Pith Number

pith:PTXZJ4WZ

pith:2026:PTXZJ4WZSTHZP7XZA3UMM42DY5

not attested not anchored not stored refs pending

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network

Antonin Chodron de Courcel

arxiv:2606.05326 v1 · 2026-06-03 · math.OC · cs.AI · cs.LG · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTXZJ4WZSTHZP7XZA3UMM42DY5}

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	2026-06-05T00:13:54.041962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cef94f2d994cf97fef906e8c67343c741737156809fa62aea01cfe64ae289f9

Aliases

arxiv: 2606.05326 · arxiv_version: 2606.05326v1 · doi: 10.48550/arxiv.2606.05326 · pith_short_12: PTXZJ4WZSTHZ · pith_short_16: PTXZJ4WZSTHZP7XZ · pith_short_8: PTXZJ4WZ

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/PTXZJ4WZSTHZP7XZA3UMM42DY5 \
  | 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: 7cef94f2d994cf97fef906e8c67343c741737156809fa62aea01cfe64ae289f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa3a62fe033252ca47cb9edd3492da44d4cd652204d333f87689ae03ea0130de",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-03T18:11:33Z",
    "title_canon_sha256": "03519e7f376e590a6fde6a205d87842fd5113115b87eeddbcd23975ad7a38379"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05326",
    "kind": "arxiv",
    "version": 1
  }
}