Pith Number

pith:QU4T6OOM

pith:2010:QU4T6OOMAZZALHPJ4BBYYMOUOU

not attested not anchored not stored refs pending

A geometric study of Wasserstein spaces: Hadamard spaces

Beno\^it Kloeckner (IF), J\'er\^ome Bertrand (IMT)

arxiv:1010.0590 v2 · 2010-10-04 · math.MG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QU4T6OOMAZZALHPJ4BBYYMOUOU}

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	2026-05-18T03:34:16.511563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85393f39cc0672059de9e0438c31d4750f37b4d5f70034cdc45fdeea4c013bed

Aliases

arxiv: 1010.0590 · arxiv_version: 1010.0590v2 · doi: 10.48550/arxiv.1010.0590 · pith_short_12: QU4T6OOMAZZA · pith_short_16: QU4T6OOMAZZALHPJ · pith_short_8: QU4T6OOM

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/QU4T6OOMAZZALHPJ4BBYYMOUOU \
  | 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: 85393f39cc0672059de9e0438c31d4750f37b4d5f70034cdc45fdeea4c013bed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6812bb0912debf78610d59cfc198babbeac46298e4d80999ac44de74aec90810",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-10-04T13:56:18Z",
    "title_canon_sha256": "69a54352a5f2a93a928ba98bf9a27e24274823a1f4c80221bc682bcd685c5af5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0590",
    "kind": "arxiv",
    "version": 2
  }
}