Pith Number

pith:KRAKTQ26

pith:2015:KRAKTQ26UZTMK25ECW3HO7FNFN

not attested not anchored not stored refs pending

Hybrid Precoding for Physical Layer Multicasting

Bruno Clerckx, Mingbo Dai

arxiv:1511.06715 v1 · 2015-11-20 · 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{KRAKTQ26UZTMK25ECW3HO7FNFN}

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	2026-05-18T00:58:10.010677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5440a9c35ea666c56ba415b6777cad2b567f50000c3f31a1c37173cdda03401a

Aliases

arxiv: 1511.06715 · arxiv_version: 1511.06715v1 · doi: 10.48550/arxiv.1511.06715 · pith_short_12: KRAKTQ26UZTM · pith_short_16: KRAKTQ26UZTMK25E · pith_short_8: KRAKTQ26

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/KRAKTQ26UZTMK25ECW3HO7FNFN \
  | 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: 5440a9c35ea666c56ba415b6777cad2b567f50000c3f31a1c37173cdda03401a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07308149dab900253c6b6842fceb5e801c9837fca5ee3243e5f78ebf5d35d750",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-11-20T18:12:58Z",
    "title_canon_sha256": "a6be155c42e655b37bcbc84e8eab30e0da22c8a0631a9923d1215832256bb6de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06715",
    "kind": "arxiv",
    "version": 1
  }
}