Pith Number

pith:YNOJFVNM

pith:2026:YNOJFVNMUSPBGSXDYEHPH2CXA5

not attested not anchored not stored refs pending

Non-Euclidean Gradient Descent Operates at the Edge of Stability

Jeremy Cohen, Michael Crawshaw, Robert Gower, Rustem Islamov

arxiv:2603.05002 v2 · 2026-03-05 · cs.LG · math.OC · 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{YNOJFVNMUSPBGSXDYEHPH2CXA5}

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.

Cited by

2 papers in Pith

Does Weight Decay Enhance Training Stability?

Muon is Not That Special: Random or Inverted Spectra Work Just as Well

Receipt and verification

First computed	2026-05-29T02:05:42.459399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c35c92d5aca49e134ae3c10ef3e857077d02ab40836f5e8e6af8bd0c9a681f8a

Aliases

arxiv: 2603.05002 · arxiv_version: 2603.05002v2 · doi: 10.48550/arxiv.2603.05002 · pith_short_12: YNOJFVNMUSPB · pith_short_16: YNOJFVNMUSPBGSXD · pith_short_8: YNOJFVNM

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/YNOJFVNMUSPBGSXDYEHPH2CXA5 \
  | 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: c35c92d5aca49e134ae3c10ef3e857077d02ab40836f5e8e6af8bd0c9a681f8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2286e7b45f48068b528c423ac3cb684d9a371e339a8827c45caa99f010d181ea",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-05T09:49:33Z",
    "title_canon_sha256": "ff111847a471989a6cd7b951ae030d13dbcf591a13edb0cfff879e6fa20f9ddf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.05002",
    "kind": "arxiv",
    "version": 2
  }
}