Pith Number

pith:XKCYNVVG

pith:2016:XKCYNVVGCMTVKR6H4ZCISAPDLG

not attested not anchored not stored refs pending

On the support of extremal martingale measures with given marginals: the countable case

Claude Martini, Luciano Campi

arxiv:1607.07197 v4 · 2016-07-25 · math.PR · 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{XKCYNVVGCMTVKR6H4ZCISAPDLG}

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	2026-05-17T23:51:55.009674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba8586d6a613275547c7e6448901e359add1a19d7f809074037f9ff81aa337e9

Aliases

arxiv: 1607.07197 · arxiv_version: 1607.07197v4 · doi: 10.48550/arxiv.1607.07197 · pith_short_12: XKCYNVVGCMTV · pith_short_16: XKCYNVVGCMTVKR6H · pith_short_8: XKCYNVVG

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/XKCYNVVGCMTVKR6H4ZCISAPDLG \
  | 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: ba8586d6a613275547c7e6448901e359add1a19d7f809074037f9ff81aa337e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2f0d8861dc68a638bd584f21fdf89179a0b8a7cd72f6110ec7b33da4f0ded88",
    "cross_cats_sorted": [
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-25T10:21:25Z",
    "title_canon_sha256": "f798a726549aca822262ce5174f2053724cbe3cc6cfc44c1509a4bc9e3eadf3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.07197",
    "kind": "arxiv",
    "version": 4
  }
}