Pith Number

pith:TCKLUMXX

pith:2016:TCKLUMXXKAFZJAD6RVGRIEFNLO

not attested not anchored not stored refs pending

Hybrid Beamforming for Massive MIMO - A Survey

Andreas F. Molisch, Katsuyuki Haneda, Linsheng Li, Shengqian Han, Sinh Le Hong Nguyen, Vishnu V. Ratnam, Zheda Li

arxiv:1609.05078 v2 · 2016-09-16 · 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{TCKLUMXXKAFZJAD6RVGRIEFNLO}

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	2026-05-18T00:45:22.340477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9894ba32f7500b94807e8d4d1410ad5bab37186a417f17a9d1aa54e3453a55e8

Aliases

arxiv: 1609.05078 · arxiv_version: 1609.05078v2 · doi: 10.48550/arxiv.1609.05078 · pith_short_12: TCKLUMXXKAFZ · pith_short_16: TCKLUMXXKAFZJAD6 · pith_short_8: TCKLUMXX

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/TCKLUMXXKAFZJAD6RVGRIEFNLO \
  | 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: 9894ba32f7500b94807e8d4d1410ad5bab37186a417f17a9d1aa54e3453a55e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ece415e22fcaf06797a7ecfd890c42a71907d36926a3f27cf80a13f5fb05df12",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-09-16T14:28:44Z",
    "title_canon_sha256": "61f8ab166a62e3a83ae03db7e35a2489bd24f6824ec13e12c8f382743fcf6784"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05078",
    "kind": "arxiv",
    "version": 2
  }
}