Pith Number

pith:BTMBLFKP

pith:2026:BTMBLFKPJQX4JQDGSTSOQXQW3C

not attested not anchored not stored refs pending

GRPO, Dr. GRPO, and DAPO Are Three Operations on One Number: The Group-Standard-Deviation Identity

Kathleen A. Yearick, Yong Yi Bay

arxiv:2607.00152 v1 · 2026-06-30 · cs.LG · cs.AI · cs.CL · 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{BTMBLFKPJQX4JQDGSTSOQXQW3C}

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	2026-07-02T00:18:36.803099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cd815954f4c2fc4c06694e4e85e16d8a3d88df840cd12b2ef88a13820c3de1a

Aliases

arxiv: 2607.00152 · arxiv_version: 2607.00152v1 · doi: 10.48550/arxiv.2607.00152 · pith_short_12: BTMBLFKPJQX4 · pith_short_16: BTMBLFKPJQX4JQDG · pith_short_8: BTMBLFKP

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/BTMBLFKPJQX4JQDGSTSOQXQW3C \
  | 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: 0cd815954f4c2fc4c06694e4e85e16d8a3d88df840cd12b2ef88a13820c3de1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d61f1a48e47a4fbadecd334b4cb98ca4974823539c300d94324bbdcebd54ebc0",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-30T20:28:08Z",
    "title_canon_sha256": "968dc1fba3e051dc7b2ab47f5808a7b327b0ea295a4eda96c0828f7da0dbd3a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00152",
    "kind": "arxiv",
    "version": 1
  }
}