Pith Number

pith:X72NNNIS

pith:2016:X72NNNISX5M6QO3ATX3RCDM6DS

not attested not anchored not stored refs pending

Bounds on Integrals with Respect to Multivariate Copulas

Michael Preischl

arxiv:1606.08661 v2 · 2016-06-28 · 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{X72NNNISX5M6QO3ATX3RCDM6DS}

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	2026-05-18T01:11:40.790138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bff4d6b512bf59e83b609df7110d9e1cab8c289f7c2f1aed984bb30e070f91dd

Aliases

arxiv: 1606.08661 · arxiv_version: 1606.08661v2 · doi: 10.48550/arxiv.1606.08661 · pith_short_12: X72NNNISX5M6 · pith_short_16: X72NNNISX5M6QO3A · pith_short_8: X72NNNIS

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/X72NNNISX5M6QO3ATX3RCDM6DS \
  | 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: bff4d6b512bf59e83b609df7110d9e1cab8c289f7c2f1aed984bb30e070f91dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9f0c0e5193dafa645bd0eda1fe352b7595296020141b432fd4011c4468a24cf",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-06-28T11:46:06Z",
    "title_canon_sha256": "efe018f14294d896d9f9d31c8adf4e5ee95c43bba5ff595404772a67a1ff2e26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08661",
    "kind": "arxiv",
    "version": 2
  }
}