Pith Number

pith:U6ZZ5FCD

pith:2021:U6ZZ5FCD7PJT3KAVPUYULOBZEB

not attested not anchored not stored refs pending

The Linearized Hellinger--Kantorovich Distance

Bernhard Schmitzer, Junyi Cheng, Matthew Thorpe, Tianji Cai

arxiv:2102.08807 v2 · 2021-02-17 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U6ZZ5FCD7PJT3KAVPUYULOBZEB}

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	2026-07-05T03:17:01.881638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7b39e9443fbd33da8157d3145b839207050a563a690dbea962f0c8b639caf68

Aliases

arxiv: 2102.08807 · arxiv_version: 2102.08807v2 · doi: 10.48550/arxiv.2102.08807 · pith_short_12: U6ZZ5FCD7PJT · pith_short_16: U6ZZ5FCD7PJT3KAV · pith_short_8: U6ZZ5FCD

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/U6ZZ5FCD7PJT3KAVPUYULOBZEB \
  | 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: a7b39e9443fbd33da8157d3145b839207050a563a690dbea962f0c8b639caf68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a87c4ef92d56896e7a3a93e69ec667a1f12f8cc4a0caa3b985e056fe8eac4b1e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-02-17T15:12:41Z",
    "title_canon_sha256": "fab345dd7125226e4f8b2c376ae933238fbdd4e190efb00b148c56d2c059f180"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.08807",
    "kind": "arxiv",
    "version": 2
  }
}