Pith Number

pith:2TMPNNKG

pith:2016:2TMPNNKGULMK5WAJRWX2LOQIO6

not attested not anchored not stored refs pending

Asymptotic Optimality in Stochastic Optimization

Feng Ruan, John Duchi

arxiv:1612.05612 v4 · 2016-12-16 · math.ST · math.OC · stat.ML · 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{2TMPNNKGULMK5WAJRWX2LOQIO6}

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	2026-05-17T23:44:23.107853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4d8f6b546a2d8aed8098dafa5ba08779d1c658e43dffb42cd60702a521e1919

Aliases

arxiv: 1612.05612 · arxiv_version: 1612.05612v4 · doi: 10.48550/arxiv.1612.05612 · pith_short_12: 2TMPNNKGULMK · pith_short_16: 2TMPNNKGULMK5WAJ · pith_short_8: 2TMPNNKG

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/2TMPNNKGULMK5WAJRWX2LOQIO6 \
  | 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: d4d8f6b546a2d8aed8098dafa5ba08779d1c658e43dffb42cd60702a521e1919

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f271314d4b488a73264e1cca38607e5cd63337807fb7b00979d2801052092ad",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2016-12-16T19:54:22Z",
    "title_canon_sha256": "5d6c7741dc6310c36ec749f657193669e5faed5207ef2bbc6e5512fa21c8e3a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05612",
    "kind": "arxiv",
    "version": 4
  }
}