Pith Number

pith:TXUXL5J6

pith:2022:TXUXL5J64TGN5A6SSRKTV7GP3W

not attested not anchored not stored refs pending

The prescribed point area estimate for minimal submanifolds in constant curvature

Jonathan J. Zhu, Keaton Naff

arxiv:2206.08302 v2 · 2022-06-16 · 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{TXUXL5J64TGN5A6SSRKTV7GP3W}

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

Monotonicity formulas for minimal submanifolds involving M\"obius transformations

Receipt and verification

First computed	2026-07-05T05:04:13.762758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9de975f53ee4ccde83d294553afccfdda60f5a052d002b2f52df6585bb8d49de

Aliases

arxiv: 2206.08302 · arxiv_version: 2206.08302v2 · doi: 10.48550/arxiv.2206.08302 · pith_short_12: TXUXL5J64TGN · pith_short_16: TXUXL5J64TGN5A6S · pith_short_8: TXUXL5J6

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/TXUXL5J64TGN5A6SSRKTV7GP3W \
  | 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: 9de975f53ee4ccde83d294553afccfdda60f5a052d002b2f52df6585bb8d49de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a393b7ff80c21c768f76d7c0bcdbb512caf81ea7be32c44a15961836dbcf85d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2022-06-16T17:02:50Z",
    "title_canon_sha256": "366a3fbba09a33ca282ed61a5dc6997aba0abf8c943c6b97144be7984129d05d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2206.08302",
    "kind": "arxiv",
    "version": 2
  }
}