Pith Number

pith:IZG7GBQD

pith:2026:IZG7GBQDZIQJVDMNAINQZPOOS5

not attested not anchored not stored refs pending

Mean curvature and sharp Willmore inequalities in metric spaces

Ivan Yuri Violo, Nicola Gigli

arxiv:2607.27012 v1 · 2026-07-29 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IZG7GBQDZIQJVDMNAINQZPOOS5}

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	2026-07-30T01:23:20.215219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

464df30603ca209a8d8d021b0cbdce9766785edc23bbc2b0c65430a3228378e2

Aliases

arxiv: 2607.27012 · arxiv_version: 2607.27012v1 · doi: 10.48550/arxiv.2607.27012 · pith_short_12: IZG7GBQDZIQJ · pith_short_16: IZG7GBQDZIQJVDMN · pith_short_8: IZG7GBQD

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/IZG7GBQDZIQJVDMNAINQZPOOS5 \
  | 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: 464df30603ca209a8d8d021b0cbdce9766785edc23bbc2b0c65430a3228378e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6daa409f2900fbf4864bac4d15eca45cadc5c3109d5f1de51e7eb4365aef57f",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-29T15:09:24Z",
    "title_canon_sha256": "e3c77f941f94eb5bdfc4e8dbaaeacfb60ea49ad69c6d2b38f70e687bbf5836b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27012",
    "kind": "arxiv",
    "version": 1
  }
}