Pith Number

pith:5A2HRVK7

pith:2025:5A2HRVK7NGN2PYMLEOETJU5RO5

not attested not anchored not stored refs pending

Hellinger-Kantorovich Gradient Flows: Global Exponential Decay of Entropy Functionals

Alexander Mielke, Jia-Jie Zhu

arxiv:2501.17049 v1 · 2025-01-28 · math.AP · cs.LG · math.OC · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5A2HRVK7NGN2PYMLEOETJU5RO5}

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	2026-07-05T10:06:33.481816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e83478d55f699ba7e18b238934d3b177782a3463632ce46575c92021fc9985e2

Aliases

arxiv: 2501.17049 · arxiv_version: 2501.17049v1 · doi: 10.48550/arxiv.2501.17049 · pith_short_12: 5A2HRVK7NGN2 · pith_short_16: 5A2HRVK7NGN2PYML · pith_short_8: 5A2HRVK7

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/5A2HRVK7NGN2PYMLEOETJU5RO5 \
  | 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: e83478d55f699ba7e18b238934d3b177782a3463632ce46575c92021fc9985e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73add58a8356ecc1f13c25b24a0f4450be95df98065ae6a15550dc61f12a7fcd",
    "cross_cats_sorted": [
      "cs.LG",
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-01-28T16:17:09Z",
    "title_canon_sha256": "e82102c40a818bdad683e8e4763262a164d9d18943186c0ce9bcd611f492ed5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.17049",
    "kind": "arxiv",
    "version": 1
  }
}