Pith Number

pith:7XXWUDI3

pith:2013:7XXWUDI3CICW57FC5EIMZ722VK

not attested not anchored not stored refs pending

A Lyapunov Optimization Approach to Repeated Stochastic Games

Michael J. Neely

arxiv:1310.2648 v3 · 2013-10-09 · cs.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7XXWUDI3CICW57FC5EIMZ722VK}

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	2026-05-18T03:00:25.738709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdef6a0d1b12056efca2e910ccff5aaa9fe258787961dc47c43b86d102e9071e

Aliases

arxiv: 1310.2648 · arxiv_version: 1310.2648v3 · doi: 10.48550/arxiv.1310.2648 · pith_short_12: 7XXWUDI3CICW · pith_short_16: 7XXWUDI3CICW57FC · pith_short_8: 7XXWUDI3

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/7XXWUDI3CICW57FC5EIMZ722VK \
  | 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: fdef6a0d1b12056efca2e910ccff5aaa9fe258787961dc47c43b86d102e9071e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd5a7b17c7f8e65d4bc37f883a37fe32287d4b04fd33c73e4987da5eff521e6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2013-10-09T22:46:37Z",
    "title_canon_sha256": "969711c9f637e1e849a0f2399e8d201a09b61f2ff0b52e8a2897500d243981ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.2648",
    "kind": "arxiv",
    "version": 3
  }
}