Pith Number

pith:Q2VFAZ44

pith:2015:Q2VFAZ44UQKJX5VGXOPFIS7IH4

not attested not anchored not stored refs pending

Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices

Erhan Bayraktar, Xiang Yu

arxiv:1504.00310 v8 · 2015-04-01 · q-fin.MF · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q2VFAZ44UQKJX5VGXOPFIS7IH4}

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	2026-05-18T00:07:24.029538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86aa50679ca4149bf6a6bb9e544be83f0eee077e26900505a6090b09b46f7f23

Aliases

arxiv: 1504.00310 · arxiv_version: 1504.00310v8 · doi: 10.48550/arxiv.1504.00310 · pith_short_12: Q2VFAZ44UQKJ · pith_short_16: Q2VFAZ44UQKJX5VG · pith_short_8: Q2VFAZ44

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/Q2VFAZ44UQKJX5VGXOPFIS7IH4 \
  | 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: 86aa50679ca4149bf6a6bb9e544be83f0eee077e26900505a6090b09b46f7f23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "555565c4e7c35f621f95e2f690a70f2729c3fdd36c7024e74c310624c78d3cba",
    "cross_cats_sorted": [
      "math.OC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.MF",
    "submitted_at": "2015-04-01T17:34:37Z",
    "title_canon_sha256": "49a79e6330f8e7f11d3a9427125547854070109da80aab584ba132cd16b242a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00310",
    "kind": "arxiv",
    "version": 8
  }
}