Pith Number

pith:BMPFAGOP

pith:2025:BMPFAGOPSLTOKR47LAUGXHN6RT

not attested not anchored not stored refs pending

Extensions of Robbins-Siegmund Theorem with Applications in Reinforcement Learning

Shangtong Zhang, Xinyu Liu, Zixuan Xie

arxiv:2509.26442 v2 · 2025-09-30 · cs.LG · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BMPFAGOPSLTOKR47LAUGXHN6RT}

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	2026-05-28T02:04:43.130157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b1e5019cf92e6e5479f58286b9dbe8ccb6a248a0d26ded094131565f66b74dd

Aliases

arxiv: 2509.26442 · arxiv_version: 2509.26442v2 · doi: 10.48550/arxiv.2509.26442 · pith_short_12: BMPFAGOPSLTO · pith_short_16: BMPFAGOPSLTOKR47 · pith_short_8: BMPFAGOP

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/BMPFAGOPSLTOKR47LAUGXHN6RT \
  | 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: 0b1e5019cf92e6e5479f58286b9dbe8ccb6a248a0d26ded094131565f66b74dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eefdd0011de804b572412b639d982c3c64d5284639602c45e633204accfc4d45",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-09-30T16:00:36Z",
    "title_canon_sha256": "229109871c24c2b41bf114584b628777188ec15b73bac88c6c465a2c61310951"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.26442",
    "kind": "arxiv",
    "version": 2
  }
}