Pith Number

pith:6YP52TAJ

pith:2026:6YP52TAJEMRURLOAC6YXCFXKIM

not attested not anchored not stored refs pending

Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway

Hee-Sung Kim, Sungyoon Lee

arxiv:2606.05219 v1 · 2026-05-29 · cs.LG · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6YP52TAJEMRURLOAC6YXCFXKIM}

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	2026-06-05T00:13:49.136735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f61fdd4c09232348adc017b17116ea4329c56b925fe14e1b8f82c74980a1c417

Aliases

arxiv: 2606.05219 · arxiv_version: 2606.05219v1 · doi: 10.48550/arxiv.2606.05219 · pith_short_12: 6YP52TAJEMRU · pith_short_16: 6YP52TAJEMRURLOA · pith_short_8: 6YP52TAJ

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/6YP52TAJEMRURLOAC6YXCFXKIM \
  | 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: f61fdd4c09232348adc017b17116ea4329c56b925fe14e1b8f82c74980a1c417

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5be535b910f3205cccc65e395a708f9cb1666d940a6077a58fde289937e0e85",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-29T13:32:18Z",
    "title_canon_sha256": "ff05512d80e5a4b2b579c12b136e8a4e858f3a2ff2517d90bf0825ffbfbb2f2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05219",
    "kind": "arxiv",
    "version": 1
  }
}