bfaa4d260538a11f

Aliases

arxiv: 1012.5117 · arxiv_version: 1012.5117v1 · doi: 10.48550/arxiv.1012.5117 · pith_short_12: 6PCYSP37UYFC · pith_short_16: 6PCYSP37UYFCAJ5G · pith_short_8: 6PCYSP37

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/6PCYSP37UYFCAJ5G6GSI4W2ZTH \
  | 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: f3c5893f7fa60a2027a6f1a48e5b5999f6bb04c7e7815b27bfaa4d260538a11f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a84d12137a0db83a46e23cd6fc93742ac41b1d9bf7bf68fec6ed6b495a1fc137",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-22T22:21:58Z",
    "title_canon_sha256": "dd66d194e2f1e6669d026039b5dcf30669132fc0995dc96f9d674ac70ef45d30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5117",
    "kind": "arxiv",
    "version": 1
  }
}