Pith Number

pith:UJ73HUKJ

pith:2016:UJ73HUKJMAHZCOITLGE3TVLQT4

not attested not anchored not stored refs pending

A discrete stochastic Gronwall Lemma

Michael Scheutzow, Raphael Kruse

arxiv:1601.07503 v1 · 2016-01-27 · math.PR · math.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{UJ73HUKJMAHZCOITLGE3TVLQT4}

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	2026-05-18T00:52:55.441660Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a27fb3d149600f9139135989b9d5709f32973eee5face97d6a75f78ea758f9a5

Aliases

arxiv: 1601.07503 · arxiv_version: 1601.07503v1 · doi: 10.48550/arxiv.1601.07503 · pith_short_12: UJ73HUKJMAHZ · pith_short_16: UJ73HUKJMAHZCOIT · pith_short_8: UJ73HUKJ

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/UJ73HUKJMAHZCOITLGE3TVLQT4 \
  | 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: a27fb3d149600f9139135989b9d5709f32973eee5face97d6a75f78ea758f9a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eefc44b582e2715d59c28f5d5ba2289e35970379d76a6374b1913743379514a5",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-01-27T19:03:29Z",
    "title_canon_sha256": "13043a042c3ba6c881c6b6c9bb905216b40681b227a6c8f401f1a1725d9ea8e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.07503",
    "kind": "arxiv",
    "version": 1
  }
}