Pith Number

pith:WMNKGAKI

pith:2015:WMNKGAKI6KPOKDFHRBRQPYEHBD

not attested not anchored not stored refs pending

Energy Efficiency and Sum Rate when Massive MIMO meets Device-to-Device Communication

Emil Bj\"ornson, Ki Won Sung, Marios Kountouris, M\'erouane Debbah, Serveh Shalmashi

arxiv:1505.01858 v1 · 2015-05-07 · 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{WMNKGAKI6KPOKDFHRBRQPYEHBD}

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	2026-05-18T00:59:01.888066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b31aa30148f29ee50ca7886307e08708c983ba47ebba27d4f000975d9ca1d899

Aliases

arxiv: 1505.01858 · arxiv_version: 1505.01858v1 · doi: 10.48550/arxiv.1505.01858 · pith_short_12: WMNKGAKI6KPO · pith_short_16: WMNKGAKI6KPOKDFH · pith_short_8: WMNKGAKI

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/WMNKGAKI6KPOKDFHRBRQPYEHBD \
  | 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: b31aa30148f29ee50ca7886307e08708c983ba47ebba27d4f000975d9ca1d899

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70b4bf4f2705820c3ba965fd840b8cf036ebac33125552d82c811df9ca588ab0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-05-07T20:06:03Z",
    "title_canon_sha256": "56891c6ace7677da10fcca5e0b346f417636407e363047e3f06c5e975620beb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.01858",
    "kind": "arxiv",
    "version": 1
  }
}