Pith Number

pith:7OLHKB5J

pith:2016:7OLHKB5J66B6ITLON7HB2OUKEJ

not attested not anchored not stored refs pending

On the change of variables formula for multiple integrals

Shibo Liu, Yashan Zhang

arxiv:1603.08428 v2 · 2016-03-28 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7OLHKB5J66B6ITLON7HB2OUKEJ}

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	2026-05-18T00:44:24.816526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb967507a9f783e44d6e6fce1d3a8a227e72f3c95081a0a6bea34457f845fd1a

Aliases

arxiv: 1603.08428 · arxiv_version: 1603.08428v2 · doi: 10.48550/arxiv.1603.08428 · pith_short_12: 7OLHKB5J66B6 · pith_short_16: 7OLHKB5J66B6ITLO · pith_short_8: 7OLHKB5J

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/7OLHKB5J66B6ITLON7HB2OUKEJ \
  | 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: fb967507a9f783e44d6e6fce1d3a8a227e72f3c95081a0a6bea34457f845fd1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f862b0834ff942ace4780807957ad0dbeb0a9422ee77e7c4250279dc715a5fdd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-03-28T16:17:03Z",
    "title_canon_sha256": "a5c39f56baa759a94115e0978c308d534530105f619e7688fba1f9c1c8b0dc52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08428",
    "kind": "arxiv",
    "version": 2
  }
}