Pith Number

pith:BCWOKX2T

pith:2018:BCWOKX2TFXDBYWWT7FITMTYSWQ

not attested not anchored not stored refs pending

On optimal transport of matrix-valued measures

Dmitry Vorotnikov, Yann Brenier

arxiv:1808.05064 v2 · 2018-08-15 · math.OC · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BCWOKX2TFXDBYWWT7FITMTYSWQ}

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	2026-05-17T23:40:41.647633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08ace55f532dc61c5ad3f951364f12b403aafade340c02d3d58cc4fbf268b6ad

Aliases

arxiv: 1808.05064 · arxiv_version: 1808.05064v2 · doi: 10.48550/arxiv.1808.05064 · pith_short_12: BCWOKX2TFXDB · pith_short_16: BCWOKX2TFXDBYWWT · pith_short_8: BCWOKX2T

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/BCWOKX2TFXDBYWWT7FITMTYSWQ \
  | 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: 08ace55f532dc61c5ad3f951364f12b403aafade340c02d3d58cc4fbf268b6ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "265f7a5a627bab2eaf6e87d151b6a262c2e4a27c3fc0bac949ffc86610763639",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-08-15T13:13:08Z",
    "title_canon_sha256": "7ce752ec71461df4edafb604db319861071157b758e4af31315396001a666dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05064",
    "kind": "arxiv",
    "version": 2
  }
}