Pith Number

pith:VVR7NX7L

pith:2015:VVR7NX7LCO22OSHREIL2XQ676R

not attested not anchored not stored refs pending

Optional and predictable projections of normal integrands and convex-valued processes

Ari-Pekka Perkki\"o, Matti Kiiski

arxiv:1508.02176 v2 · 2015-08-10 · math.PR · 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{VVR7NX7LCO22OSHREIL2XQ676R}

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	2026-05-18T01:10:41.785716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad63f6dfeb13b5a748f12217abc3dff4417a93b2500caef644119f60cb7478fb

Aliases

arxiv: 1508.02176 · arxiv_version: 1508.02176v2 · doi: 10.48550/arxiv.1508.02176 · pith_short_12: VVR7NX7LCO22 · pith_short_16: VVR7NX7LCO22OSHR · pith_short_8: VVR7NX7L

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/VVR7NX7LCO22OSHREIL2XQ676R \
  | 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: ad63f6dfeb13b5a748f12217abc3dff4417a93b2500caef644119f60cb7478fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e9905f1e0a7281b98db8073deeb21ae87552e70fe2ceab857364acbfe7628cd",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-10T09:12:00Z",
    "title_canon_sha256": "8549f2a47c99167a81c1f7335573d8a4400c33300fd767b8a1db6d8965d7ec5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02176",
    "kind": "arxiv",
    "version": 2
  }
}