Pith Number

pith:BPFV5YVZ

pith:2017:BPFV5YVZIYWQD4WSC4LLJRUZVR

not attested not anchored not stored refs pending

An Elementary Proof for the Structure of Wasserstein Derivatives

Cong Wu, Jianfeng Zhang

arxiv:1705.08046 v2 · 2017-05-23 · 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{BPFV5YVZIYWQD4WSC4LLJRUZVR}

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	2026-05-18T00:14:56.993716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bcb5ee2b9462d01f2d21716b4c699ac53776aad2df19d232656f885e07f1c12

Aliases

arxiv: 1705.08046 · arxiv_version: 1705.08046v2 · doi: 10.48550/arxiv.1705.08046 · pith_short_12: BPFV5YVZIYWQ · pith_short_16: BPFV5YVZIYWQD4WS · pith_short_8: BPFV5YVZ

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/BPFV5YVZIYWQD4WSC4LLJRUZVR \
  | 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: 0bcb5ee2b9462d01f2d21716b4c699ac53776aad2df19d232656f885e07f1c12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "661e2b32e23689ef24d4177aca6f2e948baeea1eb1d3b06d2d181a819705d3f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-05-23T00:00:32Z",
    "title_canon_sha256": "24ee933560a914534fe179bb21da70055d5ae24bae514a2641959199838da19f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.08046",
    "kind": "arxiv",
    "version": 2
  }
}