Pith Number

pith:CSXY7LAT

pith:2012:CSXY7LAT3LP3TBGBHUT3QCQY4V

not attested not anchored not stored refs pending

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

(2) IMT, 3) ((1) IMB, (3) ENAC), J\'er\'emie Bigot (1), Thierry Klein (2

arxiv:1212.2562 v6 · 2012-12-11 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CSXY7LAT3LP3TBGBHUT3QCQY4V}

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	2026-05-18T00:29:21.557028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14af8fac13dadfb984c13d27b80a18e55cf98718de885a8900e24087dabeec26

Aliases

arxiv: 1212.2562 · arxiv_version: 1212.2562v6 · doi: 10.48550/arxiv.1212.2562 · pith_short_12: CSXY7LAT3LP3 · pith_short_16: CSXY7LAT3LP3TBGB · pith_short_8: CSXY7LAT

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/CSXY7LAT3LP3TBGBHUT3QCQY4V \
  | 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: 14af8fac13dadfb984c13d27b80a18e55cf98718de885a8900e24087dabeec26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "578c5a1a11adc675cb7b01a8e89e92b00fcea313e0c42db8be47ef7bfd06da0c",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-12-11T17:58:28Z",
    "title_canon_sha256": "d97257762d5d528b8732a495a96f952d969881adcc98390acc9358394a1d924d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2562",
    "kind": "arxiv",
    "version": 6
  }
}