Pith Number

pith:HIO27ZPX

pith:2012:HIO27ZPXRJLOSRA5MSRAI6QUDE

not attested not anchored not stored refs pending

The relation between Granger causality and directed information theory: a review

Olivier J. J. Michel, Pierre-Olivier Amblard

arxiv:1211.3169 v1 · 2012-11-14 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HIO27ZPXRJLOSRA5MSRAI6QUDE}

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	2026-05-18T01:53:15.900152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a1dafe5f78a56e9441d64a2047a14190f98def4a82803b2fa1eae625e8d189f

Aliases

arxiv: 1211.3169 · arxiv_version: 1211.3169v1 · doi: 10.48550/arxiv.1211.3169 · pith_short_12: HIO27ZPXRJLO · pith_short_16: HIO27ZPXRJLOSRA5 · pith_short_8: HIO27ZPX

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/HIO27ZPXRJLOSRA5MSRAI6QUDE \
  | 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: 3a1dafe5f78a56e9441d64a2047a14190f98def4a82803b2fa1eae625e8d189f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b520003cab0a59a13d876a4f8c674abf42b35286bb3d87f134f0b0a91b5d00a",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-11-14T00:13:27Z",
    "title_canon_sha256": "575321b0368c3fa535945908b735cc466a38aaab5b607d3099606e5018ae6e5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3169",
    "kind": "arxiv",
    "version": 1
  }
}