Pith Number

pith:DRMNMBWW

pith:2004:DRMNMBWWUYN232DFYUEQYLHQCV

not attested not anchored not stored refs pending

On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel

Moshe Zakai

arxiv:math/0409548 v2 · 2004-09-28 · math.PR · cs.IT · math.IT · 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{DRMNMBWWUYN232DFYUEQYLHQCV}

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	2026-05-18T00:57:44.949470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c58d606d6a61bade865c5090c2cf0155ddb128b65ad26e0017aa9f436d68b8b

Aliases

arxiv: math/0409548 · arxiv_version: math/0409548v2 · doi: 10.48550/arxiv.math/0409548 · pith_short_12: DRMNMBWWUYN2 · pith_short_16: DRMNMBWWUYN232DF · pith_short_8: DRMNMBWW

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/DRMNMBWWUYN232DFYUEQYLHQCV \
  | 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: 1c58d606d6a61bade865c5090c2cf0155ddb128b65ad26e0017aa9f436d68b8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60db45467cf0c67e5aa49629369f4d5783e2313d39f364e5255020fcb6a1be7b",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.ST",
      "stat.TH"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-09-28T12:04:54Z",
    "title_canon_sha256": "f9bb0faf4a99e8c7b240099303ebd50c091cf42f0e22260d8a349b5db0072fa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409548",
    "kind": "arxiv",
    "version": 2
  }
}