Pith Number

pith:PNCPXILI

pith:2015:PNCPXILISXNQTAZCJGNL7FTI6M

not attested not anchored not stored refs pending

Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves

Alexander Mielke, Giuseppe Savar\'e, Matthias Liero

arxiv:1509.00068 v2 · 2015-08-31 · math.MG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PNCPXILISXNQTAZCJGNL7FTI6M}

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	2026-05-18T00:26:02.476182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b44fba16895db098322499abf9668f32a8db7a09db507d9485e46fec70891fa

Aliases

arxiv: 1509.00068 · arxiv_version: 1509.00068v2 · doi: 10.48550/arxiv.1509.00068 · pith_short_12: PNCPXILISXNQ · pith_short_16: PNCPXILISXNQTAZC · pith_short_8: PNCPXILI

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/PNCPXILISXNQTAZCJGNL7FTI6M \
  | 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: 7b44fba16895db098322499abf9668f32a8db7a09db507d9485e46fec70891fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d949e64c941de1371a7f756aab448e1b02dcd77b379a676d7bad44c390c35460",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-08-31T21:02:42Z",
    "title_canon_sha256": "9e5ed3863a586162f1a7a982debd954d45ebc328343d9c333eb4be8e744358be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00068",
    "kind": "arxiv",
    "version": 2
  }
}