Pith Number

pith:UJM3ZGMO

pith:2025:UJM3ZGMOU5L4UXUGU7GITSE2RS

not attested not anchored not stored refs pending

Self-shrinkers with any number of ends in $\mathbb{R}^{3}$ by stacking $\mathbb{R}^{2}$

Guanhua Shao, Jiahua Zou

arxiv:2507.18825 v1 · 2025-07-24 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UJM3ZGMOU5L4UXUGU7GITSE2RS}

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

Self-expanders of positive genus

Receipt and verification

First computed	2026-07-05T11:42:58.966603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a259bc998ea757ca5e86a7cc89c89a8ca2dc76b36a4cd281aa02f9c604dd6279

Aliases

arxiv: 2507.18825 · arxiv_version: 2507.18825v1 · doi: 10.48550/arxiv.2507.18825 · pith_short_12: UJM3ZGMOU5L4 · pith_short_16: UJM3ZGMOU5L4UXUG · pith_short_8: UJM3ZGMO

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/UJM3ZGMOU5L4UXUGU7GITSE2RS \
  | 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: a259bc998ea757ca5e86a7cc89c89a8ca2dc76b36a4cd281aa02f9c604dd6279

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b7e485a644900ec7604e8c0691aa7a0776043ad8292d9f798fb3c9b76e15cd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-24T21:51:40Z",
    "title_canon_sha256": "bde2d756657a95e11efd819926acca2e9ea43ba0e8905857dd7ea1faf7ab3774"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.18825",
    "kind": "arxiv",
    "version": 1
  }
}