Pith Number

pith:76AWT43X

pith:2021:76AWT43XPQXGOBUSWLMUKM3GKQ

not attested not anchored not stored refs pending

Big-Step-Little-Step: Efficient Gradient Methods for Objectives with Multiple Scales

Aaron Sidford, Annie Marsden, Gregory Valiant, Honglin Yuan, Jonathan Kelner, Vatsal Sharan

arxiv:2111.03137 v1 · 2021-11-04 · math.OC · cs.DS · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{76AWT43XPQXGOBUSWLMUKM3GKQ}

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	2026-07-05T03:29:21.125430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff8169f3777c2e670692b2d94533665420c4bd97992faf9c0e241f0972391c1c

Aliases

arxiv: 2111.03137 · arxiv_version: 2111.03137v1 · doi: 10.48550/arxiv.2111.03137 · pith_short_12: 76AWT43XPQXG · pith_short_16: 76AWT43XPQXGOBUS · pith_short_8: 76AWT43X

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/76AWT43XPQXGOBUSWLMUKM3GKQ \
  | 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: ff8169f3777c2e670692b2d94533665420c4bd97992faf9c0e241f0972391c1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fac73e6bf3581016d33e58fae2bc60be8b7788471acd2bf399af98580b82dd18",
    "cross_cats_sorted": [
      "cs.DS",
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-11-04T20:09:12Z",
    "title_canon_sha256": "d0f202a12bcceff1bde3d7d2420bf47075f2b3c538b537e0af2ae22ffe55500e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.03137",
    "kind": "arxiv",
    "version": 1
  }
}