Pith Number

pith:7MBLRRX4

pith:2016:7MBLRRX4VR5ERW7YFIC5NSGTCW

not attested not anchored not stored refs pending

Quantum Game Theory for Beam Alignment in Millimeter Wave Device-to-Device Communications

Mehdi Bennis, Merouane Debbah, Qianqian Zhang, Walid Saad

arxiv:1610.01982 v1 · 2016-10-06 · cs.IT · cs.GT · 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{7MBLRRX4VR5ERW7YFIC5NSGTCW}

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	2026-05-18T01:03:04.218123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb02b8c6fcac7a48dbf82a05d6c8d315b31106942d3fc9ea9222404aa64059a4

Aliases

arxiv: 1610.01982 · arxiv_version: 1610.01982v1 · doi: 10.48550/arxiv.1610.01982 · pith_short_12: 7MBLRRX4VR5E · pith_short_16: 7MBLRRX4VR5ERW7Y · pith_short_8: 7MBLRRX4

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/7MBLRRX4VR5ERW7YFIC5NSGTCW \
  | 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: fb02b8c6fcac7a48dbf82a05d6c8d315b31106942d3fc9ea9222404aa64059a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "079625efc53c77eff68f45746fde6ab48bf3f80569d0820563bb1bc75e0bf391",
    "cross_cats_sorted": [
      "cs.GT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-10-06T18:23:25Z",
    "title_canon_sha256": "63918b77e3e7eaebf289cc62b4152c0ae3506a595f7760b2af86a8a0947d6ecf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01982",
    "kind": "arxiv",
    "version": 1
  }
}