Pith Number

pith:LA6N77SD

pith:2015:LA6N77SDQYIH7K7AI3NWG4BD5H

not attested not anchored not stored refs pending

Minimum Energy to Send $k$ Bits Over Multiple-Antenna Fading Channels

Giuseppe Durisi, Wei Yang, Yury Polyanskiy

arxiv:1507.03843 v2 · 2015-07-14 · 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{LA6N77SDQYIH7K7AI3NWG4BD5H}

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	2026-05-18T01:14:25.986946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

583cdffe4386107fabe046db637023e9cf448b836efbaa26d1e303c9f835d59f

Aliases

arxiv: 1507.03843 · arxiv_version: 1507.03843v2 · doi: 10.48550/arxiv.1507.03843 · pith_short_12: LA6N77SDQYIH · pith_short_16: LA6N77SDQYIH7K7A · pith_short_8: LA6N77SD

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/LA6N77SDQYIH7K7AI3NWG4BD5H \
  | 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: 583cdffe4386107fabe046db637023e9cf448b836efbaa26d1e303c9f835d59f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f00e35dc60e94b49803f9b076d03a419f84dbc52d2bf7d9b7297175fc9883b46",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-07-14T13:27:11Z",
    "title_canon_sha256": "504b48faf2ab698c3b890fb823a20173035ba33a6ac5e4c9b56bf2a5acdca1e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03843",
    "kind": "arxiv",
    "version": 2
  }
}