Pith Number

pith:I7BL7YJN

pith:2015:I7BL7YJNOF5HXLY6BH4TL3AT2E

not attested not anchored not stored refs pending

Products of Generalized Stochastic Sarymsakov Matrices

Ji Liu, Karl H. Johansson, Ming Cao, Tamer Basar, Weiguo Xia

arxiv:1509.03900 v1 · 2015-09-13 · 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{I7BL7YJNOF5HXLY6BH4TL3AT2E}

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	2026-05-18T01:33:08.777563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47c2bfe12d717a7baf1e09f935ec13d13b913396303161c9724337f40e6a9e4f

Aliases

arxiv: 1509.03900 · arxiv_version: 1509.03900v1 · doi: 10.48550/arxiv.1509.03900 · pith_short_12: I7BL7YJNOF5H · pith_short_16: I7BL7YJNOF5HXLY6 · pith_short_8: I7BL7YJN

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/I7BL7YJNOF5HXLY6BH4TL3AT2E \
  | 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: 47c2bfe12d717a7baf1e09f935ec13d13b913396303161c9724337f40e6a9e4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f10cd0cfbba673a761d634f2172b3f666218f6e35abae7cb88c5b6186a9e08b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-09-13T21:47:51Z",
    "title_canon_sha256": "6083f9cde667b4860304361fb4e3f8d3cfe0deac51661a3adf7e7046f06fd151"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03900",
    "kind": "arxiv",
    "version": 1
  }
}