Pith Number

pith:ED66CFUD

pith:2026:ED66CFUDUGYNHJYYYCSAYFEFGP

not attested not anchored not stored refs pending

Homogenization of $\ell_2$-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent

Fabrizzio Sabelli

arxiv:2607.00207 v1 · 2026-06-30 · math.OC · cs.LG · math.PR · 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{ED66CFUDUGYNHJYYYCSAYFEFGP}

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	2026-07-02T00:18:39.077478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20fde11683a1b0d3a718c0a40c148533e51441da54253fc37907a12847e7c724

Aliases

arxiv: 2607.00207 · arxiv_version: 2607.00207v1 · doi: 10.48550/arxiv.2607.00207 · pith_short_12: ED66CFUDUGYN · pith_short_16: ED66CFUDUGYNHJYY · pith_short_8: ED66CFUD

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/ED66CFUDUGYNHJYYYCSAYFEFGP \
  | 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: 20fde11683a1b0d3a718c0a40c148533e51441da54253fc37907a12847e7c724

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89f0ae6d3130b9356caf7a8b1e40df24bc49896ce5caa7d9e4ebb5d6e5bd523c",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-30T21:38:10Z",
    "title_canon_sha256": "42ddfb30d942a2dd57494cf63dd99f253724e2c826ff90a2f99f2d32336a38a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00207",
    "kind": "arxiv",
    "version": 1
  }
}