Pith Number

pith:HRWIPV5C

pith:2025:HRWIPV5CW5CG53FWEODQQ76NHD

not attested not anchored not stored refs pending

$W$-entropy formulas and Langevin deformation on the $L^q$-Wasserstein space over Riemannian manifolds

Rong Lei, Xiang-Dong Li, Yu-Zhao Wang

arxiv:2506.01279 v2 · 2025-06-02 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HRWIPV5CW5CG53FWEODQQ76NHD}

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	2026-07-05T11:25:45.406388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c6c87d7a2b7446eecb62387087fcd38dc5777424f7e029ed5ca896e4db0fff9

Aliases

arxiv: 2506.01279 · arxiv_version: 2506.01279v2 · doi: 10.48550/arxiv.2506.01279 · pith_short_12: HRWIPV5CW5CG · pith_short_16: HRWIPV5CW5CG53FW · pith_short_8: HRWIPV5C

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/HRWIPV5CW5CG53FWEODQQ76NHD \
  | 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: 3c6c87d7a2b7446eecb62387087fcd38dc5777424f7e029ed5ca896e4db0fff9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f23592b8e35b6a1c681baaff30207866ca2fb70723c0961a58a51750a9dfa701",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-06-02T03:21:36Z",
    "title_canon_sha256": "f0da2f4f0213e843b52e328151625f6489261c5c63cc1c5dfb62aee28b22488f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.01279",
    "kind": "arxiv",
    "version": 2
  }
}