Pith Number

pith:A4YPBI3B

pith:2018:A4YPBI3BUU3SMC2NWD7FMAMMYT

not attested not anchored not stored refs pending

Zero-sum Stochastic Games: Limit Optimal Trajectories

Guillaume Vigeral (CEREMADE), Sylvain Sorin (IMJ-PRG)

arxiv:1812.08414 v1 · 2018-12-20 · 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{A4YPBI3BUU3SMC2NWD7FMAMMYT}

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	2026-05-17T23:57:50.036886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0730f0a361a537260b4db0fe56018cc4f18e0615dd93a6398dabbd7836ce5f27

Aliases

arxiv: 1812.08414 · arxiv_version: 1812.08414v1 · doi: 10.48550/arxiv.1812.08414 · pith_short_12: A4YPBI3BUU3S · pith_short_16: A4YPBI3BUU3SMC2N · pith_short_8: A4YPBI3B

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/A4YPBI3BUU3SMC2NWD7FMAMMYT \
  | 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: 0730f0a361a537260b4db0fe56018cc4f18e0615dd93a6398dabbd7836ce5f27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdd7d56cf03ea2732e806571d85817ffdb99d7bb54a4158ad771f5d39f499058",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-12-20T08:33:33Z",
    "title_canon_sha256": "0c47475ca06bfd5f966c1844b9f040daed76e10da6f99fbd502de493499b4a33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.08414",
    "kind": "arxiv",
    "version": 1
  }
}