Pith Number

pith:UPY2HQ7Z

pith:2023:UPY2HQ7ZHY7F2F3PNHD4VNQ6XO

not attested not anchored not stored refs pending

Area-minimizing surfaces with fractal singular sets: prevalence, moduli space, and refinements on strata

Zhenhua Liu

arxiv:2306.07271 v3 · 2023-06-12 · 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{UPY2HQ7ZHY7F2F3PNHD4VNQ6XO}

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	2026-07-05T07:04:16.891205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3f1a3c3f93e3e5d176f69c7cab61ebb8af90630a8f29677258989a6f0fcc578

Aliases

arxiv: 2306.07271 · arxiv_version: 2306.07271v3 · doi: 10.48550/arxiv.2306.07271 · pith_short_12: UPY2HQ7ZHY7F · pith_short_16: UPY2HQ7ZHY7F2F3P · pith_short_8: UPY2HQ7Z

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/UPY2HQ7ZHY7F2F3PNHD4VNQ6XO \
  | 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: a3f1a3c3f93e3e5d176f69c7cab61ebb8af90630a8f29677258989a6f0fcc578

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7023c05ea8ce5dd64e305b7888040fdf29be2bcb9c712c9f1240a45cfd10359",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2023-06-12T17:55:43Z",
    "title_canon_sha256": "3fc7b793f440ae00d3630b2a3e6c9511a129d6691383540a32418f42bae4c522"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.07271",
    "kind": "arxiv",
    "version": 3
  }
}