Pith Number

pith:5G6ID73H

pith:2015:5G6ID73H2ELXGULXYW2TPOHPG5

not attested not anchored not stored refs pending

Duality and optimality conditions in stochastic optimization and mathematical finance

Ari-Pekka Perkki\"o, Sara Biagini, Teemu Pennanen

arxiv:1504.06683 v1 · 2015-04-25 · 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{5G6ID73H2ELXGULXYW2TPOHPG5}

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	2026-05-18T02:17:52.775009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9bc81ff67d117735177c5b537b8ef376454a33fdc308b5fce57edbf3840cd52

Aliases

arxiv: 1504.06683 · arxiv_version: 1504.06683v1 · doi: 10.48550/arxiv.1504.06683 · pith_short_12: 5G6ID73H2ELX · pith_short_16: 5G6ID73H2ELXGULX · pith_short_8: 5G6ID73H

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/5G6ID73H2ELXGULXYW2TPOHPG5 \
  | 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: e9bc81ff67d117735177c5b537b8ef376454a33fdc308b5fce57edbf3840cd52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c8cf24c6d880786fddf1711a413510799b46b35bd09ecb287961b14b784c885",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-04-25T04:49:40Z",
    "title_canon_sha256": "165f77f7aee4cc2d3f80cae5b26c4ea1a4397e9f70b5f73b33214d9cd65dd747"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.06683",
    "kind": "arxiv",
    "version": 1
  }
}