Pith Number

pith:YPGK4I6I

pith:2026:YPGK4I6IGPLYFDECF42HGHRTRE

not attested not anchored not stored refs pending

On the Differential-Geometric Equivalence of Hellinger-Kantorovich and Cone-Wasserstein Spaces

Florian Gunsilius, Gonzalo Mena, Tristan Luca Saidi

arxiv:2605.24329 v1 · 2026-05-23 · 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{YPGK4I6IGPLYFDECF42HGHRTRE}

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	2026-05-26T01:03:00.264977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3ccae23c833d7828c822f34731e3389299a3549021bebb70c7ead9724c3080b

Aliases

arxiv: 2605.24329 · arxiv_version: 2605.24329v1 · doi: 10.48550/arxiv.2605.24329 · pith_short_12: YPGK4I6IGPLY · pith_short_16: YPGK4I6IGPLYFDEC · pith_short_8: YPGK4I6I

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/YPGK4I6IGPLYFDECF42HGHRTRE \
  | 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: c3ccae23c833d7828c822f34731e3389299a3549021bebb70c7ead9724c3080b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "177977440b5445f55be3dedc072cd0799b064fffbe7057ef363a8f8a90d46f11",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-05-23T01:17:44Z",
    "title_canon_sha256": "bd7cf03bf3d2c3d32e6abec9e82c6d3446d908b5431574037a131d621950d61b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.24329",
    "kind": "arxiv",
    "version": 1
  }
}