Pith Number

pith:56LC5JGV

pith:2019:56LC5JGVZLRDDBM47WVSTECZFA

not attested not anchored not stored refs pending

A Wasserstein Inequality and Minimal Green Energy on Compact Manifolds

Stefan Steinerberger

arxiv:1907.09023 v1 · 2019-07-21 · math.CA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{56LC5JGVZLRDDBM47WVSTECZFA}

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	2026-05-17T23:40:02.390543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef962ea4d5cae231859cfdab299059282a911baa5157a9766f4ca52abef841bb

Aliases

arxiv: 1907.09023 · arxiv_version: 1907.09023v1 · doi: 10.48550/arxiv.1907.09023 · pith_short_12: 56LC5JGVZLRD · pith_short_16: 56LC5JGVZLRDDBM4 · pith_short_8: 56LC5JGV

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/56LC5JGVZLRDDBM47WVSTECZFA \
  | 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: ef962ea4d5cae231859cfdab299059282a911baa5157a9766f4ca52abef841bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "331ca312275d1f68cda6bfa3f5145beb1fd0a985191fab4edd993b8de588e959",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-07-21T20:00:46Z",
    "title_canon_sha256": "ef7f0c6988e2135d2f1c3003cc4e3bf39c5e874f72767ff820b901128c2c7e9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.09023",
    "kind": "arxiv",
    "version": 1
  }
}