Pith Number

pith:65SGZPQE

pith:2015:65SGZPQE5CTBT2KYBKUGGIGOI2

not attested not anchored not stored refs pending

The Shannon's mutual information of a multiple antenna time and frequency dependent channel: an ergodic operator approach

Aris Moustakas, Leonid Pastur, Walid Hachem

arxiv:1504.00847 v1 · 2015-04-03 · cs.IT · math-ph · math.IT · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{65SGZPQE5CTBT2KYBKUGGIGOI2}

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	2026-05-18T02:19:36.892583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7646cbe04e8a619e9580aa86320ce46aef3d07de73988a0ce7cb57a2d3f40f4

Aliases

arxiv: 1504.00847 · arxiv_version: 1504.00847v1 · doi: 10.48550/arxiv.1504.00847 · pith_short_12: 65SGZPQE5CTB · pith_short_16: 65SGZPQE5CTBT2KY · pith_short_8: 65SGZPQE

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/65SGZPQE5CTBT2KYBKUGGIGOI2 \
  | 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: f7646cbe04e8a619e9580aa86320ce46aef3d07de73988a0ce7cb57a2d3f40f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc57839eac5f7689e21d7a74bdeb2785814fef3b615bf65bc54b47d0a4e672f7",
    "cross_cats_sorted": [
      "math-ph",
      "math.IT",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-04-03T14:00:35Z",
    "title_canon_sha256": "0e5384eab95bdbfb8d02f550e63b826189123f7f2fc81739930e5662edef237a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00847",
    "kind": "arxiv",
    "version": 1
  }
}