Pith Number

pith:VL3Z7PCW

pith:2025:VL3Z7PCWFJ4O6TOYW3WBKXOFSH

not attested not anchored not stored refs pending

Monotonicity formulas for minimal submanifolds involving M\"obius transformations

Doanh Pham

arxiv:2504.12199 v2 · 2025-04-16 · 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{VL3Z7PCWFJ4O6TOYW3WBKXOFSH}

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	2026-05-25T02:01:03.548504Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaf79fbc562a78ef4dd8b6ec155dc591c9429aff6d06b1baf8abc9c39ad77de8

Aliases

arxiv: 2504.12199 · arxiv_version: 2504.12199v2 · doi: 10.48550/arxiv.2504.12199 · pith_short_12: VL3Z7PCWFJ4O · pith_short_16: VL3Z7PCWFJ4O6TOY · pith_short_8: VL3Z7PCW

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/VL3Z7PCWFJ4O6TOYW3WBKXOFSH \
  | 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: aaf79fbc562a78ef4dd8b6ec155dc591c9429aff6d06b1baf8abc9c39ad77de8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fb0957edb9976e4c15d0b13d7c71616fb5252713eb73123f6266e84d270055d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-04-16T15:48:34Z",
    "title_canon_sha256": "3331cf8ea538c273d3479c615fd204226f08d1c21e1e0ee04a1ececc450f2acd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.12199",
    "kind": "arxiv",
    "version": 2
  }
}