Pith Number

pith:UDTNJYKV

pith:2019:UDTNJYKV36RSQA5Q6MNZZVJMBR

not attested not anchored not stored refs pending

The Heintze-Karcher inequality for metric measure spaces

Christian Ketterer

arxiv:1908.06146 v3 · 2019-08-16 · 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{UDTNJYKV36RSQA5Q6MNZZVJMBR}

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	2026-07-05T00:34:42.832312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0e6d4e155dfa32803b0f31b9cd52c0c4cdbc80ffdac5ffafcb2f4da73b6c5fb

Aliases

arxiv: 1908.06146 · arxiv_version: 1908.06146v3 · doi: 10.48550/arxiv.1908.06146 · pith_short_12: UDTNJYKV36RS · pith_short_16: UDTNJYKV36RSQA5Q · pith_short_8: UDTNJYKV

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/UDTNJYKV36RSQA5Q6MNZZVJMBR \
  | 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: a0e6d4e155dfa32803b0f31b9cd52c0c4cdbc80ffdac5ffafcb2f4da73b6c5fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5436445f80e0d14e7fe3bf4e1b0c2d982e32aca67df4242fafd403da242c05a",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-08-16T19:50:58Z",
    "title_canon_sha256": "72f65a104f8d3224b61aab4320f8c3cefb58928f2ccbcfe9c8b8c1d5b0542682"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06146",
    "kind": "arxiv",
    "version": 3
  }
}