Pith Number

pith:WZMOY3P5

pith:2026:WZMOY3P5OA5OB5T22XMRBOGZOP

not attested not anchored not stored refs pending

Area-minimizing submanifolds are not generically smooth, except for geodesics, minimal surfaces, and minimal hypersurfaces

Zhenhua Liu

arxiv:2607.24735 v1 · 2026-07-27 · 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{WZMOY3P5OA5OB5T22XMRBOGZOP}

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	2026-07-28T02:24:24.890247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b658ec6dfd703ae0f67ad5d910b8d973e094df7d2f051f034b2053bb5c490a51

Aliases

arxiv: 2607.24735 · arxiv_version: 2607.24735v1 · doi: 10.48550/arxiv.2607.24735 · pith_short_12: WZMOY3P5OA5O · pith_short_16: WZMOY3P5OA5OB5T2 · pith_short_8: WZMOY3P5

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/WZMOY3P5OA5OB5T22XMRBOGZOP \
  | 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: b658ec6dfd703ae0f67ad5d910b8d973e094df7d2f051f034b2053bb5c490a51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f492e3f65b1d8b78049edef165446aaf420eb05933abada039c1bb19b5f39215",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-27T17:57:36Z",
    "title_canon_sha256": "a16680594716eee6f098ce6a37e90bbbe8b4ffeeec9d66553cdfa8da944d040e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24735",
    "kind": "arxiv",
    "version": 1
  }
}