Pith Number

pith:64BFXZCB

pith:2016:64BFXZCB5GGBJGS3YSGUVD2OD5

not attested not anchored not stored refs pending

Monotonicity of Entropy and Fisher Information: A Quick Proof via Maximal Correlation

Thomas A. Courtade

arxiv:1610.04174 v1 · 2016-10-13 · cs.IT · math.IT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{64BFXZCB5GGBJGS3YSGUVD2OD5}

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.

Cited by

1 paper in Pith

Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator

Receipt and verification

First computed	2026-05-18T01:02:21.702674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7025be441e98c149a5bc48d4a8f4e1f791d36b30b4c6e55d5ce9d311b5db9aa

Aliases

arxiv: 1610.04174 · arxiv_version: 1610.04174v1 · doi: 10.48550/arxiv.1610.04174 · pith_short_12: 64BFXZCB5GGB · pith_short_16: 64BFXZCB5GGBJGS3 · pith_short_8: 64BFXZCB

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/64BFXZCB5GGBJGS3YSGUVD2OD5 \
  | 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: f7025be441e98c149a5bc48d4a8f4e1f791d36b30b4c6e55d5ce9d311b5db9aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9ced254924b6b48cd7c88bef0119f943dbae94e49467840fe293ab3c71d5860",
    "cross_cats_sorted": [
      "math.IT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-10-13T16:56:26Z",
    "title_canon_sha256": "8778b88ae5fcb6633bb5eabff86d64bcbb73777be00c84a6cf8f328264145089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.04174",
    "kind": "arxiv",
    "version": 1
  }
}