Pith Number

pith:VO37FG46

pith:2017:VO37FG467DAFY2RI56E6WEF5ZF

not attested not anchored not stored refs pending

Marginal and dependence uncertainty: bounds, optimal transport, and sharpness

Antonis Papapantoleon, Daniel Bartl, Michael Kupper, Stephan Eckstein (appendix), Thibaut Lux

arxiv:1709.00641 v2 · 2017-09-02 · 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{VO37FG467DAFY2RI56E6WEF5ZF}

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	2026-05-18T00:07:55.534244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abb7f29b9ef8c05c6a28ef89eb10bdc97c5b7c12fd084970666afcd4476d27d0

Aliases

arxiv: 1709.00641 · arxiv_version: 1709.00641v2 · doi: 10.48550/arxiv.1709.00641 · pith_short_12: VO37FG467DAF · pith_short_16: VO37FG467DAFY2RI · pith_short_8: VO37FG46

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/VO37FG467DAFY2RI56E6WEF5ZF \
  | 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: abb7f29b9ef8c05c6a28ef89eb10bdc97c5b7c12fd084970666afcd4476d27d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8348637b86ee7d40a1b6403b9837c3de3eb34977be1309089582256a004dfd6b",
    "cross_cats_sorted": [
      "math.OC",
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-09-02T22:27:07Z",
    "title_canon_sha256": "4e831151e9e07b067528deccd9736fd4a270a428d31148f244beb8179f922927"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.00641",
    "kind": "arxiv",
    "version": 2
  }
}