Pith Number

pith:FYWIZVUE

pith:2009:FYWIZVUEQPOO4WJBSL2JO4USSM

not attested not anchored not stored refs pending

A General Duality Theorem for the Monge--Kantorovich Transport Problem

Christian Leonard, Mathias Beiglboeck, Walter Schachermayer

arxiv:0911.4347 v2 · 2009-11-23 · math.OC · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FYWIZVUEQPOO4WJBSL2JO4USSM}

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	2026-05-18T04:41:25.165478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e2c8cd68483dcee592192f49772929329f592f87e19fd50c40ab5a91f61ff7f

Aliases

arxiv: 0911.4347 · arxiv_version: 0911.4347v2 · doi: 10.48550/arxiv.0911.4347 · pith_short_12: FYWIZVUEQPOO · pith_short_16: FYWIZVUEQPOO4WJB · pith_short_8: FYWIZVUE

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/FYWIZVUEQPOO4WJBSL2JO4USSM \
  | 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: 2e2c8cd68483dcee592192f49772929329f592f87e19fd50c40ab5a91f61ff7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "903cb5a3e6bfaf6282b0317d0d56e0c2697ebcf996b329b8c7f6719166710bdd",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2009-11-23T20:26:28Z",
    "title_canon_sha256": "dd6d3d699aedc789fbf907d3ee564c745e4947446fde5d2cd5556038a511a55c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4347",
    "kind": "arxiv",
    "version": 2
  }
}