Pith Number

pith:N6VL4BW5

pith:2009:N6VL4BW5G47CKUH5GJZ7IKBRHT

not attested not anchored not stored refs pending

Relating Granger causality to directed information theory for networks of stochastic processes

Olivier J. J. Michel, Pierre-Olivier Amblard

arxiv:0911.2873 v4 · 2009-11-15 · 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{N6VL4BW5G47CKUH5GJZ7IKBRHT}

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	2026-05-18T04:09:53.838190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6faabe06dd373e2550fd3273f428313cef05bf180614cd8e0cb5dc5ce585c034

Aliases

arxiv: 0911.2873 · arxiv_version: 0911.2873v4 · doi: 10.48550/arxiv.0911.2873 · pith_short_12: N6VL4BW5G47C · pith_short_16: N6VL4BW5G47CKUH5 · pith_short_8: N6VL4BW5

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/N6VL4BW5G47CKUH5GJZ7IKBRHT \
  | 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: 6faabe06dd373e2550fd3273f428313cef05bf180614cd8e0cb5dc5ce585c034

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88107a055393feb6fbcb86aa3b6ee48fbc3e97dc20943ab15e018b43d578863e",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2009-11-15T14:47:45Z",
    "title_canon_sha256": "23fda60806540e8cf0b94787cc4bc2c061b04fb2fae069e4fd4bf68b01665273"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2873",
    "kind": "arxiv",
    "version": 4
  }
}