Pith Number

pith:VOAXO2OA

pith:2026:VOAXO2OAQJMDGQNOSCOXYBKT7G

not attested not anchored not stored refs pending

Sectional Curvature for Kantorovich-Wasserstein and Hellinger-Kantorovich Geometries

Karl-Theodor Sturm

arxiv:2606.14318 v2 · 2026-06-12 · math.DG · math.FA · math.MG · 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{VOAXO2OAQJMDGQNOSCOXYBKT7G}

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	2026-07-17T01:21:51.784650Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab817769c082583341ae909d7c0553f9b1bb64c84a5cbaac538f40d1a0ac0cd8

Aliases

arxiv: 2606.14318 · arxiv_version: 2606.14318v2 · doi: 10.48550/arxiv.2606.14318 · pith_short_12: VOAXO2OAQJMD · pith_short_16: VOAXO2OAQJMDGQNO · pith_short_8: VOAXO2OA

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/VOAXO2OAQJMDGQNOSCOXYBKT7G \
  | 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: ab817769c082583341ae909d7c0553f9b1bb64c84a5cbaac538f40d1a0ac0cd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01458e3619493b829fc0e8cdc164e2abbbfcecd29febd36362e6b06ea4e05125",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-12T09:58:00Z",
    "title_canon_sha256": "0e3a08b72d9772ca9d4e3a91752a170b1c8955e6795a2ab2dab1bd1c9d8c362e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.14318",
    "kind": "arxiv",
    "version": 2
  }
}