Pith Number

pith:6WGDUODO

pith:2025:6WGDUODORA5255ASDY74QV3IW6

not attested not anchored not stored refs pending

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality

Arnulf Jentzen, Konrad Kleinberg, Thomas Kruse

arxiv:2506.22851 v1 · 2025-06-28 · math.OC · cs.LG · cs.NA · math.NA · math.PR · 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{6WGDUODORA5255ASDY74QV3IW6}

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	2026-07-05T11:28:46.654546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f58c3a386e883baef4121e3fc85768b79160fb9f70be7b65140f399e7a63ae41

Aliases

arxiv: 2506.22851 · arxiv_version: 2506.22851v1 · doi: 10.48550/arxiv.2506.22851 · pith_short_12: 6WGDUODORA52 · pith_short_16: 6WGDUODORA5255AS · pith_short_8: 6WGDUODO

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/6WGDUODORA5255ASDY74QV3IW6 \
  | 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: f58c3a386e883baef4121e3fc85768b79160fb9f70be7b65140f399e7a63ae41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a59da2abd1293ce3b68d211c33bf26b3f77ddd5cf4dfc396ab57e6533bf7e59c",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA",
      "math.PR",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-06-28T11:25:44Z",
    "title_canon_sha256": "201d4915bb53a8e8a7fee36a03228572b5cc790232bad6b3810d0fc4633c678d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.22851",
    "kind": "arxiv",
    "version": 1
  }
}