Pith Number

pith:NUQE5PWA

pith:2025:NUQE5PWAPJ6NO5YIYYWGSULGN6

not attested not anchored not stored refs pending

Barycenter curvature-dimension condition for extended metric measure spaces

Bang-Xian Han, Deng-Yu Liu, Zhuo-Nan Zhu

arxiv:2502.06793 v2 · 2025-01-27 · math.MG · math.FA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NUQE5PWAPJ6NO5YIYYWGSULGN6}

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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.

Cited by

1 paper in Pith

Absolute continuity of generalized Wasserstein barycenters of finitely many measures

Receipt and verification

First computed	2026-07-05T11:23:23.340052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d204ebec07a7cd77708c62c6951666fb9da5529ff906f6829a9b153a4c67809

Aliases

arxiv: 2502.06793 · arxiv_version: 2502.06793v2 · doi: 10.48550/arxiv.2502.06793 · pith_short_12: NUQE5PWAPJ6N · pith_short_16: NUQE5PWAPJ6NO5YI · pith_short_8: NUQE5PWA

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/NUQE5PWAPJ6NO5YIYYWGSULGN6 \
  | 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: 6d204ebec07a7cd77708c62c6951666fb9da5529ff906f6829a9b153a4c67809

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32aecb2f1ce448a391a199594a6789c92b0bce3ff05242fc497be6dd59ee33cc",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2025-01-27T02:51:09Z",
    "title_canon_sha256": "51c52df07e76028201ba53dd30065388f86e8ced6b7659da25d40e96bb37bcbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.06793",
    "kind": "arxiv",
    "version": 2
  }
}