Pith Number

pith:VR4DV7LB

pith:2015:VR4DV7LBRTR7HCIE57652FBYLZ

not attested not anchored not stored refs pending

Complete Duality for Martingale Optimal Transport on the Line

Marcel Nutz, Mathias Beiglb\"ock, Nizar Touzi

arxiv:1507.00671 v3 · 2015-07-02 · math.PR · math.OC · q-fin.MF

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VR4DV7LBRTR7HCIE57652FBYLZ}

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	2026-05-18T01:12:36.258939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac783afd618ce3f38904effddd14385e619de03970411d0d081490038648c805

Aliases

arxiv: 1507.00671 · arxiv_version: 1507.00671v3 · doi: 10.48550/arxiv.1507.00671 · pith_short_12: VR4DV7LBRTR7 · pith_short_16: VR4DV7LBRTR7HCIE · pith_short_8: VR4DV7LB

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/VR4DV7LBRTR7HCIE57652FBYLZ \
  | 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: ac783afd618ce3f38904effddd14385e619de03970411d0d081490038648c805

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "265fa4aa66b9815ed12e9e4f9a1a9572a2de5fcf42713e9489d33c4330471d14",
    "cross_cats_sorted": [
      "math.OC",
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-07-02T17:32:17Z",
    "title_canon_sha256": "5fdbd0ed3d0b04ea61d9493005d8b32ef8555034bf2937a6b3dd2d525b43e6c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00671",
    "kind": "arxiv",
    "version": 3
  }
}