Pith Number

pith:CPPJ6QUS

pith:2026:CPPJ6QUSNZF4BBRQGNKEVFPO6L

not attested not anchored not stored refs pending

High-Probability Last-Iterate Guarantees for Two-Point Gaussian Zeroth-Order Stochastic Gradient Descent

Haishan Ye

arxiv:2606.20446 v1 · 2026-06-18 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CPPJ6QUSNZF4BBRQGNKEVFPO6L}

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	2026-06-19T16:13:12.638128Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13de9f42926e4bc0863033544a95eef2eea4a7f4729f07e4c08339ec33fccf35

Aliases

arxiv: 2606.20446 · arxiv_version: 2606.20446v1 · doi: 10.48550/arxiv.2606.20446 · pith_short_12: CPPJ6QUSNZF4 · pith_short_16: CPPJ6QUSNZF4BBRQ · pith_short_8: CPPJ6QUS

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/CPPJ6QUSNZF4BBRQGNKEVFPO6L \
  | 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: 13de9f42926e4bc0863033544a95eef2eea4a7f4729f07e4c08339ec33fccf35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d7224a974ae080f10efd322cb5a1afc0a2ffc9bc87f598af486258f3dcf9484",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-18T16:24:24Z",
    "title_canon_sha256": "09a38d49e5c5c3a5a453ca681a1a5dd537892798dd3e9461b820ceac97a319ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20446",
    "kind": "arxiv",
    "version": 1
  }
}