Pith Number

pith:CFKVLJFG

pith:2026:CFKVLJFGKU4BC6W73XJRMW55PG

not attested not anchored not stored refs pending

Predictable GRPO: A Closed-Form Model of Training Dynamics

Aryan Singhal, Datta Nimmaturi, Debojyoti Dutta, Henry Wong, Johnu George, Rajat Ghosh, Vaishnavi Bhargava

arxiv:2606.30789 v1 · 2026-06-29 · cs.LG · 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{CFKVLJFGKU4BC6W73XJRMW55PG}

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	2026-07-01T00:17:17.011111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

115555a4a65538117adfddd3165bbd79acedf758ea8e302e0b6359a6a899ae30

Aliases

arxiv: 2606.30789 · arxiv_version: 2606.30789v1 · doi: 10.48550/arxiv.2606.30789 · pith_short_12: CFKVLJFGKU4B · pith_short_16: CFKVLJFGKU4BC6W7 · pith_short_8: CFKVLJFG

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/CFKVLJFGKU4BC6W73XJRMW55PG \
  | 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: 115555a4a65538117adfddd3165bbd79acedf758ea8e302e0b6359a6a899ae30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eae770a13e2720a171be55a78ede261936dbc0773fee79b835aa7cd23289cae0",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-29T18:19:09Z",
    "title_canon_sha256": "582931b4e21e1bc0c184ca56e1ab3ad200b769ba6d90250b3923699bc2c83bf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30789",
    "kind": "arxiv",
    "version": 1
  }
}