Pith Number

pith:HNWP5G5Z

pith:2016:HNWP5G5ZFZGLD3SXBVEAW374JZ

not attested not anchored not stored refs pending

Integration by parts on the law of the modulus of the Brownian bridge

Martin Grothaus, Robert Vo{\ss}hall

arxiv:1609.02438 v2 · 2016-09-08 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HNWP5G5ZFZGLD3SXBVEAW374JZ}

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	2026-05-18T00:41:53.502488Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b6cfe9bb92e4cb1ee570d480b6ffc4e458023fbc250a670e2a8da554f83d057

Aliases

arxiv: 1609.02438 · arxiv_version: 1609.02438v2 · doi: 10.48550/arxiv.1609.02438 · pith_short_12: HNWP5G5ZFZGL · pith_short_16: HNWP5G5ZFZGLD3SX · pith_short_8: HNWP5G5Z

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/HNWP5G5ZFZGLD3SXBVEAW374JZ \
  | 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: 3b6cfe9bb92e4cb1ee570d480b6ffc4e458023fbc250a670e2a8da554f83d057

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a80c56f4af40b0e21b7c45d08df9dc9cabdce391bba768c44e9418e02aa2329",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-08T14:08:33Z",
    "title_canon_sha256": "acb12b268d2096b52d11f3e957b92f56e7537fcb0aee254a1e25995481b2e4da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02438",
    "kind": "arxiv",
    "version": 2
  }
}