Pith Number

pith:TULQSAOK

pith:2011:TULQSAOK6TF6EHH7V3AXT2SYYX

not attested not anchored not stored refs pending

Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case

Pedro Cruz

arxiv:1105.5231 v1 · 2011-05-26 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TULQSAOK6TF6EHH7V3AXT2SYYX}

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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	2026-05-18T04:21:13.012865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d170901caf4cbe21cffaec179ea58c5e1492c2d7fd58e935465593f40559e88

Aliases

arxiv: 1105.5231 · arxiv_version: 1105.5231v1 · doi: 10.48550/arxiv.1105.5231 · pith_short_12: TULQSAOK6TF6 · pith_short_16: TULQSAOK6TF6EHH7 · pith_short_8: TULQSAOK

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/TULQSAOK6TF6EHH7V3AXT2SYYX \
  | 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: 9d170901caf4cbe21cffaec179ea58c5e1492c2d7fd58e935465593f40559e88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f80c0e9093c1f6be621f506e945d6d617fcec1f5172b0fa35cb0ce5015d569b7",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2011-05-26T08:40:55Z",
    "title_canon_sha256": "f6cd0a9d433f09ab3433c4233cd1d8f5e959c63afc6227469d759a79ae829c07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5231",
    "kind": "arxiv",
    "version": 1
  }
}