Pith Number

pith:VKRJBQC3

pith:2026:VKRJBQC3LWR3Q3OQZMLM7RWL47

not attested not anchored not stored refs pending

Lipschitzian SLLNs for random functions

Johannes O. Royset, Lai Tian

arxiv:2607.20411 v1 · 2026-07-22 · math.OC · cs.LG · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKRJBQC3LWR3Q3OQZMLM7RWL47}

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	2026-07-23T01:25:19.619968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaa290c05b5da3b86dd0cb16cfc6cbe7e7d5e4f880c266a53f724bbd71f8110b

Aliases

arxiv: 2607.20411 · arxiv_version: 2607.20411v1 · doi: 10.48550/arxiv.2607.20411 · pith_short_12: VKRJBQC3LWR3 · pith_short_16: VKRJBQC3LWR3Q3OQ · pith_short_8: VKRJBQC3

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/VKRJBQC3LWR3Q3OQZMLM7RWL47 \
  | 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: aaa290c05b5da3b86dd0cb16cfc6cbe7e7d5e4f880c266a53f724bbd71f8110b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "473ae462a32a8b84fc7cc41092eb2d85ebd074012081d30e13126b0091b63faf",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-22T17:50:53Z",
    "title_canon_sha256": "9275bbb0945adf64e128f357bba9199237419416f34c24e375ba9cb58775f1f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20411",
    "kind": "arxiv",
    "version": 1
  }
}