Pith Number

pith:LPQKFSGD

pith:2023:LPQKFSGD4FDMS6VADAGVECBULM

not attested not anchored not stored refs pending

Growth dichotomy for unimodular random rooted trees

Ben Hayes, Mikl\'os Abert, Miko{\l}aj Fr\k{a}czyk

arxiv:2312.04611 v1 · 2023-12-07 · math.PR · math.CO · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPQKFSGD4FDMS6VADAGVECBULM}

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

A unimodular random graph with large upper growth and no growth

Receipt and verification

First computed	2026-07-05T07:21:48.539112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5be0a2c8c3e146c97aa0180d5208345b35917c5694b05c8ff5d3e601d2700c79

Aliases

arxiv: 2312.04611 · arxiv_version: 2312.04611v1 · doi: 10.48550/arxiv.2312.04611 · pith_short_12: LPQKFSGD4FDM · pith_short_16: LPQKFSGD4FDMS6VA · pith_short_8: LPQKFSGD

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/LPQKFSGD4FDMS6VADAGVECBULM \
  | 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: 5be0a2c8c3e146c97aa0180d5208345b35917c5694b05c8ff5d3e601d2700c79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96e12cc90e4eb8fa6787ea95e4bcde15d15a8add36fdf83c7bb2271da8986ada",
    "cross_cats_sorted": [
      "math.CO",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-12-07T16:18:27Z",
    "title_canon_sha256": "b99d00c09a2f51791742f746223662e00470cddd679f806fb07c5302488e6e57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.04611",
    "kind": "arxiv",
    "version": 1
  }
}