Pith Number

pith:XZL3QIVZ

pith:2015:XZL3QIVZM5KPXRXHRRJES7HI4B

not attested not anchored not stored refs pending

Optimal Skorokhod embedding under finitely-many marginal constraints

Gaoyue Guo, Nizar Touzi, Xiaolu Tan

arxiv:1506.04063 v2 · 2015-06-12 · 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{XZL3QIVZM5KPXRXHRRJES7HI4B}

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	2026-05-18T01:09:58.012520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be57b822b96754fbc6e78c52497ce8e065bf2cc7816ce18fcd8fa3408a9d8f13

Aliases

arxiv: 1506.04063 · arxiv_version: 1506.04063v2 · doi: 10.48550/arxiv.1506.04063 · pith_short_12: XZL3QIVZM5KP · pith_short_16: XZL3QIVZM5KPXRXH · pith_short_8: XZL3QIVZ

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/XZL3QIVZM5KPXRXHRRJES7HI4B \
  | 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: be57b822b96754fbc6e78c52497ce8e065bf2cc7816ce18fcd8fa3408a9d8f13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0398afbc2b105ecfe9a921e204237a7427d372ec14ade353a1c77a0f30fd6cd1",
    "cross_cats_sorted": [
      "math.OC",
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-12T16:36:38Z",
    "title_canon_sha256": "090b84ca7da244d9caf5280ea4f28e5185392a7b2500087a6f026c15f3bc1256"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04063",
    "kind": "arxiv",
    "version": 2
  }
}