Pith Number

pith:2TRZA4OP

pith:2013:2TRZA4OPRNYLVCXQOYSQV25DKD

not attested not anchored not stored refs pending

A closed-form estimator for the multivariate GARCH(1,1) model

Federico Poloni, Giacomo Sbrana

arxiv:1303.3740 v1 · 2013-03-15 · 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{2TRZA4OPRNYLVCXQOYSQV25DKD}

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	2026-05-18T02:44:32.379591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4e39071cf8b70ba8af076250aeba350f442b2ec3e6b5fd0c7e4ecf4b05f2646

Aliases

arxiv: 1303.3740 · arxiv_version: 1303.3740v1 · doi: 10.48550/arxiv.1303.3740 · pith_short_12: 2TRZA4OPRNYL · pith_short_16: 2TRZA4OPRNYLVCXQ · pith_short_8: 2TRZA4OP

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/2TRZA4OPRNYLVCXQOYSQV25DKD \
  | 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: d4e39071cf8b70ba8af076250aeba350f442b2ec3e6b5fd0c7e4ecf4b05f2646

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "377fb27b360142dbd5f8d5deb432f3dd7fc2aca8fa7bb333ff7a89c78161e58c",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-03-15T11:24:46Z",
    "title_canon_sha256": "c1da48917fb4f207be25b5902c1af9d66300a1ec16041a389cca5db8e491d458"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3740",
    "kind": "arxiv",
    "version": 1
  }
}