Pith Number

pith:4BECDABH

pith:2019:4BECDABHVMICY5LOFKM4QFGMWJ

not attested not anchored not stored refs pending

Critical Parameters for Loop and Bernoulli Percolation

Peter M\"uhlbacher

arxiv:1908.10213 v1 · 2019-08-27 · 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{4BECDABHVMICY5LOFKM4QFGMWJ}

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	2026-07-05T00:00:10.518717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e048218027ab102c756e2a99c814ccb259f82ce3ceba3ae3760a968608251b58

Aliases

arxiv: 1908.10213 · arxiv_version: 1908.10213v1 · doi: 10.48550/arxiv.1908.10213 · pith_short_12: 4BECDABHVMIC · pith_short_16: 4BECDABHVMICY5LO · pith_short_8: 4BECDABH

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/4BECDABHVMICY5LOFKM4QFGMWJ \
  | 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: e048218027ab102c756e2a99c814ccb259f82ce3ceba3ae3760a968608251b58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97644a71a84df229d6caa271833948ef1f3c2ce0dd12a49420146b71c71637aa",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-08-27T14:06:32Z",
    "title_canon_sha256": "ca477052bc5495bc557086c2a5cd172913435e7eb198268582bfcc6411e63031"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.10213",
    "kind": "arxiv",
    "version": 1
  }
}