Pith Number

pith:CYJHYOVH

pith:2023:CYJHYOVH5PF7TTVSWXO3KPNLQL

not attested not anchored not stored refs pending

Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory

Chulhee Yun, Minhak Song

arxiv:2307.04204 v2 · 2023-07-09 · 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{CYJHYOVH5PF7TTVSWXO3KPNLQL}

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

1 paper in Pith

From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes

Receipt and verification

First computed	2026-07-05T07:05:31.556550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16127c3aa7ebcbf9ceb2b5ddb53dab82cc7d8835de8af652c18b3eae69503322

Aliases

arxiv: 2307.04204 · arxiv_version: 2307.04204v2 · doi: 10.48550/arxiv.2307.04204 · pith_short_12: CYJHYOVH5PF7 · pith_short_16: CYJHYOVH5PF7TTVS · pith_short_8: CYJHYOVH

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/CYJHYOVH5PF7TTVSWXO3KPNLQL \
  | 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: 16127c3aa7ebcbf9ceb2b5ddb53dab82cc7d8835de8af652c18b3eae69503322

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8ce54b006bb98edbfd0a8deb52d9945d5453fa7beda643287966e9477d8520f",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-07-09T15:16:45Z",
    "title_canon_sha256": "fb4e396a9125c7c1eb46ff83fbe2c0394995360145bd545d6b14590df88f0023"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.04204",
    "kind": "arxiv",
    "version": 2
  }
}