Pith Number

pith:SFXKWMX7

pith:2011:SFXKWMX7EZEVVK44VYCTRLHBWO

not attested not anchored not stored refs pending

Critical window for the vacant set left by random walk on random regular graphs

Augusto Teixeira, Jiri Cerny

arxiv:1101.1978 v1 · 2011-01-10 · 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{SFXKWMX7EZEVVK44VYCTRLHBWO}

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	2026-05-18T04:31:50.929545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

916eab32ff26495aab9cae0538ace1b3b12316f7a41a4bc1f3221bc88c2aec4d

Aliases

arxiv: 1101.1978 · arxiv_version: 1101.1978v1 · doi: 10.48550/arxiv.1101.1978 · pith_short_12: SFXKWMX7EZEV · pith_short_16: SFXKWMX7EZEVVK44 · pith_short_8: SFXKWMX7

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/SFXKWMX7EZEVVK44VYCTRLHBWO \
  | 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: 916eab32ff26495aab9cae0538ace1b3b12316f7a41a4bc1f3221bc88c2aec4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14d28160d9482159dbce5227996b7380f4af1e471d0d83a63a70b73fa62ba8fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-10T22:06:02Z",
    "title_canon_sha256": "bdc2964d2849622ee47acf2e330ec58e6fb6a570981cbba8d070ad5ad5e04448"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1978",
    "kind": "arxiv",
    "version": 1
  }
}