Pith Number

pith:VVO7F4KQ

pith:2026:VVO7F4KQGP4DZEHMVYRO2A4S7G

not attested not anchored not stored refs pending

Wasserstein barycenters on metric graphs

J\'er\^ome Bertrand (IMT), Jianyu Ma (IMT)

Wasserstein barycenters on metric graphs are absolutely continuous away from vertices under appropriate conditions.

arxiv:2604.17924 v2 · 2026-04-20 · math.MG · math.OC

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\usepackage{pith}
\pithnumber{VVO7F4KQGP4DZEHMVYRO2A4S7G}

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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.

Claims

C1strongest claim

In this paper we provide conditions for a Wasserstein barycenter to be absolutely continuous with respect to its Hausdorff measure away from the vertices of the graph.

C2weakest assumption

The abstract does not specify the precise assumptions on the metric graph, the input measures, or the barycenter weights; without these details the reasonableness of the conditions cannot be evaluated.

C3one line summary

Conditions are provided for Wasserstein barycenters on metric graphs to be absolutely continuous away from vertices with respect to Hausdorff measure.

Receipt and verification

First computed	2026-06-02T02:04:53.303683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad5df2f15033f83c90ecae22ed0392f997aabe34bd85f9952240d27f308abb68

Aliases

arxiv: 2604.17924 · arxiv_version: 2604.17924v2 · doi: 10.48550/arxiv.2604.17924 · pith_short_12: VVO7F4KQGP4D · pith_short_16: VVO7F4KQGP4DZEHM · pith_short_8: VVO7F4KQ

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/VVO7F4KQGP4DZEHMVYRO2A4S7G \
  | 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: ad5df2f15033f83c90ecae22ed0392f997aabe34bd85f9952240d27f308abb68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8a5d5888257c31ea2eb0bfa876c0b01b0b1980279f0f23b400b3962cfb266fe",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-04-20T08:04:21Z",
    "title_canon_sha256": "48972f142e305c349567a3e4fdf0a6bf75d1a7dcf50c049dfc39ec27dd97726e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.17924",
    "kind": "arxiv",
    "version": 2
  }
}