Pith Number

pith:4RI2G7AX

pith:2018:4RI2G7AXATFEUS3SSYDX7XK3BB

not attested not anchored not stored refs pending

Optimal transport natural gradient for statistical manifolds with continuous sample space

Wuchen Li, Yifan Chen

arxiv:1805.08380 v4 · 2018-05-22 · math.OC · cs.IT · cs.LG · math.IT · math.ST · stat.ML · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4RI2G7AXATFEUS3SSYDX7XK3BB}

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	2026-07-05T08:56:09.945301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e451a37c1704ca4a4b7296077fdd5b086f9dc241068b2d2707fb80a8de8be401

Aliases

arxiv: 1805.08380 · arxiv_version: 1805.08380v4 · doi: 10.48550/arxiv.1805.08380 · pith_short_12: 4RI2G7AXATFE · pith_short_16: 4RI2G7AXATFEUS3S · pith_short_8: 4RI2G7AX

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/4RI2G7AXATFEUS3SSYDX7XK3BB \
  | 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: e451a37c1704ca4a4b7296077fdd5b086f9dc241068b2d2707fb80a8de8be401

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db07c3c0e28d4462f7885aaa4a2bad072d9d13a276b2ef71ccb009b9195acae2",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.LG",
      "math.IT",
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-05-22T03:58:18Z",
    "title_canon_sha256": "266f605b67a6fbbfb67f9ef9dfc47021c338540103ea32e828f46a67d363ab70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.08380",
    "kind": "arxiv",
    "version": 4
  }
}