Pith Number

pith:QULLDGDW

pith:2012:QULLDGDWIE5NSFHL3YWWNP47GV

not attested not anchored not stored refs pending

Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs

Gordan Zitkovic, Jin Hyuk Choi, Mihai Sirbu

arxiv:1204.0305 v2 · 2012-04-02 · q-fin.PM · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QULLDGDWIE5NSFHL3YWWNP47GV}

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	2026-05-18T03:53:31.384082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8516b19876413ad914ebde2d66bf9f357e2eb8ca8a87d965d8ae8c741e5d8330

Aliases

arxiv: 1204.0305 · arxiv_version: 1204.0305v2 · doi: 10.48550/arxiv.1204.0305 · pith_short_12: QULLDGDWIE5N · pith_short_16: QULLDGDWIE5NSFHL · pith_short_8: QULLDGDW

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/QULLDGDWIE5NSFHL3YWWNP47GV \
  | 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: 8516b19876413ad914ebde2d66bf9f357e2eb8ca8a87d965d8ae8c741e5d8330

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b71bfa63d9e862094d9d3a24f7dca28a50257bd51fbf9a5bee01a6301f8698ef",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.PM",
    "submitted_at": "2012-04-02T03:12:21Z",
    "title_canon_sha256": "0083da1ff9288134fdc0b7b5abe1fc9497f298aac530f480fe359fbcd482e51a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0305",
    "kind": "arxiv",
    "version": 2
  }
}