Pith Number

pith:ZMVMLKGZ

pith:2026:ZMVMLKGZZBECEKJDU6NU2KMLLG

not attested not anchored not stored refs pending

Tail exponents of the three-dimensional uniform spanning tree and Abelian sandpile

Daisuke Shiraishi, Runsheng Liu, Xinyi Li

arxiv:2605.19419 v1 · 2026-05-19 · 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{ZMVMLKGZZBECEKJDU6NU2KMLLG}

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	2026-05-20T01:05:44.784760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb2ac5a8d9c848222923a79b4d298b59b018b7da6e1dd25fb9eafbcb3aa057b0

Aliases

arxiv: 2605.19419 · arxiv_version: 2605.19419v1 · doi: 10.48550/arxiv.2605.19419 · pith_short_12: ZMVMLKGZZBEC · pith_short_16: ZMVMLKGZZBECEKJD · pith_short_8: ZMVMLKGZ

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/ZMVMLKGZZBECEKJDU6NU2KMLLG \
  | 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: cb2ac5a8d9c848222923a79b4d298b59b018b7da6e1dd25fb9eafbcb3aa057b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed157dd39821855d2b2e1a58d653624c983d60e133fe24da632ca7a3f4f91cb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-19T06:12:01Z",
    "title_canon_sha256": "97218187301ea9bb5df65621872632240c041be994272f45bc19dbfea2889350"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19419",
    "kind": "arxiv",
    "version": 1
  }
}