Pith Number

pith:HCOJV4FW

pith:2013:HCOJV4FWTSDODXXA3BK5SCWJZ7

not attested not anchored not stored refs pending

On martingale problems with continuous-time mixing and values of zero-sum games without Isaacs condition

Mihai S\^irbu

arxiv:1307.4686 v4 · 2013-07-17 · 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{HCOJV4FWTSDODXXA3BK5SCWJZ7}

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	2026-05-18T02:54:14.162672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

389c9af0b69c86e1dee0d855d90ac9cfccae7c046f318248ff326bdfc54f2a0d

Aliases

arxiv: 1307.4686 · arxiv_version: 1307.4686v4 · doi: 10.48550/arxiv.1307.4686 · pith_short_12: HCOJV4FWTSDO · pith_short_16: HCOJV4FWTSDODXXA · pith_short_8: HCOJV4FW

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/HCOJV4FWTSDODXXA3BK5SCWJZ7 \
  | 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: 389c9af0b69c86e1dee0d855d90ac9cfccae7c046f318248ff326bdfc54f2a0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4138d790fefd3570b8e3d36fcc8d58f382035e4bfd8780a4fa9597c4a8d80004",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-07-17T16:27:16Z",
    "title_canon_sha256": "e33e1fa536379507826383c5cc1a69ca0a797e8228583369e099046c0834acfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4686",
    "kind": "arxiv",
    "version": 4
  }
}