Pith Number

pith:HZIIKPXT

pith:2007:HZIIKPXTZ443MLZLKU66AXGU3H

not attested not anchored not stored refs pending

Vacant Set of Random Interlacements and Percolation

Alain-Sol Sznitman

arxiv:0704.2560 v3 · 2007-04-19 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HZIIKPXTZ443MLZLKU66AXGU3H}

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

Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity

Receipt and verification

First computed	2026-07-04T17:30:03.781281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e50853ef3cf39b62f2b553de05cd4d9f011a67875629f926aeb6c81243d6a1c

Aliases

arxiv: 0704.2560 · arxiv_version: 0704.2560v3 · doi: 10.48550/arxiv.0704.2560 · pith_short_12: HZIIKPXTZ443 · pith_short_16: HZIIKPXTZ443MLZL · pith_short_8: HZIIKPXT

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/HZIIKPXTZ443MLZLKU66AXGU3H \
  | 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: 3e50853ef3cf39b62f2b553de05cd4d9f011a67875629f926aeb6c81243d6a1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc4a769f24dcb90b336b1f3ec5dba49eaea6fc78d422b6315adabdec97c161c9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2007-04-19T15:45:50Z",
    "title_canon_sha256": "349707f501cbfe07fb4776098285059b65d625247954ecb9fea176a65ae082b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0704.2560",
    "kind": "arxiv",
    "version": 3
  }
}