Pith Number

pith:5C62KV77

pith:2025:5C62KV77MOFBNLLOOQSB5RCZC3

not attested not anchored not stored refs pending

Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow

Alexander Mielke, Jia-Jie Zhu, Matthias Liero, Oliver Tse

arxiv:2504.20400 v1 · 2025-04-29 · math.AP · math.PR · 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{5C62KV77MOFBNLLOOQSB5RCZC3}

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	2026-07-05T10:55:41.886423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8bda557ff638a16ad6e74241ec45916e29bcda737883944198efcbe4997d0f2

Aliases

arxiv: 2504.20400 · arxiv_version: 2504.20400v1 · doi: 10.48550/arxiv.2504.20400 · pith_short_12: 5C62KV77MOFB · pith_short_16: 5C62KV77MOFBNLLO · pith_short_8: 5C62KV77

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/5C62KV77MOFBNLLOOQSB5RCZC3 \
  | 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: e8bda557ff638a16ad6e74241ec45916e29bcda737883944198efcbe4997d0f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a04f9356e8de57653966753fb544d36b8e5f9b8afe97e153bd9d6461d80b49fd",
    "cross_cats_sorted": [
      "math.PR",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-04-29T03:54:56Z",
    "title_canon_sha256": "6b0507920c25fa6af8e2caaaac39165d3e1bdcf0aa6681a82a4a493e4b062aa2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.20400",
    "kind": "arxiv",
    "version": 1
  }
}