Pith Number

pith:PWBLLEAB

pith:2012:PWBLLEABBZRRCPXLY6VIM3P6LW

not attested not anchored not stored refs pending

The dynamics of doubly stochastic operators on finite dimensional simplex

Farruh Shahidi, Rasul Ganikhodzhaev

arxiv:1211.5639 v3 · 2012-11-24 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PWBLLEABBZRRCPXLY6VIM3P6LW}

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	2026-05-18T00:01:39.569826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d82b590010e63113eebc7aa866dfe5d9d932144c3dfe485e4207f4925f350b4

Aliases

arxiv: 1211.5639 · arxiv_version: 1211.5639v3 · doi: 10.48550/arxiv.1211.5639 · pith_short_12: PWBLLEABBZRR · pith_short_16: PWBLLEABBZRRCPXL · pith_short_8: PWBLLEAB

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/PWBLLEABBZRRCPXLY6VIM3P6LW \
  | 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: 7d82b590010e63113eebc7aa866dfe5d9d932144c3dfe485e4207f4925f350b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50505a1ebcb47098e2e68814ad2ba598573d48643c7abed2e3a33eb89419e529",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-11-24T02:53:50Z",
    "title_canon_sha256": "08bc5d68949dd353305f48bc6fd87a7f0ee950d8faef35afbe9ff3cd6a90e530"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5639",
    "kind": "arxiv",
    "version": 3
  }
}