Pith Number

pith:NHYBJROV

pith:2018:NHYBJROVIDAQFYCQ5ISQKP2ZKL

not attested not anchored not stored refs pending

Approximative Theorem of Incomplete Riemann-Stieltjes Sum of Stochastic Integral

Jingwei Liu

arxiv:1803.05182 v2 · 2018-03-14 · math.PR · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NHYBJROVIDAQFYCQ5ISQKP2ZKL}

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	2026-05-17T23:52:53.294762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69f014c5d540c102e050ea25053f5952ee2f4043f3b02253c969d97daf9262d3

Aliases

arxiv: 1803.05182 · arxiv_version: 1803.05182v2 · doi: 10.48550/arxiv.1803.05182 · pith_short_12: NHYBJROVIDAQ · pith_short_16: NHYBJROVIDAQFYCQ · pith_short_8: NHYBJROV

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/NHYBJROVIDAQFYCQ5ISQKP2ZKL \
  | 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: 69f014c5d540c102e050ea25053f5952ee2f4043f3b02253c969d97daf9262d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c330c2578fe787c45847940d158c69b01a5ebec1bbdf467bdad3e0d14a84145f",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-03-14T09:56:47Z",
    "title_canon_sha256": "2837f9aa140802696d0b83cfedff05b5d5eb2312678c413213a7410f1f3c4348"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.05182",
    "kind": "arxiv",
    "version": 2
  }
}