Pith Number

pith:GNBXW2AT

pith:2015:GNBXW2ATGJORBERJC7LWSHYQTP

not attested not anchored not stored refs pending

Granger Causality in Multi-variate Time Series using a Time Ordered Restricted Vector Autoregressive Model

Dimitris Kugiumtzis, Elsa Siggiridou

arxiv:1511.03463 v1 · 2015-11-11 · stat.ME · math.ST · physics.data-an · stat.CO · stat.ML · 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{GNBXW2ATGJORBERJC7LWSHYQTP}

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	2026-05-18T01:16:45.654331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33437b6813325d10922917d7691f109bcb1af537578488e57cc34901229d5537

Aliases

arxiv: 1511.03463 · arxiv_version: 1511.03463v1 · doi: 10.48550/arxiv.1511.03463 · pith_short_12: GNBXW2ATGJOR · pith_short_16: GNBXW2ATGJORBERJ · pith_short_8: GNBXW2AT

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/GNBXW2ATGJORBERJC7LWSHYQTP \
  | 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: 33437b6813325d10922917d7691f109bcb1af537578488e57cc34901229d5537

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cc69546ab4621409f12bedde166b409ea3253cd4220329b19b2bf34a9556e04",
    "cross_cats_sorted": [
      "math.ST",
      "physics.data-an",
      "stat.CO",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2015-11-11T11:35:21Z",
    "title_canon_sha256": "4cf69db8766a6fe0e0676fedf62057e8841dda356bc10702f9980305534cf53f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03463",
    "kind": "arxiv",
    "version": 1
  }
}