Pith Number

pith:K57IBDCR

pith:2016:K57IBDCRO3UK6YYEGSOO5LC6PH

not attested not anchored not stored refs pending

Goodness-of-fit tests for extended Log-GARCH models

Christian Francq (LFA), Jean-Michel Zako\"ian (LFA), Olivier Wintenberger (LSTA)

arxiv:1601.05560 v2 · 2016-01-21 · 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{K57IBDCRO3UK6YYEGSOO5LC6PH}

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	2026-05-18T01:12:55.011642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

577e808c5176e8af6304349ceeac5e79c91c1539d6cb7f17d25c845b1acd6cb1

Aliases

arxiv: 1601.05560 · arxiv_version: 1601.05560v2 · doi: 10.48550/arxiv.1601.05560 · pith_short_12: K57IBDCRO3UK · pith_short_16: K57IBDCRO3UK6YYE · pith_short_8: K57IBDCR

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/K57IBDCRO3UK6YYEGSOO5LC6PH \
  | 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: 577e808c5176e8af6304349ceeac5e79c91c1539d6cb7f17d25c845b1acd6cb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65fc9669cfb80d281da3fdd679d4f419e0baaeb16a9c2125e7c3d84dd6defc70",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2016-01-21T09:16:23Z",
    "title_canon_sha256": "3b9e02da854fe3e6841f150616c0d58711c5142e32a07dbb43151924a2b6d07e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05560",
    "kind": "arxiv",
    "version": 2
  }
}