Pith Number

pith:OCEW23XC

pith:2026:OCEW23XCELDUCGTCBNBLFNXFR4

not attested not anchored not stored refs pending

Critical curve of loop percolation on the $d$-regular tree

Artem Sapozhnikov, Luca Makowiec

arxiv:2606.27520 v1 · 2026-06-25 · 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{OCEW23XCELDUCGTCBNBLFNXFR4}

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	2026-06-29T00:14:08.876071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70896d6ee222c7411a620b42b2b6e58f1fe03dad6ab0231915ff7f911ac7bee7

Aliases

arxiv: 2606.27520 · arxiv_version: 2606.27520v1 · doi: 10.48550/arxiv.2606.27520 · pith_short_12: OCEW23XCELDU · pith_short_16: OCEW23XCELDUCGTC · pith_short_8: OCEW23XC

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/OCEW23XCELDUCGTCBNBLFNXFR4 \
  | 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: 70896d6ee222c7411a620b42b2b6e58f1fe03dad6ab0231915ff7f911ac7bee7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac7ecee8c77b58d8a354a9ad8ff21cc98c09f73f6e1796f0d0a17e0879b9fa78",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-25T20:05:57Z",
    "title_canon_sha256": "f239ec0bb7706770a6ab77043b67de6ba848f2b41279dc587b5d04fdc586d83e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.27520",
    "kind": "arxiv",
    "version": 1
  }
}