Pith Number

pith:AZ3JVNWJ

pith:2012:AZ3JVNWJIRVDQBGOXC54GEVADP

not attested not anchored not stored refs pending

Comments on Proakis Analysis of the Characteristic Function of Complex Gaussian Quadratic Forms

Eduardo Martos-Naya, Jos\'e F. Paris, Jos\'e T. Entrambasaguas, Unai Fern\'andez-Plazaola

arxiv:1212.0382 v1 · 2012-12-03 · 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{AZ3JVNWJIRVDQBGOXC54GEVADP}

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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	2026-05-18T03:39:17.669568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06769ab6c9446a3804ceb8bbc312a01bc02b6906a29f52a6752c2e7df66fd527

Aliases

arxiv: 1212.0382 · arxiv_version: 1212.0382v1 · doi: 10.48550/arxiv.1212.0382 · pith_short_12: AZ3JVNWJIRVD · pith_short_16: AZ3JVNWJIRVDQBGO · pith_short_8: AZ3JVNWJ

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/AZ3JVNWJIRVDQBGOXC54GEVADP \
  | 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: 06769ab6c9446a3804ceb8bbc312a01bc02b6906a29f52a6752c2e7df66fd527

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d09afa3ac0c9d0c5bbeeab7c4faa61acc6d532b9c00e7e46d447e57c62f304a0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-12-03T13:27:54Z",
    "title_canon_sha256": "e19bc57acd4acb6372c4aacfe04e3a0e16b047e5b90522c08401a2fa2c815da9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0382",
    "kind": "arxiv",
    "version": 1
  }
}