Pith Number

pith:JSPXI5O2

pith:2026:JSPXI5O2ZQOFP4MXLEKSITXQSL

not attested not anchored not stored refs pending

A Theory of Training Profit-Optimal LLMs

Sophie Hao, William Merrill

arxiv:2605.16430 v1 · 2026-05-14 · 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{JSPXI5O2ZQOFP4MXLEKSITXQSL}

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	2026-05-20T00:02:21.740377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c9f7475dacc1c57f1975915244ef092fa271161790cdef200dfd7e4642c433f

Aliases

arxiv: 2605.16430 · arxiv_version: 2605.16430v1 · doi: 10.48550/arxiv.2605.16430 · pith_short_12: JSPXI5O2ZQOF · pith_short_16: JSPXI5O2ZQOFP4MX · pith_short_8: JSPXI5O2

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/JSPXI5O2ZQOFP4MXLEKSITXQSL \
  | 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: 4c9f7475dacc1c57f1975915244ef092fa271161790cdef200dfd7e4642c433f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "971f5eacd00dcfe45a551bc86d6564abb57f3650f8dc2c64ac5c117bb15a170c",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T18:57:40Z",
    "title_canon_sha256": "7804d1c64ce080ff3954f71675e3fc4861902b592949d8972772d50e8a557cf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16430",
    "kind": "arxiv",
    "version": 1
  }
}