Pith Number

pith:7QS2NI6R

pith:2026:7QS2NI6RZM2FNBHGSGU2Q4YC6G

not attested not anchored not stored refs pending

Can the root cluster remain largest forever in random recursive tree percolation?

Yushu Zheng

arxiv:2606.01881 v1 · 2026-06-01 · 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{7QS2NI6RZM2FNBHGSGU2Q4YC6G}

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	2026-06-02T02:04:59.439186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc25a6a3d1cb345684e691a9a87302f1bab726e1726a5c625ef635b6037366ce

Aliases

arxiv: 2606.01881 · arxiv_version: 2606.01881v1 · doi: 10.48550/arxiv.2606.01881 · pith_short_12: 7QS2NI6RZM2F · pith_short_16: 7QS2NI6RZM2FNBHG · pith_short_8: 7QS2NI6R

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/7QS2NI6RZM2FNBHGSGU2Q4YC6G \
  | 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: fc25a6a3d1cb345684e691a9a87302f1bab726e1726a5c625ef635b6037366ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "830c68534a3783625de96c5ea930a9275400bd7498f43a6479e3401c4b53ce41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-01T08:27:52Z",
    "title_canon_sha256": "52432ee4c5119049c40f92d7a80f5a656c957de56ae08d53425438acf1cf039b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.01881",
    "kind": "arxiv",
    "version": 1
  }
}