Pith Number

pith:2BCEDVT3

pith:2026:2BCEDVT3WOXEMTBGIUJISANF5O

not attested not anchored not stored refs pending

Training with (Swap) Regret Loss in a Single-Layer Self-Attention Model: A Case Study on the Probability Simplex

Asuman Ozdaglar, Chanwoo Park

arxiv:2607.23333 v1 · 2026-07-25 · 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{2BCEDVT3WOXEMTBGIUJISANF5O}

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	2026-07-28T01:22:48.132727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d04441d67bb3ae464c2645128901a5ebb2765e284491033927d1f50515748048

Aliases

arxiv: 2607.23333 · arxiv_version: 2607.23333v1 · doi: 10.48550/arxiv.2607.23333 · pith_short_12: 2BCEDVT3WOXE · pith_short_16: 2BCEDVT3WOXEMTBG · pith_short_8: 2BCEDVT3

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/2BCEDVT3WOXEMTBGIUJISANF5O \
  | 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: d04441d67bb3ae464c2645128901a5ebb2765e284491033927d1f50515748048

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "068d36beb51bccf7c74a4604f3ca05960c3dc87586c363eed29ad7ea31c1d221",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-25T19:11:15Z",
    "title_canon_sha256": "09d90817ed083202552767db5bc27dc8d2e4a490db473d33796de30fd282e182"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23333",
    "kind": "arxiv",
    "version": 1
  }
}