Pith Number

pith:Q5P4VOS3

pith:2015:Q5P4VOS3WYE3OTODSKI3JCNGHQ

not attested not anchored not stored refs pending

The extremogram and the cross-extremogram for a bivariate GARCH(1,1) process

Muneya Matsui, Thomas Mikosch

arxiv:1505.05385 v1 · 2015-05-20 · math.ST · math.PR · 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{Q5P4VOS3WYE3OTODSKI3JCNGHQ}

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	2026-05-18T02:03:56.524749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802

Aliases

arxiv: 1505.05385 · arxiv_version: 1505.05385v1 · doi: 10.48550/arxiv.1505.05385 · pith_short_12: Q5P4VOS3WYE3 · pith_short_16: Q5P4VOS3WYE3OTOD · pith_short_8: Q5P4VOS3

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/Q5P4VOS3WYE3OTODSKI3JCNGHQ \
  | 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: 875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a458e8aae25baebc42287180c9135e99e242bade780a121b6b99bf8de6a98e41",
    "cross_cats_sorted": [
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2015-05-20T13:49:54Z",
    "title_canon_sha256": "2b86c7ae0692e9556d4ab43b1b280b996dfab43005b34926b7041fdc6f8d6d77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05385",
    "kind": "arxiv",
    "version": 1
  }
}